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Expressive microtimings and groove in Scottish Gaelic fiddle music Glen, Katherine Marshall 2015

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Expressive Microtimings and Groove in Scottish Gaelic Fiddle Music  by Katherine Marshall Glen B. Mus., Acadia University, 2008  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS in The Faculty of Graduate and Postdoctoral Studies (Music Theory)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) August 2015  ©Katherine Marshall Glen 2015ii  Abstract This project examines how “groove” can be created through the microtimings of a solo instrument, rather than as discrepancies between multiple instruments or parts, as is often the case in similar studies.  Groove is the nuanced rhythmic element of music in which microtiming patterns play upon listeners’ bodies in complex ways and stimulate movement.   My study focuses on the reel, a type of dance tune used in the Scottish Gaelic tradition.  Despite the repetitiveness and relative simplicity of the melody in this genre, these tunes have been widely played and performed for many years, and this seems to be due, in large part, to their rhythmic features.  I analyze five recordings of a popular reel, “Jenny Dang the Weaver,” by different performers, using methodologies typically applied to the jazz canon.  Each recording features only a solo fiddle, so any expressive microtimings are the result of the single performer and musical line, not influenced by interaction with other instruments.  My analysis demonstrates that these recordings create groove through beat subdivisions and subversion of expected microtiming patterns. The primary method for analysis is a comparison of beat-upbeat ratios (BUR) and upbeat-beat-ratios (UBR) throughout the measure to determine any trends or significant outliers. The analysis shows that these performers, despite their different backgrounds, share certain microtiming trends and patterns (particularly in the performance of beats 2 and 3, and the presence of phenomenal accents on beat 2), which could therefore be understood as characteristic features of the Gaelic style.  Conversely, I also demonstrate that while conforming to those patterns, each musician nevertheless has idiosyncrasies of microtiming that distinguish them from each other.  iii  Preface This thesis is original, unpublished, independent work by the author, Katherine Glen.                                      iv  Table of Contents  Abstract ...................................................................................................................................................................................................ii Preface ................................................................................................................................................................................................... iii Table of Contents ............................................................................................................................................................................. iv List of Figures ...................................................................................................................................................................................... v Acknowledgements......................................................................................................................................................................... vi Chapter 1: Introduction ..................................................................................................................................................................1 Aim and scope ................................................................................................................................................................................1 Gaelic culture and puirt-a-beul..............................................................................................................................................2 Dance tunes and traditions ......................................................................................................................................................9 Rhythm and meter in music scholarship ....................................................................................................................... 13 Groove ............................................................................................................................................................................................. 16 Chapter 2: Methodology and Approach to Analysis ..................................................................................................... 21 Selecting a tune ........................................................................................................................................................................... 21 Notation and style ..................................................................................................................................................................... 22 Rhythmic nuance and classifying groove ...................................................................................................................... 23 BUR and UBR................................................................................................................................................................................ 25 Studying "Jenny Dang the Weaver” .................................................................................................................................. 28 Applying a jazz methodology............................................................................................................................................... 33 Chapter 3: Results and Analysis .............................................................................................................................................. 40 Generic observations ............................................................................................................................................................... 40 Outliers and individual style ................................................................................................................................................ 44 Performance: Neil Cameron ................................................................................................................................................. 47 Performance: Jim Blair............................................................................................................................................................ 55 Performance: Hanneke Cassel ............................................................................................................................................ 62 Performance: Bruce Macgregor ......................................................................................................................................... 69 Performance: Farquhar MacRae ........................................................................................................................................ 74 Conclusions and areas for future research................................................................................................................... 82 Bibliography ...................................................................................................................................................................................... 86 Appendix ............................................................................................................................................................................................. 91 Neil Cameron’s performance calculations .................................................................................................................... 91 Jim Blair’s performance calculations ............................................................................................................................... 97 Hanneke Cassel’s performance calculations............................................................................................................. 106 Bruce Macgregor’s performance calculations ......................................................................................................... 112 Farquhar MacRae’s performance calculations ........................................................................................................ 116    v  List of Figures Figure 1: Transcription of Cameron’s Performance….………………………………………….…………48 Figure 2: BUR trends in Cameron’s A Section…..………………………………………………….…….……49 Figure 3: UBR trends in Cameron’s A Section……..………………………………………..……….………..49 Figure 4: BUR trends in Cameron’s B Section………..…………………………………….…….……………49 Figure 5: UBR trends in Cameron’s B Section…………...………………………………….......…………….49 Figure 6: Transcription of Blair’s Performance……………...…………………………………….…………56 Figure 7: BUR trends in Blair’s A Section…………………………....………………………………….……….57 Figure 8: UBR trends in Blair’s A Section………………..………………………….…………………….……..57 Figure 9: BUR trends in Blair’s B Section……………………………………...…….…………………….…….57 Figure 10: UBR trends in Blair’s B Section……………………………………………………..……………….57 Figure 11: Transcription of Cassel’s Performance……………………………………….……….……....…63 Figure 12: BUR trends in Cassel’s A Section……………………………………………….….……………..…63 Figure 13: UBR trends in Cassel’s A Section……………………………………………….……….………..…63 Figure 14: BUR trends in Cassel’s B Section……………………………………………….……….………..…64 Figure 15: UBR trends in Cassel’s B Section……………………………………………….……….………..…64 Figure 16: Transcription of Macgregor’s Performance……………………………….…………………...70 Figure 17: BUR trends in Macgregor’s A Section………………………………………...…………………..70 Figure 18: UBR trends in Macgregor’s A Section……………………………………….…………...…….…70 Figure 19: Transcription of MacRae’s Performance…………………………………………………..…....75 Figure 20: BUR trends in MacRae’s A Section……………………………………………………………...….76 Figure 21: UBR trends in MacRae’s A Section…………………………………………………………….…...76 Figure 22: BUR trends in MacRae’s B Section..……...……………… ………………………………………..76 Figure 23: UBR trends in MacRae’s B Section..……………………… ………………….……………………76    vi  Acknowledgements I offer my humble gratitude to the faculty, staff, and my fellow students at UBC, who have inspired me to grow not only academically but also personally.  In particular, I would like to thank Dr. John Roeder for being a thorough and encouraging advisor and helping me explore music theory from new perspectives.  I would also like to thank Dr. Alan Dodson, whose teaching and guidance have both inspired and enriched me.  I owe special thanks to Dr. Jeffrey Hennessy of Acadia University, who first encouraged me to pursue music theory and whose continued mentorship and friendship is invaluable to me.  I offer special appreciation to my parents and sisters who have supported me in this endeavour in more ways than I can count.  Their love, support, and help were priceless to me.   1  Chapter 1: Introduction Aim and scope The primary aim of this thesis is to examine how “groove” can be created through the microtimings of a solo instrument, rather than as discrepancies between multiple instruments or parts, as is often the case in similar studies.  Groove is the nuanced rhythmic element of music in which microtiming patterns play upon listeners’ bodies in complex ways and stimulate movement.  In order to demonstrate this, I will examine five different performances of the same Scottish Gaelic tune, using a methodology put forth by Matthew Butterfield and usually applied to the jazz canon.  The five musicians of this study hail from different parts of the world, but nonetheless are all considered part of the Scottish Gaelic tradition.  This investigation will shed light on whether they, despite their different backgrounds, share consistent metrical characteristics that therefore may be understood to define the Gaelic fiddling style, a style which is typically hard for insiders to define or describe technically.   While the investigation of cultural and social aspects of Scottish traditional music has been an area of scholarship in musicology for some time, I believe that approaching this music from a music-theoretical standpoint will foster appreciation of its distinctiveness and subtlety. In areas like Nova Scotia, traditional Scottish music is present in many forms and most children are exposed to the music on a regular basis.  This project has personal resonance for me as well, as traditional Scottish music was some of the first music to which I was exposed.  Scottish Country Dancing was another significant activity for me during my formative years, and when I learned to play an instrument, traditional Scottish (as well as traditional Irish) music was the main genre I was familiar with as a performer.   2  The Scottish Gaelic music scene is not only thriving, but it is also a large part of the tourism industry, which means that both Nova Scotians and visitors to the province come into contact with the music.  Therefore, it is part of the musical framework which will inform their future musical preferences and understanding.1  Through this project, I hope to create a better understanding of the metrical and rhythmic features that constitute the overall groove of this music, and thereby shed light on one part of a formative musical experience for many people around the world.  This will also help us to better understand the formative musical experiences of people in regions where this music is widely played, such as Atlantic Canada and the United Kingdom.   Gaelic culture and puirt-a-beul There is a consensus in Celtic scholarship that for centuries, music accompanied most facets of Scottish Gaelic culture: work, play, celebration, and socialization.2 Even today, this musical tradition is alive and well, not only in Scotland but in Scottish communities around the world, most notably in Cape Breton, Nova Scotia.  Although Gaelic cultural influence once stretched much wider, its geographic boundaries have been reduced to Maritime Canada and Scotland itself, two communities separated by an ocean. 3  A 2011 study by Mark Sheridan, Iona MacDonald, and Charles Byrne sought to identify trends within the culture by interviewing cultural experts, that is, singers and storytellers who were held in high regard by the Gaelic community.  The interviews revealed strong                                                           1 Daniel Levitin, This is Your Brain on Music (New York: Penguin, 2006), 224. 2 Heather Sparling, “Music is Language and Language is Music: Language Attitudes and Musical Choices in Cape Breton, Nova Scotia,” Ethnologies 25, no. 2 (2003): 145. 3 John Gibson, Traditional Gaelic Bagpiping, 1745 - 1945 (Montreal: McGill-Queen's University Press, 2000). 3  trends, suggesting that community and family were extremely significant to Gaelic culture.   In addition, the interviews confirmed that music was ever-present in the daily life of the Gaels, and that songs that accompanied working were sometimes “more important than the job.”4 Gaelic music has remained popular and widely played both as its own genre and as part of a wider “Celtic” or “trad.” genre, where it is often combined with Irish and English traditions.5  Thomas Pease’s writings about the Celtic revival of the 1990s kindled a fascination with traditional Irish and Scottish music as well as quasi-Celtic spectacles like Michael Flatley’s Lord of the Dance.6  Flatley’s stage show helped augment the interest in “Celtic” culture, and Scottish Gaelic musicians from Nova Scotia and Scotland alike became more popular and more widely heard.7  Traditional fiddlers like Natalie MacMaster and Ashley MacIsaac became internationally famous.   In 1997, Mary Jane Lamond, an activist and Gaelic singer, released her second album Suas e8! to commercial and critical acclaim.  The album featured Gaelic songs as well as puirt-a-beul,9 all sung in the original Gaelic, albeit in contemporary arrangements.  The album was not only commercially successful, but also received multiple nominations for Juno Awards and East Coast Music Awards.10  “Horo Ghoid Thu Nighean” is the leadoff track for the album and was one of the most successful singles from the album.  “Horo Ghoid Thu                                                           4 Mark Sheridan, Iona MacDonald, and Charles Byrne, “Gaelic Singing and Oral Tradition,” International Journal of Music Education 29, no. 2 (May 2011): 183. 5Thomas Pease, “Gaelic Music of Cape Breton Island: the Last Fifteen Years,” Notes: Second Series 63, no. 2 (December 2006): 402. 6 Ibid., 401. 7 Pease, “Gaelic Music of Cape Breton,” 401. 8 Mary Jane Lamond, Suas e!, Wicklow Records 09026 63246 2-CD, 1997, compact disc. 9 “Puirt-a-beul” is a Scottish Gaelic term translating to “tunes from the mouth”, and refers to a repertory of Gaelic vocal tunes originally used for dancing.  This term is explained more fully on page 6. 10 “Contemporary Musicians: Mary Jane Lamond,” Encyclopedia.com, last modified 2002, accessed April 28, 2014, http://www.encyclopedia.com/doc/1G2-3495100053.html 4  Nighean” is often known in English as “Jenny Dang the Weaver”, the fiddle tune which serves here as a case study.  The song, along with the album as a whole, was a success. It received wide radio play, with the music video even being featured on the popular Canadian music video channel Much Music.11 These successes demonstrate that Scottish Gaelic music is a living tradition and remains a vibrant and evolving genre, particularly in the United Kingdom and Atlantic Canada. One of the biggest struggles faced by the worldwide Gaelic community is the loss of their language.  Beginning in the eighteenth century, the British government made a strong effort to eliminate the language altogether.12  Even in the twentieth century, Gaelic speakers in Britain were sometimes punished for speaking their native language at school.13  Statistics from 2011 estimated that a meagre 1% of the population in Scotland spoke Gaelic,14 and just over 2300 people in all of Canada.  (The number of those fluent in Scottish Gaelic is likely smaller, as the Canada census did not distinguish between Irish Gaelic and Scottish Gaelic.)15  A 2011 UNESCO report classified Scottish Gaelic as an endangered language.16  The consensus of these sources is clear: the Gaelic language itself is facing extinction.                                                             11 "Music Video Programming," Billboard, April 5, 1997, 82. 12 Katherine Spadaro, Colloquial Scottish Gaelic: The Complete Course for Beginners, (London: Taylor & Francis Group, 2005), 1. 13 Ibid. 14 “Census 2011: Release 2A,” National Records of Scotland, last modified September 26, 2013, http://www.scotlandscensus.gov.uk/news/census-2011-release-2a 15 “Detailed Mother Tongue, Single and Multiple Language Responses, Age Groups, and Sex for the Population Excluding Institutional Residents of Canada, 2011 Census,” Statistics Canada, last modified November 26, 2013, http://www12.statcan.gc.ca/census-recensement/2011/dp-pd/tbt-tt/Rp-eng.cfm?LANG=E&APATH=3&DETAIL=0&DIM=0&FL=A&FREE=0&GC=0&GID=0&GK=0&GRP=1&PID=103251&PRID=0&PTYPE=101955&S=0&SHOWALL=0&SUB=0&Temporal=2011&THEME=90&VID=0&VNAMEE=&VNAMEF= 16 Sheridan et al., “Gaelic Singing and Oral Tradition,” 172  5  Music and language are often seen by Gaels as inextricably linked.  Jonathan Dembling asserts there is a widespread belief that the music “depends explicitly on Gaelic for its distinctive character, and that its proper articulation is possible only through a familiarity with the language.”17  However, because the music has grown in popularity while the use of the language has declined, many practitioners of this style are no longer fluent Gaelic speakers.  As the Gaelic language becomes more imperilled, Gaelic traditional music becomes even more important for cultural preservation, as “it is infused with the sense of place, environment and cultural identity.”18 The music’s close connection to language does not preclude its transmission through common music notation. Kate Dunlay, an American fiddler and ethnomusicologist who studied fiddle music and dance extensively in Cape Breton, expressed surprise that many of her teachers learned music from written sources as well as by ear.19  Although reading the notation is a common first step in learning a tune, Cape Breton fiddlers are vehemently opposed, Dunlay emphasizes, to playing a tune exactly as written.  Instead, musicians ornament or vary the tune slightly. Dunlay notes that stylistic correctness is very important, but, like other scholars, does not elaborate exactly what characteristics define the style.  This leads me to hypothesize that part of the Gaelic music style is made of subtler elements like microtimings. In examining the fiddle dance music of Gaeldom, it is important to recognize the origins of these tunes and how it has affected the tunes in their current instrumental form.                                                            17 Jonathan Dembling, “Instrumental Music and Gaelic Revitalization in Scotland and Nova Scotia,”  International Journal of the Sociology of Language 206 (November 2010): 246. 18 Sheridan et al., “Gaelic Singing and Oral Tradition,” 183. 19 Kate Dunlay, "Correctness in Cape Breton Fiddle Music", liner notes to Traditional Fiddle Music of Cape Breton Volume 4: MacKinnon's Brook, Various Artists, Rounder Records 7040, CD, 2008. 6  According to Lamb, “it is a commonly expressed belief amongst Gaelic speakers that their dance music originated as song.”20  Vocal versions of dance tunes were often used for dancing when no instruments were available.  This form of music is part of the repertoire known as puirt-a-beul (singular: port-a-beul).   Puirt-a-beul is a Scottish Gaelic term translating to “tunes from the mouth”21.  Note that puirt is translated as “tunes” rather than “songs”.  It is a general consensus among music and Gaelic scholars that these tunes were originally for voice but then were adapted for instruments as they became available, and for the past hundred years, the instrumental versions have been preferred. 22  Today the tunes are seldom performed vocally, since the lyrics are often nonsensical or non-narrative, and the Gaelic community tends to value other vocal genres – such as Gaelic song – above puirt-a-beul.  These tunes in their instrumental form, however, are among some of the most popular dance music in this style.  Without the explicit link to language, what is it about this music that makes it still so distinctive in character?  The answer can perhaps be found in the rhythm and meter of these tunes.  Reverend William Matheson, an expert in Gaelic song and dance and a native Gaelic speaker himself, claimed that he was sometimes unsure whether certain puirt-a-beul are meant to be sung in reel or strathspey time.23  He indicated that the deciding factor was not the pitch material or any structural element, but the rhythmic implications of the Gaelic lyrics.  Though not all performers in this style may know the Gaelic lyrics, Reverend                                                           20 William Lamb, “Reeling in the Strathspey: The Origins of Scotland’s National Music,” Scottish Studies 36: 72. 21 Heather Sparling, “Music is Language and Language is Music,” 146. 22 Ibid. 23 Heather Sparling, “Music is Language and Language is Music,” 66.  While they are both in quadruple simple time, strathspeys and reels incorporate different grooves and are often performed at different tempos.  Strathspeys tend to be performed slower, and with extreme beat subdivisions, similar to double dotted rhythms, whereas reels are performed faster and with more even eighth note divisions.  The difference can be easily heard in the following performance: https://www.youtube.com/watch?v=B6Oq3ZFVjAk (The strathspey lasts from 0:00 to 0:50, at which point a reel begins).   7  Matheson makes it clear that stylistic elements rather than structural ones are the primary factor in defining this form.  In his 2008 dissertation on Celtic Fiddle music, Jeffrey Hennessy concluded that the “Gaelic sound” associated with this music refers to “a particular stylistic attribute of the music associated with rhythmic articulation.”24 Like a great deal of dance music, this repertoire has a distinctive rhythmic feel, akin to the “groove” of popular music.  Though the tunes are highly repetitive, they are anything but boring.  At performances, it is not unusual to witness audiences spontaneously clapping along or cheering when a fast-tempo reel is played.  Musicological research into puirt-a-beul has yielded many interviews with insiders who emphasize the rhythmic subtlety of the genre. Although most of these tunes are notated with straightforward rhythms of eighth notes and quarters, interviewees assert that the rhythms “have to be just so,”25 implying that there is nuance beyond what can be achieved with notation.  Furthermore, it seems to be a widely held belief among cultural insiders that the inflections of the lyrics have been absorbed into the instrumental renditions of these tunes, and that “these inflections…largely constitute the Gaelic expression as it shapes the fiddle style.”26 Because informants describe the rhythmic nuance, or groove, in these general terms, rather than with reference to music notation, perhaps the actual nature of the groove can be illuminated by examining actual timings of performances, making use of methodologies usually applied to the jazz canon.  Though recordings of traditional sung puirt-a-beul are scarce, there are more easily accessible recordings of the instrumental renditions of these tunes, which have superseded their vocal predecessors in terms of widespread popularity                                                           24 Jeffrey Hennessy, “Fiddle Grooves: Identity, Representation, and the Sound of Cape Breton Fiddle Music in Popular Culture” (doctoral thesis, University of Toronto, 2008), 41. 25 Catriona Parsons, qtd. in Sparling, “Puirt-a-Beul,” 205. 26 Elizabeth Doherty, qtd. in Sparling “Puirt-a-Beul,” 258. 8  and prevalence.  Instrumental are more accessible for players as well as listeners, as the tunes do not require fluency in Gaelic. Fiddle tunes based on puirt-a-beul seem a particularly fruitful avenue for this investigation as the genre provides the opportunity to study this rhythmic nuance (possibly derived from linguistic influences) on the music without the necessity of taking Gaelic lyrics into account as a non-Gaelic speaker.  Glenn Graham, a noted Cape Breton fiddler in this style, seems to affirm that it is possible to do the music justice in this way, claiming that “it is the cultivation of an intuitive recognition of the language’s rhythms and accents combined with digital ornamentation and bowing applications that help to create a Gaelic sound in the fiddle, not the ability to speak it.”27  Graham describes fiddlers with various exposures to spoken Gaelic and claims that simply becoming familiar with the basic sound of the language is enough to help influence fiddling style, even if the fiddler doesn’t understand or speak the language.  Based on what Graham describes, this seems to be on par with attempting to mimic the basic sounds and cadence of a foreign language while speaking, without necessarily knowing any vocabulary. In addition, the fiddle has been a vibrant part of the Gaelic tradition for years.  In Scotland, only the bagpipe presents any challenge to the fiddle’s claim as principal traditional instrument for the country.  Until recently, solo fiddle playing was the norm, often used to provide music for dancing.  Historically it has been popular with both high and low classes in Scotland, since both groups share the same repertory of dance music.  In                                                           27 Glenn Graham, The Cape Breton Fiddle: Making and Maintaining Tradition (Sydney: Cape Breton University Press, 2006), 64. 9  fact, it was the richer class’s penchant for fiddle dance tunes that led to the large number of published collections of these tunes in the eighteenth century.28 The cultural implications of puirt-a-beul and instrumental dance tunes are heatedly debated as often as they are discussed in scholarship.  There is disagreement about the “Gaelic-ness” of different communities, as Gaels in Cape Breton have been separated from Scotland for generations and the culture has grown and changed in different ways.  This disagreement calls into question the authenticity of Gaelic musicians in Cape Breton, Scotland, and elsewhere.  While it is important to acknowledge the political and social background of Gaelic music, this paper aims to address the musical qualities and therefore the political concerns described above are beyond the scope of this project. Dance tunes and traditions The dance music repertory consists of several forms such as reels, strathspeys, and jigs.  William Lamb painstakingly edited and republished Keith Norman MacDonald’s Puirt-a-Beul: The Vocal Dance Music of the Scottish Gaels in 2012.  This collection is considered “a fair sampling of the genre.”29  Out of this sampling, 55% are reels, implying that the reel is the most common of these dance forms, and therefore a good starting place for a study of the style. Though the reel is present in other related styles, such as Irish and American fiddle playing, it is believed that the genre originated in Scotland.30                                                             28 Robin Stowell, The Cambridge Companion to the Violin, (Cambridge: Cambridge University Press,1992), 240. 29 William Lamb, Keith Norman MacDonald’s Puirt-a-Beul: The Vocal Dance Music of the Scottish Gaels. (Isle of Skye: Taigh na Teud, 2012), 20. 30 Rebecca McGowan and Andrea Levitt, "A comparison of Rhythm in English Dialects and Music," Music Perception: An Interdisciplinary Journal 28, no. 3 (February 2011): 308. 10  Lamb defines the reel as “a rapid but smooth-flowing quaver movement in alla breve.”31  Indeed, reels are typically notated in 4/4 or cut time, and tend to feature running eighths. The 'smooth-flowing' or rhythmically consistent way in which they are commonly played today is referred to as a 'round' style.  Another defining characteristic of these tunes is their melodic brevity, meaning that short melodic material is repeated again and again during a full-length performance.32  As a general rule, puirt-a-beul have a maximum of one verse and one chorus, with both sections being repeated. 33 This convention carries over, as a binary AABB form, into the instrumental genre that utilises the melodies of puirt-a-beul.  Most tunes are therefore divided into two sections, which often contrast one another either in melodic material or in pitch register.34  In other words, there are (at most) two differing sections which are repeated at will. My case study for this project, “Jenny Dang the Weaver,” fits this binary mold. Differently named tunes share a number of melodic similarities.  Many of the tunes use motives of a few beats as building blocks for larger phrases.  The pitch material is often straightforward, sometimes with surprisingly few non-chord tones.  Hennessy observes that "the tunes are not melodies in the classical sense, with many of them simply arpeggiating triads or seventh chords. In essence then, the tunes are constructed as rhythmically prolonged chords rather than as melodies to be harmonized. As instrumental dance music, this is perhaps not surprising."35  However this feature seems more                                                           31 Lamb, “Reeling in the Strathspey”, 67. 32 Heather Sparling, "Categorically Speaking: Towards a Theory of (Musical) Genre in Cape Breton Gaelic Culture," Ethnomusicology 52, no. 3 (Fall 2008): 402. 33 Ibid., 415. 34 Hennessy, “Fiddle Grooves,” 215. 35 Ibid. 11  noteworthy when one considers the vocal origins of these pieces.  The relative simplicity of the pitch material makes it even clearer that performers create interest through other means.  Hennessy speculates that some of these methods might include accents, syncopation, and ornamentation,36 but I hypothesize that microtimings also play an important role. When analyzing the groove of dance music, it is essential to consider the dance movements which accompany the music.  Puirt-a-beul and the instrumental tunes that descend from it are used in several dance traditions associated with Scotland, including step dance, sword dance, Highland dance, and Scottish Country Dancing, all with extensive and varied techniques.37  Any given reel can be used in any of these styles and it seems likely that the groove and microtimings of a reel would interact differently with different styles and steps.  Therefore I believe it best to focus on just one associated dance tradition.   Scottish Country Dancing seems like an appropriate choice.  This style enjoys the most widespread popularity, so it is likely more people have participated in this sort of dance with traditional Gaelic music, rather than the specialized few who study Highland Dance.  Despite the British government’s attempt to eradicate the Gaelic language, Scottish Country Dancing was a part of worldwide British school curricula for many decades. 38  Even today, this style of dancing is a popular social activity across the world, with groups as                                                           36 Hennessy, “Fiddle Grooves,” 215. 37 Jean Milligan, "Scottish Country Dancing," Journal of the International Folk Music Council 2 (1950): 32. 38 Gigi Beradi, “Scottish Country Dancing Has a Young Soul,” Dance Magazine 74, no. 11 (November 2000): 64. 12  far away as New Zealand and Japan.39  The tradition not only has deep roots, but has also continued to grow, with new dances being written each year.40 In addition, the culture of Scottish Country Dance supports the findings of Sheridan et al., cited above, about the centrality of music.  The dance is a strongly social group activity.  Dancers are put into sets consisting of a number of couples arranged in two lines or a square, depending on the dance.  There are a number of basic figures and formations which are combined in various ways to form a full dance.  Usually a dance will leave the dancers in a new order and is repeated until everyone has returned to their starting position.41  Though traditional dances are often associated with certain tunes, dances can in fact be danced with any tune of the same type and duration.  Other dances have no particular tune association, and can be danced with any music with the correct number of bars. The most frequently used step in Scottish country dancing is the skip-change step, which is used for travelling, so this step likely interacts with the groove of its accompanying music.  Some version of this step has been documented as far back as 180542.  The step is described as “advancing the right foot forward, the left following behind: in advancing the same foot a second time, you hop upon it, and one step is finished.”  The step is then repeated, except the dancer advances the left foot first this time.  It takes a full measure to                                                           39 “Dancing Across Cultures,” The Nelson Mail, January 4, 2005, accessed May 29, 2014, http://www.lexisnexis.com.ezproxy.library.ubc.ca/hottopics/lnacademic/?verb=sr&csi=161929 40 “What is Scottish Country Dancing?” , The Royal Scottish Dance Society, accessed January 22, 2014,  https://www.rscds.org/article/what-is-scottish-country-dancing 41 Ibid. 42 George Emmerson, A Social History of Scottish Dance: Ane Celestial Recreatioun (Montreal: McGill-Queen’s University Press, 1972), 168. 13  complete a slip step on the right foot and the left foot, meaning that beat 1 is the beginning of a new skip-change on the right foot.43    Rhythm and meter in music scholarship The foundation for my approach can be found in such influential theories as Justin London’s Hearing in Time: Psychological Aspects of Musical Meter and Christopher Hasty’s Meter as Rhythm.  Although these texts focus on the analysis of rhythm and meter not specific to Gaelic music, they, along with more traditional music theory, provide the basis for many contemporary scholars’ more specialized inquiries.  London’s theory of meter is cyclic and incorporates beat subdivisions as part of the defining feature of meter.  London hypothesizes that different tempos and even slight difference in subdivision ratios create different metrical experiences.44  Hasty’s metrical theory is based on the idea of durational projection, where the listener predicts the timings of upcoming events on the basis of durations that have just been completed. Hasty also discusses the qualities that characterize different metrical events, such as anacrusis, continuation, or beginnings. 45   One specialized area that has proven particularly fruitful in characterizing musical “groove” is the study of “expressive microtimings” or “participatory discrepancies”,46 which involve the comparison of the precise timings of musical events with each other and with inferred or explicit metrical beats.  Usually measured in milliseconds, these timing                                                           43 Ibid., 310. 44 Justin London, Hearing in Time: Psychological Aspects of Musical Meter (New York: Oxford University Press 2004), 143. 45 Christopher Hasty, Meter as Rhythm (New York, USA: Oxford University Press, 1997). 46 Charles Keil, "Participatory Discrepancies and the Power of Music," Cultural Anthropology 2, no. 3 (August 1987): 275-283. 14  differences sometimes exist on the fringe of human perception, but nonetheless have an impact on how music is heard.  As Matthew Davies writes, “A key feature of human performance is variability.”47  Some features of variability, such as dynamics, are often notated in a piece of music’s score, but other factors are too small or nuanced to be effectively notated.  Microtimings fall into this category.48  Davies also differentiates between “unsystematic” microtiming, which can be due to the physical limitations or error of the performer, and “systematic” microtiming, which is the deliberate manipulation of timing.49  It is obviously difficult to determine whether microtimings are systematic or unsystematic, as even the performer may not be fully aware of them.  In order to help determine whether there is purposeful use of microtimings in this style, I will consider both trends as well as outliers in the microtiming data, and attempt to explicate the effects of these timings on the listener.  For this reason, I will analyze microtiming trends and outliers and consider the musical implications and possible effects on listeners Despite widespread scholarly interest, the relationship between timing measurements and the experience of groove remains somewhat mysterious. Some studies, such as a project by Jan Fruhauf et al., found that students rated a mathematically accurate drum pattern as having the greatest “pattern quality” when compared with the same pattern played with microtimings.50 However, Keil and Feld’s thesis posits that “all musics                                                           47 Matthew Davies et al., “The Effect of Microtiming Deviations on the Perception of Groove in Short Rhythms,” Music Perception 30, no. 5 (June 2013): 497. 48 Ibid., 498. 49 Ibid. 50 Jan Fruhauf, Reinhard Kopiez, and Friedrich Platz, "Music on the timing grid: The influence of microtiming on the perceived groove quality of a simple drum pattern performance," Musicae Scientiae 17, no. 2 (June 2013): 246. 15  have to be out of time to groove.”51 If both of these are correct, then "pattern quality" and groove must be different aspects of rhythm.   Vijay Iyer expresses a sentiment similar to Keil's and Feld's, saying that African musicians have “their own ways of relation to an isochronous pulse,”52 meaning that each individual has his/her own “feel” of the music.  Iyer investigated the microtimings of groove-based African-influenced music rather than the typical Western art music traditionally favoured by music theorists.  A methodological question in all microtiming studies is: what is the referential beat with which the actual attack timings are discrepant?  For the music he is interested in, rather than finding a theoretical beat by averaging all the instrument timings, Iyer refers them to a particular instrument, the clave, as the definitive timekeeper.  This means that, in theory, all the instruments could play marginally ahead of the beat (represented by the clave) for the duration of the piece.53  Iyer focuses on the role that groove plays in stimulating movement, citing scientific research which suggests that “the act of listening to rhythmic music involves the same mental processes that generate bodily motion.”54  Iyer’s work, like a great deal of jazz microtiming research, focuses on ensemble music rather than soloists. Matthew Butterfield applies findings of cognitive studies on expressive microtiming to jazz, as conceptualized through Hasty’s model of metrical projection.55  Butterfield states that participatory discrepancies are intrinsic to the groove of a piece, which in turn                                                           51 Charles Keil and Stephen Feld, Music Grooves: Essays and Dialogues (Chicago, USA: University of Chicago Press, 1994), 155. 52Vijay Iyer, “Embodied Mind, Situated Cognition, and Expressive Microtiming in African-American Music,” Music Perception 19, no. 3 (Spring 2002): 398. 53 Ibid., 399. 54 Iyer, “Embodied Mind, Situated Cognition,” 392. 55 Matthew Butterfield, “The Power of Anacrusis: Engendered Feeling in Groove-Based Musics.” Music Theory Online 12 (2006). http://www.mtosmt.org/issues/mto.06.12.4/mto.06.12.4.butterfield.html (accessed January 8, 2014). 16  determines whether a listener perceives the music as laid back or driving forward.  Rather than considering the timing discrepancies between instruments, Butterfield focuses on timings within a single line, the bass ostinato of Herbie Hancock’s Chameleon, examining how its microtiming affects the sensation of anacrusis.    In another article, adapting a concept of Fernando Benadon to be discussed below, Butterfield explored jazz “swing” quantitatively in terms of the ratio between the durations of performed eighth note beats and upbeats.56 A similar measure can be found in Mats Johansson’s PhD dissertation on rhythm and grooves in Norwegian fiddle music, which uses microtimings to assess what percentage of the measure or beat was occupied by a sounding event.57 Another contribution to this line of research is the work of Alan Dodson who, among other contributions to the field, addresses the ways in which accentuation and tempo rubato in J. S. Bach’s Invention No. 1 in C major interact with rhythmic structure  and prolongation.58 While this approach proves productive for this genre, rubato and expressive tempo changes are less important in music intended for dancing.    Groove Although there has been significant investigation into groove in pop and jazz music, there is some variation in how the term is defined.  Davies et al. described it as “a sensation                                                           56 Matthew Butterfield. “Why Do Jazz Musicians Swing Their Eighth Notes?” Music Theory Spectrum 33, no. 1 (Spring 2011). 57 Mats Johansson, "Rhythm into Style: Studying Asymmetrical Grooves in Norwegian Folk Music," (PhD diss., University of Oslo, 2010). 58 Alan Dodson, "Performance Strategies in Three Recordings of Bach's Invention No. 1 in C Major: A Comparative Study," Canadian Journal of Music 31, no. 2 (2011): 44. 17  of movement or wanting to move”59 when listening to music.  Vijay Iyer describes music with groove as featuring “a steady, virtually isochronous pulse that is established collectively by an interlocking composite of rhythmic entities and is either intended for or derived from dance.”60  Hennessy concludes that “the term groove carries with it two essential meanings: the acoustical repeating of a rhythmic idea that forms the metrical underpinning for a piece of groove music, and the effect this has upon individual people who respond collectively as a group to the sound of the groove.”61 Matthew Butterfield believes groove is created not only by the microtimings within a groove, but also by the specific durational sequence of the rhythmic ostinato itself.62  Lawrence Zbikowski takes a more cultural and conceptual approach, describing groove as separate from swing, a more stable concept created by the interaction of multiple musicians with pitch and rhythmic elements63, as well as the cultural experience of the listener.  By responding to a groove, on this view, a listener is demonstrating cultural knowledge. The term “swing” and its varied definitions further confuses matters.  Butterfield defines swing as not only the unevenness of the eighth notes (the expressive microtimings) that is characteristic in jazz music but also as the interaction between drums and bass which creates a “lilting groove”.64  It seems that in Butterfield’s terms, “swing” is dependent on the presence of more than one instrument. From these definitions, groove seems to be clearly linked to repetition, interaction, musical motion, and a listener’s perception or embodiment of movement within music.                                                            59 Davies et al., "The Effect of Microtiming Deviations on the Perception of Groove,” 497. 60 Vijay Iyer, "Embodied Mind, Situated Cognition,” 397. 61 Hennessy, “Fiddle Grooves,” 5. 62 Butterfield, “The Power of Anacrusis.” 63 Lawrence Zbikowski, "Modelling the Groove: Conceptual Structure and Popular Music," Journal of the Royal Musical Association 129, no. 2 (2004): 275. 64 Butterfield, “Why Do Jazz Musicians Swing Their Eighth Notes?” 3. 18  Most fundamentally, groove-based music is repetitive.  In fact, one of the remarkable characteristics of groove is that – in Iyer’s words – “[it] can sustain interest or attention for long stretches of time to an acculturated listener, even if ‘nothing is happening’ on the musical surface.”65  That is to say, groove creates an engaging musical experience even if the harmonic and melodic material is minimal, predictable or highly repetitive.  This is a concept which seems to fit well with Gaelic dance music.  Despite the repetitiveness of the melodic material, the tunes capture an audience’s interest not only as dance music, but also in commercial and concert recordings.  I suspect that expressive microtimings contribute to this interest, as a solo instrument is still able to provoke clapping, stomping, or dancing in listeners, despite the highly repetitive pitch material and rhythmic values. The cyclic nature of these tunes (an AABB form which is repeated indefinitely) can also be understood in terms of John Rahn’s idea of repetition.  The presence of repetition with expressive microtiming creates groove.  The groove is constantly in the process of being formed; the spontaneous deviances from mathematical timing and the slight variants in melody allow the tunes to “escape the dead hand of some prefigured order.”66  The groove is what imbues the music with a sense of life, preventing the repetitiveness of the pitch material from becoming stagnant and approaching what Rahn refers to as “slavery.”67 As dance tunes, reels (and other dance forms derived from puirt-a-beul) are inherently groove based.  In fact, it could be argued that the rhythm in these tunes supersedes melody in terms of importance.  Recordings of traditional puirt-a-beul reveal                                                           65 Iyer, “Embodied Mind, Situated Cognition,” 388. 66 Rahn describes “repetition” as music which, while repeated, is transformed throughout repetition, allowing the listener to experience the music process towards a telos or goal, rather than simply experiencing the goal itself.  John Rahn, "Repetition," Contemporary Music Review 7, no. 2 (1993): 50. 67 Rahn, “Repetition,” 50. 19  that the pitch tends to be more gestural than precise in nature.  Rather than singing the exact pitches of the given tune, performers of puirt-a-beul tend to follow the general pitch contour of each phrase.  This indicates that the rhythm is much more important in learning the groove of a piece.  This also seems true of the instrumental renditions of these tunes, where there is often variation in the pitch material from musician to musician, or even within a single performance. Interviews reveal that some cultural insiders themselves hold this opinion.  One is quoted as saying “it’s not the tune that matters, it’s the rhythm…like the singers might not have a note of music in their head…what you get is the rhythm, you don’t get a tune, you get rhythm.”68  Another interviewee went so far as to characterise the style as “Gaelic rap.”69  Like jazz, Gaelic fiddle playing is often described by informants as having a special “swing” that differentiates it from non-Gaelic fiddling.70  It seems likely that similar methodologies would reveal similar musical nuance in both jazz and Gaelic musics, allowing for a deeper understanding of stylistic elements not readily transmitted by notation.  This will also show if the methodology used to approach jazz can be successfully applied to other musics. One of the performers analyzed in this study, Hanneke Cassel, is featured in a video discussing groove in reels. 71   Cassel describes a reel’s groove as having a 3+3+2 accent pattern (pictured below).                                                            68 Jonathan Dembling, “You Play It as You Would Sing It: Cape Breton, Scottishness, and the Means of Cultural Production,” in Transatlantic Scots, ed. Celeste Ray (Tuscaloosa: University of Alabama Press, 2005), 187. 69 Dembling, “You Play It as You Would Sing It,” 187. 70 This concept is also described as ‘flavour’ or ‘taste’.  Joe Neil MacNeil, qtd. in John Shaw, “Language, Music, and Local Aesthetics: Views from Gaeldom and Beyond,” Scottish Language 11, no. 12: 41. 71 “Reel Groove: Scottish Fiddle Technique Tutorial,” YouTube video, 4:57, posted by "FIDDLEVIDEO," August 24, 2014, https://www.youtube.com/watch?v=EBC1pQawfy4 20  This is very different from the concept of groove discussed above.  From Cassel’s explanation and demonstration, it seems that this 3+3+2 pattern is restricted to accompaniment.  Like ornamentation, this sort of accented accompanimental pattern may be a source of individuation among players. However, as the recordings chosen for analysis have no accompaniment, I am focussing on groove created by the microtimings in the melody itself, examining this slightly more subtle element as a possible source of individual style.   In summary, a rhythm-oriented study of puirt-a-beul – and thus, the instrumental music which stems from it — seems appropriate.  Investigating the music in this way may shed light on the inner workings of the “swing” or “groove” of this music, as that seems to be one of the sources of this genre’s popularity and longevity, as well as one of the style’s defining qualities.   21  Chapter 2: Methodology and Approach to Analysis Selecting a tune One popular port-a-beul is “Horo Ghoid Thu Nighean (Horo you stole the girl)”, known most commonly as “Jenny Dang the Weaver”72 when played on fiddle or another instrument.  The tune is a popular reel not only for dancing but also for performance: witness the commercial and critical success, mentioned above, of Mary Jane Lamond’s vocal recording in the original Gaelic.  The tune was published for the first time in 1733, but it is believed that “Jenny Dang the Weaver” existed as a dance tune before this, and its many notated variations means there is no definitive score.73  In fact, William Lamb estimates that this tune is one of the most popular reels of all time.  This means that the tune has been heard widely not only in its traditional context but also in a more contemporary setting.  In some respects “Jenny Dang the Weaver” is slightly unconventional. While many reels consist of running eighths notes throughout, its A section does not, and features an accented two-sixteenth eighth note figure on the second beat of most measures that draws the attention of the listener as one of its most significant rhythmic gestures.  One of the performers, Hanneke Cassel, describes this as a “cut” and claims it is one of the defining characteristics of Scottish fiddling, present in “almost every reel.”74  Also, the A section incorporates a number of melodic leaps, whereas the B section is much more stepwise in its motion, except for the last measure of each four measure phrase, which is often similar to phrase endings in the A section.                                                            72 See Figure 1 on page 48 for a transcription of “Jenny Dang the Weaver.” 73 Lamb, Keith Norman MacDonald’s Puirt-a-Beul, 172. 74 “Jenny Dang the Weaver: Fiddle Lesson,” YouTube video, posted by "FIDDLEVIDEO," August 26, 2014, https://www.youtube.com/watch?v=StOboC96AqM. Her characterization of the "cut" appears at 1:43. 22  Though the second-beat A section figure is usually notated as , it is always performed much less evenly.  The B section is also notated as eighth notes, but as in the A section, the performed beat is not divided as evenly as the notation indicates. The combination of conventional reel rhythm and a notable rhythmic feature means that this tune is particularly interesting to analyze using microtimings.  The selection of this reel was also based on a practical concern.  Because of the popularity of “Jenny Dang the Weaver,” more recordings were available.  This allowed for  five different performances to be analyzed, whereas other tunes have only one or two suitable recordings available.    Notation and style Although traditionally these tunes were transmitted orally, fiddle tune collections began to be published as far back as the 18th century,75 and today online collections have made transmission by notation even easier.  There is a large discrepancy in how they are notated, however, for several reasons.   The tunes are, by their very nature, highly variable.  The same tune will be played differently from person to person and from performance to performance, with the basic melody being embellished or slightly altered.  This is not only a facet of the style, but also a result of many years of oral tradition before the increase in popularity of notated transmission.                                                           75 Lamb, Keith Norman MacDonald’s Puirt-a-Beul, 24. 23  In addition, each reel (and other dance tunes) has accumulated many different titles.  Every tune has numerous variations, with no single notated version being a definitive model.  For example, “Jenny Dang the Weaver” has eleven different versions on session.org,76 and is listed as appearing in 309 different tunebooks77 with eleven settings available online, all of which are slightly different.   Lastly, there are discrepancies in the way that the rhythms are transcribed. For example, while the second beat figure featured in this tune is most commonly notated as two sixteenths and an eighth, there are several other notated interpretations, such as a quarter note with a turn, a triplet figure, or two eighths.  Because the most common notation is two sixteenths and an eighth, this will be the figure used in my transcriptions.    Rhythmic nuance and classifying groove Keil claims that theorists need different approaches to evaluate music “depending upon whether the processual or syntactic aspect is dominant.”78  The repetitive, groove-based nature of a reel seems to make it a good candidate for a processual approach, one that examines the rhythmic and metrical processes at play.  For the purposes of this study, I will mainly focus on aspects of microtiming that have mainly been studied in jazz. My                                                           76 The Session is an online community dedicated to traditional music, particularly in collecting notation and recordings of various tunes.  Though their main focus is Irish music, the other Celtic traditions also find a home in this community. 77 “Jenny Dang the Weaver,” The Session, last modified December 2013, accessed February 28, 2014, http://thesession.org/tunes/380 78 Keil and Feld, Music Grooves, 73. 24  approach is informed by empirical research on the thresholds of human entrainment, as summarized in London’s Hearing in Time.79   Groove studies usually focus on the interaction of different instruments to demonstrate that despite their repetitive nature, grooves are not static, literal repetitions. However, there are some exceptions, such as Butterfield’s case study of Chameleon, that focus on microtimings within a single layer of the texture. Dance tunes of the puirt-a-beul tradition were and are commonly played or sung by a single musician, meaning that participatory discrepancies between ensemble players are not present.  Therefore it seems worth considering whether Butterfield’s approach is relevant to this genre.  There are indeed expressive variations, but these occur within a single line, not in relation to more than one musician.  Therefore interaction between instruments does not contribute to the groove, which is instead created through expressive variations by the soloist.  However Butterfield’s approach to a soloist focussed on a drum set pattern80 which, while performed by an individual, could be conceived of as multiple sounds, instruments, and lines.  My approach will take his methodology one step further and apply it not only to a single musician, but to a single melodic line.  My work is similar to that of Mats Johansson of the University of Oslo, who investigated beat durations in solo fiddle music.81  However my research will focus on how the beats are subdivided.  My intention is to explore how the groove is created by factors other than the interaction of multiple lines, namely the division of eighth notes and how these ratios change depending on their location in the measure, phrase, or section.                                                           79 London, Hearing in Time, 31-36. 80 Butterfield’s main focus is the bass vamp, but he discusses the bass in terms of how it interacts with the percussion, not as a solo line.  81 Mats Johansson, "Rhythm into Style.” 25  To proceed further, I must clearly define what groove means in the context of fiddle reels.  As discussed earlier, groove is associated with repetition and the effects of rhythm and meter on listeners (especially effects that spur movement).  In this context, groove will be defined as the way that the repetitive rhythmic material is varied with expressive microtimings, and how the trends and outliers in these timings create interest and evoke a reaction in listeners.  Iyer claims that African musicians (and presumably musicians from other cultures) each have their own individual feel of the music, or relation to the tactus, and I suspect a similar phenomenon may be present in Gaelic fiddling, a style which is often considered to be highly individual.  For this reason, I analyze recordings by five different performers, to see which trends are ubiquitous and which features may be more idiosyncratic.  My work here will demonstrate how a methodology developed for a different genre, jazz, can productively characterize rhythmic aspects of fiddle dance music, specifically in reels.    BUR and UBR In 2006, Fernando Benadon put forth the concept of Beat-Upbeat ratio (BUR) as a way to measure the variance in microtiming at the eighth-note level across phrases in jazz. As its name implies, BUR is determined by dividing the duration of the on-beat eighth note by the duration of the offbeat eighth note that follows it.  It is calculated for each beat in a passage, and so may vary according to how the durations vary as the music proceeds. Benadon used this concept as an alternative to the more subjective sounding “swing ratio,” noting that BUR takes into account that there may not be one definitive ratio to exemplify 26  the style of swing.82  Instead, the succession of BURs expresses the small variations of duration and thus implies that swing (or, for that matter, any other stylized groove) may be more of a varying process than one definitive and unchanging proportion of eighths.  Benadon’s analysis of jazz supports his notion that microtiming is closely connected to structure and phrasing.83  For example, he observes a common trend for BUR to increase at phrase endings, a phenomenon he dubs “BUR surge.”84   Subsequently, Matthew Butterfield studied swing by examining two quantitative measures of variation: the BUR again (although he handles it slightly differently) and also what he calls the Upbeat-Beat ratio (UBR) for successive pairs of swung eighths.85 UBR is found by dividing the duration of the offbeat eighth note by the duration of the on-beat eighth that follows.  BUR, UBR, and their relation are illustrated below:   Each ratio is understood as a property of the second event in the ratio, as the ratio demonstrates the division of a two-eighth-note timespan.  Thus the BUR for the second eighth note in the example is x/y, and the UBR of the third eighth note is y/z. BUR and UBR that are farther from 1.0 represent more unequal beat divisions.  A number less than 1 indicates a value where the first eighth note in the pair is shorter, whereas a number greater than 1 indicates the first eighth note is longer.                                                           82 Fernando Benadon, “Slicing the Beat: Jazz Eighth-Notes as Expressive Microrhythm,” Ethnomusicology 50, no. 1 (Winter, 2006), 75. 83 Ibid., 76 84 Ibid., 80. 85 Butterfield “Why Do Jazz Musicians Swing Their Eighth Notes?” 4. 27  Butterfield uses the BUR and UBR to characterize several aspects of jazz rhythm. Citing Iyer’s explanation, he explains that a higher BUR values on each beat place greater emphasis on the quarter note pulse, resulting in stronger entrainment.86  He also suggests a lower BUR than expected (i.e., where the second note comes earlier than anticipated) can enhance syncopation.87  Further, he claims that these ratios are essential for tracking how musicians control what he calls the “motional energy” of a phrase.  88  This can be caused locally by a change from a longer duration to a shorter one; the greater the difference in duration (as characterized by the BUR), the greater the motional energy.  Motional energy can also be created across longer timespans. When the division of each pair of eighth notes is widely varied and unpredictable, the feeling of spontaneity creates rhythmic tension. 89   Just as a stronger dissonance is more drawn toward its resolution than a weak one, so too are the uneven eighths drawn forward in time, potentially toward a more consistent and easily entrainable division.90 Adopting Butterfield’s treatment of swung eighth notes in jazz91, I will still refer to musical events as eighth notes even when the BUR implies divisions that correspond better with other notated rhythms, such as triplet eighths.  This corresponds better to the common notation of the tunes and, as such, likely corresponds to how performers conceptualize these rhythms.  Until recently, most research into microtiming in jazz has focussed on their metrical and rhythmic effects.  However, Benadon encouraged theorists to examine how                                                           86 Ibid., 8. 87 Butterfield “Why Do Jazz Musicians Swing Their Eight Notes?” 8. 88 Ibid. 89 Ibid. 90 Ibid., 4. 91 Ibid., 5. 28  microtimings interact with melody, harmony, and phrase structure.92  He identifies three main ways that pitch elements interact with Beat-Upbeat Ratio: shifts in harmony and melody can coincide with shifts in BUR value; phrase endings often resynchronize a soloist’s BUR with the rhythm section’s BUR; and motivic repetition often involves repetition of microrhythmic features as well.93  Benadon’s research also concludes that different performers play with different microrhythms.  His examination of five different musicians suggests that each performer is “characterized by their individual treatment of beat subdivision.”94  In the Gaelic community, where musicians often strive for a blend of stylistic conformity and individual expression, it is interesting to investigate if a similar trend occurs.  Studying "Jenny Dang the Weaver” This project analyzes five recordings of “Jenny Dang the Weaver” by different performers, in order to understand how microtimings contribute to the rhythmic identity and groove of the tune.  The original intent was to investigate the microtimings of multiple performances by the same performers. This required that each recording had to feature solo fiddle with no other instruments, as the timing of the fiddler would likely be affected by the presence of another musician.  Although solo performance is quite common in the field, recordings of this nature turned out to be scarce, and only five suitable performances were found.                                                             92 Benadon, “Slicing the Beat.” 93 Ibid., 74. 94 Ibid. 29  Happily, they are from a wide array of performers versed in the traditional Scottish style: Jim Blair, Neil Cameron, Hanneke Cassel, Bruce MacGregor, and Farquhar MacRae.  Jim Blair is a fiddler who has studied both in the United States, as well as Scotland, with such prestigious teachers as Catriona MacDonald.95  Neil Cameron is a Nova Scotian who has studied and performed traditional fiddle music in both the Maritimes and Scotland.96  Hanneke Cassel is a recording artist from Oregon, USA, who not only won the US National Junior Scottish Fiddle Championship twice (in 1992 and 1994), but also won the US National Scottish Fiddle Championship in 1997.97  Bruce MacGregor is one of Scotland’s most celebrated Scottish fiddlers, having recorded numerous albums both as a soloist and as part of a group.  He is also well known as a fiddle pedagogue, and in 2010, became the presenter of the BBC Radio Scotland show Travelling Folk.98  Farquhar MacRae was a Scotsman and native Gaelic speaker who became renowned in the traditional music scene in Scotland, though never as a commercial artist.  In obituaries MacRae was lauded as having “epitomised much that was best in traditional Gaelic life.”99  Another source held his name to be “synonymous with Highland music at its best.”100 These recordings are performed not only by diverse musicians, but also in varied contexts.  Cameron’s performance is taken from a YouTube video posted by the artist                                                           95 "Jim Blair: Fiddle Teacher," Facebook, last modified June 16, 2012, accessed February 12, 2014, https://www.facebook.com/fiddlesession/info 96 “About,” Neil Cameron Official Website, last modified July 2, 2012, accessed February 12, 2014, http://www.neilcameronfiddle.com/about 97 “Hanneke Cassel Biography,” Hanneke Cassel Official Website, last modified December 2013, accessed February 12, 2014, http://www.hannekecassel.com/bio.html 98 “Biography,” Bruce MacGregor Official Website, last modified 2014, accessed February 12, 2014, http://www.brucemacgregor.co.uk/about/ 99 Martin Macdonald, “Farquhar MacRae," The Herald Scotland, September 12, 2000, accessed February 5, 2014, http://www.heraldscotland.com/sport/spl/aberdeen/farquhar-MacRae-1.218830 100 Shona McMillan, "A Highland Gentleman: Farquhar MacRae, the Roshven Fiddler," Fiddler Magazine, February 1, 2008, accessed February 5, 2014, 30  himself.101  Though the performance takes place in a relaxed setting and with seemingly amateur recoding equipment, Cameron is well aware of an eventual audience.  Blair’s performance is another self-recorded video intended for the internet, though in this case it can be found on MySpace rather than YouTube.102  Cassel’s performance is also uploaded to YouTube, this time as part of a tutorial series directed at fiddlers who want to learn the tune.103  She is also featured in a more detailed lesson video based on “Jenny Dang the Weaver.”104  This recording was not analyzed for microtimings due to the presence of other instruments, but her discussion of the tune can shed light on her approach to it.  For example, Cassel refers to phrases as consisting of two bars, suggesting that she conceptualizes the tune as being broken up into even units.  Like Cassel’s, MacGregor’s performance105 appears in an instructional video.  His performance opens a video tutorial on how to play what he refers to as “triplets” (the  figure), which explains why his recording includes only the A section.  MacRae’s recording is part of a set of three tunes, recorded by Calum Iain MacLean as part of a historical archiving project by the School of Scottish Studies in Edinburgh.106 When comparing these recordings, it is important to consider how these artists may have absorbed each other’s influence, either by emulating each other or by trying to                                                           101 “Neil Cameron - fiddle set - Glencoe March/Jackie Coleman's/Silver Spear/Jenny Dang the Weaver,”  YouTube video, 3:03, posted by "NeilRHCameron," December 6, 2011, https://www.youtube.com/watch?v=0wIFDj6C1BI 102 “Jenny Dang the Weaver,” MySpace video, 1:00, posted by "Jim Blair," https://myspace.com/jimnblair/video/jenny-dang-the-weaver.../50870110 103 “Hanneke Cassel plays Jenny Dang the Weaver fast,” YouTube video,0:42, posted by "fiddlefestival," September 1, 2010, https://www.youtube.com/watch?v=SYU22NKsp2M 104 “Jenny Dang The Weaver: Fiddle Lesson,” https://www.youtube.com/watch?v=StOboC96AqM 105 “Bruce MacGregor 'Bowing : Triplets' - Fiddle Lesson,” YouTube video, 5:03, posted by "Bruce MacGregor," January 22, 2010, https://www.youtube.com/watch?v=FfwReZUXgAI 106 Farquha MacRae, “The Atholl Highlanders' Farewell to Loch Katrine/The Laird of Thrums/Jenny Dang the Weaver,” Tobaran Dualchais mp3, 3:16, June 1954, http://www.tobarandualchais.co.uk/fullrecord/79631/1 31  differentiate themselves. In an age where recordings are so widely available, the question of influence is complex and difficult to answer definitively, but a few observations can be made. Though Farquhar MacRae was a revered player in this style, he played only at local community social gatherings, and did not “perform” in concerts or recordings like the other artists.  The only available recordings of his performances were made for personal use and have been stored in archives.  For this reason, it seems unlikely that the other musicians would have heard his performances, meaning it is also unlikely they were influenced by his playing directly.  MacRae’s death in 2000 further supports this speculation.  Both Hanneke Cassel and Bruce MacGregor are popular artists who have toured extensively and released commercial recordings, so it is conceivable that Cameron and Blair have heard their playing, though I could not find definitive evidence for this.  Cameron and Blair are the two youngest musicians, and have not released any commercial recordings to date, so it is doubtful that Cassel and MacGregor are familiar with their playing.  Though previous studies have often focussed on Gaelic music in either Scotland or Cape Breton exclusively (as these are the two largest Gaelic communities in the world), I have elected to include recordings from both the United Kingdom and North America.  This was due both to the difficulty in finding appropriate recordings, and also because the accessibility of online recordings means that most of these musicians have likely heard (and thus been susceptible to influence from) fiddlers from around the world. Because different performers play the tune differently, with variations in melody and rhythm, there will be transcriptions for each.  In order to maintain maximal clarity in transcriptions, I omitted ornamentation (such as trills and turns).  In addition, most of the ornaments in these performances took place on quarter notes.  Since my analysis discusses 32  only subdivided beats, ornamented quarter notes do not have any bearing on the eighth notes which are used for the BUR and UBR values.107  The ornaments were omitted not only for clarity’s sake but also to adhere to the notational convention of this style, where ornamentation is almost never included.  The lack of ornamentation in notation of these tunes indicates that ornamentation is at the discretion of the performer.  This allows performers to individuate themselves partly by the kind of ornaments they use.  For example, both Farquhar MacRae and Hanneke Cassel seem to place embellishment on all notated quarter notes, either in the form of grace notes or upper neighbour figures.  Quarter notes occur on beats 1 and 3 only, meaning that Cassel’s ornamentation practice emphasizes a half note tactus.  This may help to counteract the downbeat displacement/backbeat effect created by the phenomenal accents on beat 2 (which I will discuss later).  In contrast, Macgregor typically embellishes only the third beat of m. 3, decorating the eighth note B with an upper neighbour C.  Like Cassel, this ornamentation may also emphasize the half-note tactus, but since Macgregor only embellishes one measure out of every four, this seems less likely.  It is possible that Macgregor’s ornament calls attention to the harmonic change which happens in measure 3 (moving from an implied D major harmony to an implied G major harmony).                                                           107 While other research such as Mats Johansson, dissertation, "Rhythm into Style: Studying Asymmetrical Grooves in Norwegian Folk Music," suggest a link between ornaments and microtimings, this avenue of investigation is beyond the scope of this project. 33   Applying a jazz methodology In jazz music, as mentioned above, expressive variations from even eighth-note rhythm, often known as “swing,” are considered essential to the style.  This is also true of the expressive variations in Gaelic fiddle music.   Even a first-time listener can distinguish wide variance in the microtimings of these five recordings.  The BUR and UBR ratios vary not only during a particular performance, but also across performances by different players, who employ different combinations of long-short and short-long.  This implies that if this music has a consistent metrical style, it would be more based upon how BUR and UBR change and develop across phrases, rather than a set ratio which is the same for all pairs of eighths. In reels, the typical tactus is a half note.  Investigating the BUR and UBR could determine if unevenness of division within the half note emphasizes the tactus as well.   As mentioned above, the eighth note division tends to be very uneven, but in order for this tune to be viable dance music, a steady pulse must be easily accessed by listeners/dancers.  It will be interesting to examine how a steady tactus is enforced while the divisions are varied and unpredictable.  Though dancers entrain to a half-note tactus, there is still a differentiation between beats 1 and 3.  Because the skip-change step takes a measure for a full cycle (a skip-change starting on the right foot followed by a skip-change starting on the left), beat 1 is reinforced as a metrical beginning for entrainment.  Though the skip-change 34  step is not the only step in Scottish Country Dancing, as the travelling step it is ubiquitous to every set dance and also occurs more frequently than any other step.108    For each recording of “Jenny Dang the Weaver,” I determined the timing of every attack, and the BUR and UBR for every pair of successive eighth notes.  The data are presented in the Appendix. Where the rhythm includes successive 16ths, as in the characteristic 16th-16th-eighth second-beat rhythm of the A section, the total duration of the 16ths is considered to be an eighth.  The purpose of this procedure was to identify any trends in the Beat-Upbeat ratio and Upbeat-Beat ratio, based on location in the measure or phrase.   Extrapolating from London’s theory that meters and entrainment are constructed partially through subdivision,109 I contend that the groove of this style is partially constructed by the subdivision of each beat and by expectations that beat-level trends create in listeners.  Further, I contend that underlying microtiming trends also affect the groove, based on how these trends are realized or subverted throughout the performance.110  It may be that the underlying microtiming trends of each beat evoke a movement response in the listener, based on how these trends are realized or subverted throughout the performance. To make this analysis as accurate as possible, the onsets of the events must be located precisely. The software package called Sonic Visualizer was used to determine the                                                           108 For more information on Scottish Country Dancing steps, see Jean Milligan, Won't You Join the Dance: Manual of Scottish Country Dancing, (Paterson's Publications: London, 1982). 109 London, Hearing in Time, 35. 110 These assumptions are informed by my own experience (as a performer, dancer, and listener), and by the anecdotal evidence cited on p. 19 (in footnotes 67–69).  While these views seem to be commonly held in the theoretical literature on jazz and other groove-based musics, there has been little research in this area by music psychologists.  The existing research does not establish a correlation between microtimings and groove, but in my belief, these studies do not rule out such a correlation, as they are based on synthetic and highly repetitive microtiming structures, rather than microtimings created by living performers.  Fruhauf et al., "Music on the timing grid,” 246 – 260.  Davies et al., "The Effect of Microtiming Deviations on the Perception of Groove.” 35  precise timing of each musical event.  This program was originally designed to facilitate research at the Centre for Digital Music at Queen Mary University.111  It has become popular as a tool for music analysis, used by scholars such as Nicholas Cook112 and Alan Dodson.113   Its original applications and much of its use since (such as Chris Sapp’s addition of the Mazurka plugins) have been focussed mainly on piano music, possibly because the program’s Onset Detection Algorithm works best on music with precise percussive attacks.114  However, because the pitch onsets in these fiddle recordings are not as precise as those on a percussion instrument, this algorithm cannot correctly detect most of the onsets, so another method was needed to supplement it.  A spectrogram of each recording (produced by another algorithm of Sonic Visualizer) combined with slowing down the recordings facilitated this manual placement.  The onsets were determined and marked by ear, and then verified by looking at the spectrogram and sound wave (which often showed a spike at pitch changes or attacks).  Once all onsets were determined, the tune was played back at a very slow speed to confirm that all onsets were correct.  The musical events found by the Onset Detection Algorithm were also verified manually using this strategy.  For the Farquhar MacRae recording, the beats (and subdivisions) themselves were also verified                                                           111 Chris Cannam et al., "The Sonic Visualiser: A visualisation Platform for Semantic Descriptors from Musical Signals," in Proceedings of the 7th International Conference on Music Information Retrieval (ISMIR-06), 2006. 112 Nicholas Cook and Daniel Leech-Wilkonson, “A Musicologist's Guide to Sonic Visualiser,” AHRC Research Centre for the History and Analysis of Recorded Music, last modified 2009, accessed May 3, 2014, http://www.charm.rhul.ac.uk/analysing/p9_1.html 113 Alan Dodson, "Research Note: Expressive Asynchrony in a Recording of Chopin's Prelude No. 6 in B Minor by Vladimir de Pachmann," Music Theory Spectrum 33, no. 1 (Spring 2011): 59 - 64. 114 Though there is a precedence for applying this technology to non-percussive instruments, in Daniel Leech-Wilkinson, The Changing Sound of Music: Approaches to Studying Recorded Musical Performance (London: CHARM, 2009), Chapter 5, www.charm.rhul.ac.uk/studies/chapters/chap5.html 36  manually in order to determine the quarter note pulse for comparison to a mathematical model (described in more detail later on).   Once all the musical events had been accounted for, the IOI (interonset interval) of each musical event was determined. These durations were rounded to the nearest thousandth of a second (millisecond, abbreviated as “ms”) and were used to calculate the BUR values.   After calculating BUR and UBR values, there were several methodological options. Other theorists, like Benadon, use this kind of information to calculate changes from beat to beat.   Butterfield discusses changes in BUR/UBR based on different instrument interactions or structural changes.  For my purposes, I decided to group the BUR and UBR based on their occurrence in the measure and section.  For example, I compared all BUR values for beat 1 of the A section, looking for overall trends in the data as well as outlying data points. The rhythmic character of this reel seems to lend itself to comparing BUR/UBR trends based on their occurrence in the measure, because whole measures of rhythms are repeated.  For example, the first eight measures of “Jenny Dang the Weaver” as played by Jim Blair can be represented as follows:  Every measure is conceived as having a very similar rhythm characterized by two sixteenths and an eighth on beat 2, except for the fourth and eighth measures, which are a 37  variant on the rhythm.  It seems logical to compare the BUR of each beat115 with the corresponding beat in other measures of the same section as they are the same component of one rhythmic idea.  The pitch contour of measures 1 through 3 is also similar, but in performance these measures are exciting rather than monotonous.  Microtiming analysis can show whether the musicians change their performances of the rhythm, in ways shown by BUR/UBR, and direct the music forward so that it doesn’t sound repetitive or static.116  Comparing all beat 2s, for example (that is, the second quarter note pulse of each measure, which here acts as a sort of backbeat), could shed light on how motional energy is directed a metrical level greater than the tactus – in this case, the whole-note, measure level.   Such analysis may also help identify how these songs’ rhythms are affected by their performative context. Reels are often – though not always – preceded by a strathspey.  Whereas reels are notated as series of equal eighth notes, strathspeys are characterized by an explicitly notated long-short division of the quarter note, typically notated as a dotted eighth followed by a  sixteenth.  A reel directly preceded by a strathspey might be expected to carry over hints of this division, maintaining a long-short division of the quarter note, though perhaps a slightly more even division than that implied by the strathspey’s notation.    After the BUR and UBR values were calculated, they were graphed on a scatter plot, on which the X axis represents the beat number, and the Y axis represents the BUR or UBR value for events on a particular beat.  Means and standard deviations for each beat group were used to help understand the data.  The mean identifies and represents the overall                                                           115 For clarity’s sake, ‘beat’ will refer to the quarter note pulse, and ‘tactus’ will refer to the half note pulse, which would typically be the entrained pulse when performed at a dancing tempo. 116 Dynamic accents could also add interest to the repetitive melodic and rhythmic material, but this is beyond the scope of this study. 38  trend for each beat, and the standard deviation was used to measure the amount of variation within the data.  This statistical analysis does assume that all measures are independent, but a comparison in this fashion is justified because of the aforementioned similarity of the measures (many measures are rhythmically identical to the other measures in the same section).  This creates grouping parallelism and means that comparison on a measure-to-measure basis can identify statistical trends that correlate to musical sensations.  However, BUR and UBR are ratios, and the difference between 0.25 and 1 is the same as that between 1 and 4 in the ratio scale but not in the absolute value. This means that a BUR of .25 is the same durational proportion as a BUR of 4 (that is, both involve a duration that is a quarter of the other duration). So in order to make trends visually evident, these two values should be represented on a graph as the same distance from an equal BUR ratio of 1. On a linear scale, this is not possible, but if these ratios are converted into logarithms base 10, 4 becomes .60206, and .25 becomes -.60206. These values are indeed equidistant from the logarithm of an equal division BUR, which converts to 0 as a logarithm. Converting all the BUR and UBR values into logarithms made the trends much easier to identify. Strictly speaking, one cannot perceive the BUR of a pair of eighth notes until the onset of the eighth note that follows them, which determines the duration of the second eighth in the pair. However, for the sake of visual clarity, the X-axis position of each BUR is plotted on the (off) beat on which the onset of the second eighth in each pair occurred.  For example, the BUR of the first two eighth notes in a measure is plotted on the graph at the X value 1.5, as pictured below.  Similarly, the UBR were graphed on the onset of the second 39  note in the set, therefore being graphed on the beats.  This means that a UBR plotted on beat 1 refers to the eighth on beat 1 and the preceding eighth note on beat 4.5.  Similarly, a UBR plotted on beat 1 refers to the eighths on beat 1 and beat 4.5.  The arrows below indicate the X value for each pair of eighths.    40  Chapter 3: Results and Analysis  Compilations of data presented in this way can seem somewhat divorced from the music and a listener’s experience of it.  Some kind of interpretation is necessary.  Even the raw microtiming data, however, illuminates some features of the music.  The measure lengths and beat lengths are quite variable, as are the durations that subdivide the beat.  This seems at odds with typical notation for this tune, which implies nothing but even duple subdivisions of the bar and beat, but Hasty’s theory of metrical projection explains how a listener may perceive regularity even if absolute evenness of duration does not occur.117  Like Keil, Butterfield, and other jazz theorists, I contend that the purpose of microtiming variations (in particular, uneven subdivisions) is to affect the listener’s perception of the groove.  In order to understand these variations in more detail, it will be helpful to examine the timing data and observe trends within individual recordings and across the whole corpus.  This information will help to sharpen our awareness of groove-generative rhythmic details in the recordings.  Generic observations Though there is a great deal of variation between performances, certain trends seem clear across all my samples of the genre (see Figures 1 through 23 below for graphed results).  Two trends observable in the first recordings are that the third beat always has the smallest BUR variance and usually also has the lowest median BUR value.  This means that the two eighths during that beat are most consistent in their ratio, and also tend to be                                                           117 Hasty states that “B can be felt as a reproduction of A’s duration without being ‘precisely’ equal, measured by the clock.”  Hasty, Meter as Rhythm, 86. 41  more consistently even than the eighths during the other beats.  I believe that the eighths need to be perceived, on the whole, as relatively even so that listeners entrain based on an eighth note subdivision rather than a triplet or dotted subdivision of the quarter note. A relatively even third beat helps establish this regularity, and therefore helps distinguish the reel from the following strathspey, where dotted eighths become the norm.  The skip-change step, when danced with a reel is danced evenly, whereas when used for a strathspey, the step, like the overall groove, is very unevenly divided.  Entraining to even eighths allows the skip-change step to be divided evenly and more smoothly. Another reason for this evenness on beat 3 may be to contrast another trend that is observable across most performances of the reel. During the second beat (timepoints 2 and 2.5) the UBR and BUR consistently have a wide range of values; in fact, in many cases this is when the widest deviation from the mean occurs.  I believe this is due to the characteristic rhythm (Cassel’s “cut,” Macgregor’s “triplet”) that consistently recurs on the second beat in the A section.  Though it is commonly notated as two sixteenths and an eighth, , in reality the two sixteenths are often played as short as possible (usually using a ricochet technique), and also with a strong dynamic accent.  They are so brief as to be perceived more as a forceful articulation of the following “offbeat eighth” rather than as distinct musical events, placing a strong durational accent on the second eighth of beat 2.  Beat 2 corresponds with a sweeping step in traditional Scottish country set dances.  A slightly longer eighth on beat 2.5 prepares the arrival of beat 3 (marked in the dancing by a definitive footfall), allowing the dancers to make a more emphatic step, thus accenting beat 3, the next tactus after beat 1. 42  Although most of the beat 2s in Section A contain this figure, some of them contain a more even division of the beat with two eighth notes.  118  This accounts for the wide variation in the data points for this beat. The fairly predictable reversion to even eighths on beat 3 after the unpredictable beat 2 perhaps helps to mark beat 3 and support entrainment to the half note pulse. Depending on the performer, the variance on beat 2 does not occur consistently in the B section.  The Cassel recording, for example, has a much tighter spread of both BUR and UBR in the B section, meaning that her eighth notes are relatively equal.  However in the Blair recording, the BUR/UBR values vary widely in both the A and B sections.  It is possible that Blair’s entrainment of the tune’s groove includes the unevenness of beat 2, and thus the phenomenon is present throughout the tune. This is in keeping with Justin London’s Many Meters Hypothesis, which posits that meters are distinguished not only by tempo and the ordering and subdivision of beats, but that entrainment to a certain meter may also include the meter’s trends in expressive variation.119  In those terms, a more uneven second beat followed by a more equal third beat could be considered to be a characteristic of this reel’s meter in Blair’s conception.  Out of the other performers, MacRae is the only other musician to demonstrate this widely spread BUR on beat 2 of the B section.  It is possible this continuation of a highly irregular beat 2 into the B section is a regional difference, for it appears in the performances of MacRae, a Scotsman and native Gaelic speaker, and of Blair, who (although a US citizen originally) has lived in Scotland for                                                           118 MacRae plays two eighths during the second beat.  He is a fluent Gaelic speaker, so perhaps he is adhering to the vocal version of this port-a-beul, in which the A section, in order to accommodate the Gaelic syllables, features straight eighth notes.  There is, however, a strong dynamic accent on the first of the eighths, reinforcing the notion that the second beat is meant to be emphasized. 119 London, Hearing in Time, 141. 43  many years.  The North American musicians Cassel and Cameron have a less varied beat 2 BUR in the B Section.120  However, a greater sample size, including more musicians, would be needed to substantiate whether such a regional difference exists. Whether it constitutes a groove or not, this trend may also be characterized in terms of metrical dissonance.  To the extent that the shortened sixteenths on beat 2 during in the A section figure are heard as articulation for the eighth note on beat 2.5, the rhythm may be heard as a quarter note with a sort of fluttertongued attack.  Since it follows shorter notes on beat 1, the onset of the perceived quarter note takes an agogic accent, and suggests the perception of beat 2 as a displaced downbeat.  The common manner of playing this figure – with a ricochet technique – also adds a dynamic accent, further supporting the perception that the  figure occurs on a downbeat.  This ambiguity continues into the B section, where the false downbeat receives a registral accent.  First-time listeners or listeners unfamiliar with the genre may experience this as the actual downbeat.   However, when this reel is performed in a dance context, any ambiguity will vanish, because the dance steps clearly follow the notated downbeat.  In this situation, the phenomenal accents on beat 2 can function as a sort of backbeat—in Zbikowski’s conception, a secondary level of meter designed to move the body.121  Butterfield posits that a dynamic accent on the second beat presents listeners with a perceptual challenge by disputing the strong-weak grouping listeners expect from two successive beats.  He suggests that listeners will focus their attention forward, waiting for their confusion to be                                                           120 Bruce MacGregor, the other Scottish musician, plays only the A section in his performance, so it is not possible to see if this trend exists in his rendition. 121 Zbikowski, “Modelling the Groove” 286. 44  remedied.122  This would account for the strong sense of forward momentum created by this rhythm. It is also worth noting that when each section is repeated, the BUR values for each beat tend to have a smaller spread on the repeat than they do on the first iteration.  This means that the second time through, the BUR values are more consistent (though not necessarily more even).   Outliers and individual style While these general observations help characterize some distinctive qualities of the puirt-a-beul reel, much insight about the genre can be gained by studying each performance individually and comparing it to the others. One possible term of comparison is suggested by Benadon’s finding that jazz performers have an individual approach to beat subdivision.123  The musical style of Gaelic culture has developed diversely due to its itinerant history, so it is reasonable to expect that the Gaelic fiddlers may also be distinguished by their ways of subdividing the beat.  This distinctiveness can be evident either in trends, that is, in the average properties of many instances of a rhythm, or in data points that do not conform to the rest. These data points will be referred to as outliers. An outlier is a data point that is a significant or abnormal distance from the rest of the values. 124                                                            122 Butterfield, “The Power of Anacrusis” 123 Benadon, “Slicing the Beat,” 74. 124 Jiawei Han and Micheline Kamber, Data Mining: Concepts and Techniques (Waltham, MA: Elsevier, 2012), 544. 45  What would be considered a significant or abnormal distance for these durational patterns? Butterfield cites data by Gert ten Hoopen et al. suggesting that the just noticeable difference (JND) between IOIs (in tempos between 83 and 250 bpm) is about 4.5%,125 equivalent to a BUR differential of ±0.045.  However, ten Hoopen’s JND estimate is based on laboratory conditions and may therefore be too low to be ecologically valid in the case of complex musical stimuli outside of the lab. Butterfield estimates that, in his own experience with jazz recordings, a BUR differential in the range of ±0.1–0.2 (equivalent to ±0.04–0.08 for BURs on a logarithmic scale) is required for a noticeable difference.126   For the purposes of this project, outliers are determined using standard deviation from the mean logarithmic BUR value for each beat.  Error bars in the figures indicate 1.5 units of standard deviation above and below the mean.  A data point falling outside of the error bars is considered an outlier as long as the distance from its nearest neighbor is at least 0.04.  This method prevents data points from being misidentified as outliers if they are close to the mean but far from their nearest neighbor, or if they belong to a cluster of points far from the mean.127  This results in all outliers being well over 20% (the outer limit of Butterfield’s estimate of JND) away from the mean, which expresses the trend for each set of data.  Using a purely numerical method for identifying outliers (rather than identifying by ear) ensures that the outliers are selected based just on the microtiming quality, rather than being influenced by dynamics or other elements.  This numerical method is also easier to transfer to different repertories or genres.                                                            125 Gert ten Hoopen et al, "The Detection of Anisochrony in Monaural and Interaural Sound Sequences" Perception & Psychophysics 56, no. 1 (January 1994): 120. 126 Butterfield, “Why Do Jazz Musicians Swing Their Eighth Notes?” 8.   127 It is also worth noting that many of these clusters or pairs of datapoints outside the error bar are from the first few or last few measures where tempo is inconsistent. 46  For example, for beat 1 of the A section of Cameron’s performance, the BUR mean is 0.080899 and the standard deviation is 0.133808, so 1.5SD is greater than 20% of the mean.  This method also ensured that outliers falling close to the mean but far away from the nearest data points were not misidentified as outliers.  Due to Butterfield’s estimate of JND, any outlier which is greater than 1.5 SD from the mean but which has a neighbouring data point closer than 10% of its absolute value was not identified as an outlier.  All calculations were computed using the logarithm values. As mentioned earlier, converting the data into logarithms makes the trends more visually evident, which in turn facilitates the identifying of outliers.  Outliers can be an indicator of an exceptional moment in the music. A data point that deviates significantly from the others would likely stand out to a listener, and be used for particular musical effect by a performer.  Outliers will be examined for their formal implications, as well as their location in the phrase, their deviation from the previously established metrical trend, and any possible perceptual effects on the listener arising from these factors.  Some outliers may not have any obvious structural or musical impacts, so I will focus on outliers that seem either to correlate to form or a structural feature, or occur consistently and therefore may be part of the performer’s individual style.   Some outliers occur in the first or last measure.  They can be attributed to the fact that the tune is just beginning and therefore the tempo is still being established by the performer, so it would be plausible to discount them as being musically insignificant.  Similarly, outliers which occur in the last measure are likely caused by the dissolution of tempo as the tune comes to a close.  Outliers will be discussed chronologically, in order to the guide the reader through the listener’s experience of each performance. 47   Performance: Neil Cameron The recording used for analysis is available at: https://www.youtube.com/watch?v=0wIFDj6C1BI starting at 2:24.  Neil Cameron seems like a good first case study as he has lived and studied fiddle in both Nova Scotia and Scotland, the two main Gaelic communities.  As he has resided in both of the world’s most vibrant Gaelic communities, Cameron may play with a general Gaelic style, rather than with more regionally specifically stylistic conventions.   Figure 1 is a transcription of Cameron’s rendition of this tune. It is particularly conducive to BUR/UBR analysis, as it presents a nearly constant stream of eighth notes with very few quarter notes.  Other performers tend to place a quarter note at the end of each A and B phrase (often on beat 3) and the beginning of each B phrase (usually beat 1), but Cameron does not.  His lack of quarter notes may help the listener engage even more firmly with the eighth-note microtimings.  Cameron also includes the characteristic A section figure at the end of the first B phrase.  This helps provide cohesion between sections. For clarity’s sake, the transcription is marked with red circles to indicate BUR outliers, and blue circles to indicate UBR outliers.  Outliers which are considered musically insignificant (due to their placement in the first or last measure) will not be indicated on the score.  The mean of each beat is indicated on the graphs in red.       48  FIGURE 1: TRANSCRIPTION      49  FIGURE 2: log(BUR) in Section A   FIGURE 3: log(UBR) in Section A   FIGURE 4: log(BUR) in Section B  FIGURE 5: log(UBR) in Section B  A section  Analysis of overall trends in the BUR and UBR values can illuminate stylistic elements in Cameron’s performance.  Outliers can demonstrate how Cameron's microtimings engage with the listener at certain structural moments.  Outliers Y3 and W2 take place in the first two measures as tempo is still being established, and can thus be discounted. Disregarding Outlier Y3, the UBRs on beat 2 actually have the smallest range when compared to the other beats.  This is in sharp contrast to the other performances, which typically have the largest range of values on beat 2.  In essence, this means that in Cameron’s performance, the on-beat eighth of beat 2 and the offbeat eighth of beat 1 are 50  fairly consistent across measures.  This gives Cameron a slightly different groove than the other musicians, as it reduces some of the durational accent on beat 2 created (in the other performances) by an extremely short “eighth”. The mean of the BURs of beat 2 in the A section is less than the BUR means of other beats.  This implies that the first “eighth” of beat 2 is, on average, shorter than the second, consistent with the fact, as discussed above, that in the A section, that timespan consist of two quick “sixteenths.”  Whereas the other three beats have mostly positive UBRs, they are mostly negative on beat 2, which could create a groove similar to the ostinato notated below:  The different division of beat 2, combined with the registral accent and distinctive sixteenth-note figure, gives Cameron’s performance a particularly strong downbeat displacement/backbeat effect (as discussed in Generic Observations). BUR outlier Y2 takes place in measure 3 (first time) and greatly exaggerates the short-long division of the second beat.  As this is the beginning of the tune, it might serve the purpose of orienting the listener to the groove by making it more audible.  Z3 occurs in measure 4 (the first time) and designates that the last eighth of beat 3 is shorter than the first eighth of beat 4.  This is not surprising given that this measure adheres to the established groove notated above.  However the extremity of Z3 indicates that this groove may be exaggerated (more extreme) in m. 4.  This may help to establish the newly established groove in the mind of the listener before the A phrase is repeated.  The structural boundary of the end of the first A phrase is further delineated by the first 51  appearance of the higher octave A on beat 3.5.  Z3 is one of only two UBR outliers in the A section.   Although several data points fall outside the error bars on this graph, those on beats 1 and 3 fall within 10% of each other, discounting them as outliers based on Butterfield’s estimate of JND.  Z3 (like Y3, the other UBR outlier) falls not only outside 1.5 standard deviation, but also exists more than 10% away from its nearest neighbouring data point. Z2 takes place in measure 1 (second time), the first measure of the repeat of A. This is obviously a significant structural moment, and Cameron differentiates this measure from the others by deviating significantly from his pre-established groove for the A section (notated above).  Not only does beat 3 have a strong short-long division (Outlier Z2), but beat 4 is also divided short-long, and the expected short-long division of beat 2 is replaced by an equal subdivision of the beat.  The purpose of these subversions of the A section groove is two-fold; firstly, the deviation from the norm helps the listener to take notice of this important structural boundary, and secondly, because the groove is already established at this point, Cameron can “play” with the groove without disorienting the listener, allowing him to provide some variation during the literal repeat of pitch material. BUR outlier X2 takes place in measure 7 (the second time), and is particularly notable because this is the last occurrence of the characteristic sixteenth-sixteenth-eighth figure.  Since this figure was essential to the groove of the A section, it is possible that Cameron is unconsciously exaggerating it—that is, making the first eighth of the beat even shorter in relation to the second eighth than it usually is—as the final A section comes to a close.   52  V2 occurs in measure 8 (second time), which is the last measure of the last A section.  V2 represents a negative– in other words, a short-long – division of beat 1.  Beat 2 is also short-long, and beat 3 has a strong long-short division.  I believe V2, in conjunction with the ratios that follow, is meant to emphasize the durational accent on beat 3, providing a slight sense of pause or rest to mark the end of the final A section.  Playing a short-long division on beats 1 and 2 makes the long-short division of beat 3 stand out in contrast.  Beat 3 is not only the last half-note tactus of the A section, but is also the beginning of the last skip-change step of each cycle, making it a logical place to imbue with a sense of pause to underline the phrase ending. Together, these outliers work together to engage the listener throughout the A section.  The groove begins with Y2, is confirmed with Z3, and is then altered in Z2 to mark a structural boundary. The groove is reasserted in X2 and once again altered with V2 to mark the end of the A section as a whole. B Section Figures 4 and 5 show, respectively, the BUR and UBR values for the B section of Cameron’s performance. Across all beats, the majority of the BURs in this section are positive, which indicates a long-short division of the beat.  This represents a somewhat consistent division of the beat which is similar to swing in jazz.  This quasi-swung groove of the B section is less even than the notated straight eighth notes, but is still not as exaggerated as in other dance forms of this style, such as the strathspey.  This gives the B section consistency with the A section’s groove, though it is worth noting that the B section contains more negative BUR values, so the long-short groove is not as omnipresent.  Because the general travelling step, the skip-change step, is used throughout a dance, 53  regardless of the section or structural area, creating cohesion between musical sections makes sense. While the BURs remain positive, their means progressively decrease, indicating that the evenness of the eighth notes tends to increase as the measure proceeds, with the next measure beginning the cycle again from least even to most even.  While the eighth notes are not continuously even in the way that the notation would suggest, I believe this trend maintains the reel groove as a comparatively more even (less swung) subdivision than that of other dance forms which may precede it.  This helps maintain the reel’s identity as distinct from other tunes it may be paired with. Outlier X4 helps to introduce the new “swung” beat division.  Outlier X4 takes place on beat 4 of m. 10 (the second measure of the first occurrence of the B section), and represents a notably inequal long-short division of the beat.  As mentioned previously, a long-short BUR division is the overall trend for the B section.  By hearing an exaggeration of this ratio in the very first measure, the listener already begins to be oriented to the new groove.   Outlier Y5 takes place on the last eighth of measure 10 and the downbeat of measure 11.  The location of this outlier does not seem to be particularly significant structurally, so it is unclear what effect this might have.  Outlier Y4 occurs in measure 11, the third measure of the first B section in this performance.  The new “swung” groove is still being established at this point, and Y4 does not conform to it.  This may be unintentional on the part of the performer, who may still be “switching gears” from Section A, where beat 4 tends to be negative more than positive.  However it may also be a more gradual transition between grooves, so as not to jar the listener.  Outlier Z5 occurs in m. 11 54  (first time), and results from the offbeat eighth of beat 3 being much shorter than the eighth note on beat 4.  This may be to facilitate the skip-change step, which is not only used for reels, but also for other dance forms such as strathspeys, which have an extremely unequal division of the beat.  This means that the skip-change step must be easily danced in forms with dotted or double dotted rhythms.   BUR outlier W4 occurs in m. 15 (the first time).  It is an exaggeration of how this swing occurs on beat 2, so perhaps Cameron performs it to emphasize this new groove as the first iteration of the B section progresses.   As in the A section, a few outliers buck the overall trend of long-short divisions.  Outlier V4 takes place in m. 9 (second time) – in other words, the first measure of the last B section – and indicates a slightly unequal short-long division of beat 1.  Though subtle, this short-long division would catch the listener’s attention as the previous eight beats (and overall trend) have strong long-short subdivisions.  The measure overall is the exact opposite of the A trend notated on page 48.  This reversal of the established groove clearly marks the beginning of the last B section. Outlier Z4 (which takes place in measure 12, second time) also subverts the normal B section eighth note pattern of long-short, and in fact, it is the lowest data point in the entire graph.  This means its division of the beat as short-long is particularly deviant from the previously established groove.  I believe it occurs in order to draw the listener’s attentional energy, so that the listener is fully engaged for the following measure, which begins the last phrase in the performance as a whole.  Another notable feature of measure 28, the A section’s characteristic  figure, serves as an indication that an important structural boundary is approaching.  55  Outlier X5 in Figure 5 refers to the ratio between the last eighth of measure 12 and the downbeat of measure 13 (second time).  The positive value indicates that, in this case, the last eighth of measure 12 is longer than the downbeat of 13.  This provides a very slight stretching effect just before the downbeat that initiates the last phrase of the performance (measure 13, second time).    Performance: Jim Blair The recording used for analysis can be found here: https://myspace.com/jimnblair/video/jenny-dang-the-weaver.../50870110  Jim Blair is an amateur fiddler who studied extensively in Scotland and briefly in the United States, suggesting that his style, like Cameron’s, may draw influence from the European and North American Gaelic communities.  His performance is the longest of the five, and it repeats the tune three times, rather than just two.  Blair also distributes his quarter notes differently than the other performers, using quarter notes for beat 4 at phrase endings, whereas most of the other performers have eighth notes at this formal boundary, leading into the next phrase.  This gives Blair’s performance a unique feature of having two successive quarter notes at every phrase ending (in this case, every four measures).  This demonstrates the variability of the tune, especially when contrasted with other performances such as Macgregor’s, which has no quarter note values.  Blair also begins the B section with straight eighth notes, whereas other performers tend to begin the B phrase with a quarter note on beat 1.  Other performers, like Cassel, play a quarter note on the third beat of measure 10.  However it seems that Blair’s B section is characterized by 56  only running eighth notes, until the last measure where the  figure from the A section returns.    Blair also plays the tune with a noticeable acceleration throughout, particularly in the B section. This may be part of his individual stylistic interpretation of the tune. Some of the outliers may be due to this quirk, but since BUR and UBR are ratios of successive eighths, the tempo shifts would have to be extremely abrupt to affect them. FIGURE 6: Transcription   57  FIGURE 7: log(BUR) in Section A  FIGURE 8: log(UBR) in Section A   FIGURE 9: log(BUR) in Section B   FIGURE 10: log(UBR) in Section   Outliers Y7, Z7, W8, Y8, and Z8 occur in the first measure and can therefore be discounted. Outliers X9 and X10 occur in the last measure of the performance and can be discounted due to the final ritard.  Outlier Z9 occurs on beat 3 of the penultimate measure which is after the tempo has begun to decrease significantly. A Section As discussed in “Generic observations,” there seems to be a trend where beat 2 has the largest BUR range.  This is due to the characteristic  figure which – despite its notation – is an extremely uneven division of the beat.  As previously mentioned, the extremes of this figure combined with the relative evenness of the beat 2s that do not 58  include this figure result in a wide range of BUR values.  In the A section, beat 3 has the smallest BUR variance.  In part, this is because Blair sometimes places a quarter note on beat 3, so there are fewer BURs for this beat.  Disregarding outliers Y7, Y8, and W8, another trend is evident: beat 4 has the largest UBR range (see the last column of Figure 8), meaning that the ratio of the last eighth in the measure to the first eighth of the next measure is inconsistent.  This reflects the wide variation in the duration of the last eighth note of the measure.128   This variation in length seems dependant on its anacrustic function, and how many levels of anacrustic function fall on beat 4 (based on Hasty’s theory of projection).  For example, the eighth note which ends m. 1 is 139 ms, whereas the last eighth note of m. 2 is 197 ms.  The latter eighth note is not only an anacrusis into the next measure, but also into the next two bar melodic unit.  A two bar melodic unit is longer than the single bar, and thus, the anacrusis can be longer as well.  Mm. 1 – 4, Jim Blair X7 occurs in m. 5, the first measure of the second A phrase. This is the second phrase in the whole performance and the first phrase where tempo has been fully established.  The low BUR of X7 indicates that the off-beat eighth note of beat 1 is longer than the downbeat eighth note.  This helps to exaggerate the  figure, as a long eighth note preceding it serves to emphasize the brevity of the sixteenths.  The descending F# and E in m. 4 hint at a dominant chord, which, if resolved to the tonic, could give a strong sense of pause.                                                            128 The eighth note on the downbeat is also variant, but the last eighth of the measure has a wider range of durations. 59  However the downbeat D is short, only 116 ms, and quickly moves back to the dominant, meaning that the effect is more like a half cadence of an antecedent phrase, providing some closure but also suggesting there is a consequent phrase to come. W7 and X8 both occur in m. 8 (third time), which is the last measure of the last A section.  W7 indicates that the second eighth of beat 1 is shorter than the first.  X8 demonstrates that the first eighth of beat 2 is longer than the off-beat of beat 1.  This could be caused by a short offbeat on beat 1, but a look at the microtimings indicates otherwise.  In fact, beat 2 is simply longer than beat 1, lasting 302 ms compared with 244 ms.  This durational accent continues the feeling of backbeat, even though the  motive is not present, providing a final confirmation of the A section groove before moving on to the last B section. Most other performers (with the exception of MacGregor) have mostly positive BUR values for beat 3 of the A section.  However, Blair has mainly negative values for this beat.  This indicates that Blair plays the repeated pitch A4 differently than the other performers: he makes the last A4, on beat 3, very short and then moves on quickly to the following G4.  Perhaps he perceives the   figure as including the eighth note A which follows it, and this colours his interpretation of this motive. B Section: In Blair’s performance of the B section, the second beats have the largest range of BURs.  This may be intended as a continuation of the groove from the A section, where beat 2 had the most often unequal division of the beat.  By contrast, his fourth beats have the smallest range of BURs, demonstrating that he divides beat 4 more evenly and consistently 60  than the other beats.  The evenness of beat 4 results in more positive UBRs on beat 1, which is discussed below. In the B section, the UBRs for beat 1 are almost all positive.  This means that the eighth note on beat 4.5 is longer than the eighth note on the downbeat of the next measure.  In contrast, the UBRs for beats 2, 3, and 4 are mostly negative.  This indicates that on beats 2, 3, and 4, the eighth note on the downbeat is longer than the eighth note that precedes it.  This sort of UBR pattern (and the corresponding pattern of mostly positive BURs for these beats) could be heard almost as a swung rhythm, in which the short notes provide an anacrustic function, leading towards the next beat129.  This propels the B section forward, giving a strong sense of momentum.  The pitch material, which gradually ascends, has a similar effect.  The UBR trend for beat 1 is particularly noteworthy, as it subverts the trend of the other beats.  This draws attention to beat 1, or at least makes a listener pay closer attention around the downbeat, as their expectation of UBR has been subverted.  Differentiating beat 1 from the others also helps the listener to hear each new measure as a new cycle, which may be particularly useful for dancers, whose skip-change step also begins a new cycle on beat 1.  The downbeat is especially important in Blair’s performance, as he accelerates throughout the tune (though particularly throughout the B section).  A Tempo Detection Algorithm on Sonic Visualizer indicated that he tends to implement a new tempo on the downbeats in the B section, so this extra emphasis on beat 1 helps dancers and listeners alike keep up with the quickening pace. In addition, the BUR values for beat 4 are mainly negative, which further indicates that the last eighth note of each measure tends to be longer.  This could help dancers and                                                           129 Butterfield, “The Power of Anacrusis.” 61  listeners alike find the downbeat.  This is especially pronounced in outliers V10 and W10 occur in measure 10 and 14 respectively.  Both are outliers on beat 1 and occur in the second measure of the B phrase.  In these cases, beat 4 not only has a long off-beat eighth, but as a whole tends to be longer than other beats.  This could give dancers more time to complete their step cycle and arrive on the downbeat together.   Outlier W9 and Outlier Y9 occur in measure 12 and measure 16, respectively, when the  figure recurs that is usually associated with the A section.  As previously noted, this figure (despite its notation as two sixteenths and an eighth note) is typically played as a very uneven division of the beat.  Because this is an A section figure, its presence in the B section is particularly noteworthy and is therefore emphasized in performance.  This emphasis is achieved by also borrowing the uneven BUR associated with the figure in the A section.  Because the B section has no other such BUR on beat 2, these two outliers stand out.  It is also worth noting that these figures both occur at the end of a four-bar phrase, and may be used as a way to mark the phrase ending for the listener while providing a link to the A section. Section B’s UBR Outlier Y10 occurs on beat 3 of the third repeat of measure 9.  Measure 9 is the first measure of B.  This outlier represents a division of the time in which the eighth note on beat 3.5 is much shorter in relation to the eighth directly on beat 4.  Section B’s Outlier Z10 occurs in m. 13, which is also the first measure of the B phrase.  This outlier represents a division of time in which the eighth note on beat 2.5 is much shorter in relation to the eighth directly on beat 3.  The musical significance of these outliers is unclear, but they may occur simply to add variation to a repetitive phrase cycle. 62  Performance: Hanneke Cassel The recording used for analysis can be found at: https://www.youtube.com/watch?v=SYU22NKsp2M  Hanneke Cassel is perhaps the most widely heard of the five performers considered here.  With a discography of fourteen titles, and acclaim not only as a solo performer but also as a member of several ensembles,130 she is a familiar voice in the traditional music scene.  It is very plausible that other performers, such as Blair and Cameron, have heard Cassel’s playing, and been influenced by it.   In Cassel’s rendition, the tune’s A section typically has a quarter note on beat 3 of every second measure, with the B section continuing this trend and adding quarter notes to the first beat of each B phrase.  But additionally, in the aforementioned Fiddle Video tutorial,131 Cassel cites an accompaniment accent pattern of 3+3+2 (below) as an influence in her reel interpretations. Despite her discussion of this pattern in the video, Cassel’s performance does not seem to strongly incorporate this figure.  Upon examination of the loudness envelope in Sonic Visualizer, it seems possible that she suggests this pattern in her playing of the last measure of each four-bar phrase, but the accents do not differ much in volume from the non-accented notes.  There are also hints of this pattern in her overall performance of the B section, but in the A section the regular appearance of the  figure on the second beat subverts the 3+3+2 accent pattern.  All the BUR values on beat 1 and 4 are positive, meaning that the eighth notes on beats 1.5 and 4.5 function as anacruses.  This is not so surprising for beat 4, but the                                                           130 “Hanneke Cassel Biography,” Hanneke Cassel Official Website, last modified December 2013, April 16, 2014, http://www.hannekecassel.com/bio.html  131 “Reel Groove: Scottish Fiddle Technique Tutorial,” YouTube video, 4:57, posted by "FIDDLEVIDEO," August 24, 2014, https://www.youtube.com/watch?v=EBC1pQawfy4 63  anacrusis on the off-beat of 1 might reinforce a feeling of beat 2 as a beginning (as previously discussed). FIGURE 11: Transcription    FIGURE 12: log(BUR) in Section A   FIGURE 13: log(UBR) in Section A   64   FIGURE 14: log(BUR) in Section B   FIGURE 15: log(UBR) in Section B   Only two outliers in Cassel’s performance can be discounted due to their placement.  Outliers Z14 and Y15 occur on the last beat of the last measure, and are therefore due to the decrease in tempo as the performance comes to a close. Overall, the UBRs yield many more even subdivisions than the BURs in this performance, particularly on beats 2 and 3.  Many of the UBRs fall within ±0.8 (the boundary for JND when expressed in logarithm form) whereas the UBRs in other performances, such as MacGregor’s, are more variable.  Mostly even subdivisions on beats 2 and 3 would suggest a pattern of long-short short-long long-short (a look at the BUR graph shows that beat 4 tends towards long-short), similar to Cameron’s performance of the reel, which could be approximated with the following notation:   As noted previously, this creates a unique sense of groove.  A listener’s entrainment to meters (or, for that matter, groove) is dependent on “a specific set of timing 65  relationships.”132  This means that if listeners entrained to a half note tactus with the above subdivisions, this would, in a sense, be a different meter than one with more even subdivisions.  In this way, the solo fiddler can create a unique sense of meter simply by expressive variations within the beat. The BUR in both Section A and B is mostly positive, but beat 2 in Section A is negative aside from one outlier.  A negative BUR on beat 2 implies that the downbeat eighth is shorter than the offbeat eighth that follows – a ratio created by the  motive.  A similar effect occurs in MacGregor’s recording, which may be to accommodate the skip-change step used in set dances.  However this step is also present on the offbeat of beat 4, and there does not seem to be a similar trend.  This may be because despite the expressive variation in the music, the dancers are likely to perform their steps with relative evenness because they entrain to the half-note tactus. This means that their steps will entrain better with the typically more even beat 4, leading to a more definitive downbeat.   Beat 2 is also contains the most uneven (and widely variable) BURs occur on the second quarter-note beat of each measure when Cassel plays the characteristic  figure.  On some of these occurrences, the BUR is as extreme as -0.35655 (a more extreme division than )—she plays the "sixteenth notes" very quickly.  This range is in sharp contrast to the beat 2 BURs when this figure does not occur.  These BUR values tend to be more even. However, the trend of more negative BUR values persists even in the B section, when the  figure is absent.  Both A and B sections follow a similar contour in the BUR                                                           132 London, Hearing in Time, 140. 66  means, with beat 2 being the lowest, and beats 3 and 4 gradually rising, with beat 1 as the highest mean.   This striking difference between the BUR mean for beat 1 and the BUR mean for beat 2 may indicate that beat 2 stands out to the listener, maintaining the backbeat effect even when other phenomenal accents (created by the  figure) are not present on beat 2. A Section Aside from one outlier, the BURs for beat 4 of the A section are all positive.  This represents a fourth beat in which the eighth note on the beat is longer than the one that follows it.  Butterfield indicates that even eighths would lead the listener to perceive the offbeat eighth notes as continuations,133 whereas swung eighth notes – which would have a positive BUR – would be perceived as having an anacrustic function.134  So the effect of the A section beat 4s is to provide anacrusis into the next downbeat.   The exception to this trend is Outlier Z12, in the fourth measure, which is the only negative BUR for beat 4 of the A section.  A negative BUR indicates that the onbeat eighth note is shorter than the offbeat eighth note which follows it.  This short-long division of the beat means that the second eighth note has a less potent anacrustic function, and the shortness of the E also suggests that the F# is the main note, with a lower neighbour E preceding it.  Measure 4 is the last measure before the A phrase is repeated for the first time, so it is possible that this ratio gives a sense of continuation to the listener, providing continuity as the A section returns.  Alternatively, the dilution of the anacrustic function of                                                           133 Hasty defines continuation as “a new event [which is] unaccented or “not beginning” in relation to the larger event which has already begin.”  In other words, a continuation is a weak or unaccented beat which continues the process of becoming, rather than beginning a new projection.  Hasty, Meter as Rhythm, 104. 134 Butterfield, “The Power of Anacrusis.” 67  the last eighth note may create a slight pause which solidifies the phrase ending in the listener’s ear. Outlier Y12 occurs in the first measure of the second A phrase, measure 5 (first time).  Y12 shows that the eighth note on beat 3 is shorter than the offbeat eighth note that follows it.  The resulting durational accent on the offbeat eighth note almost makes it sound like a new (very low-level) beginning.135  To my ear, this groups the F# on the offbeat of beat 3 with the following two eighths on beat 4, as sort of an extended anacrusis leading into the next measure.  This gives great motional energy moving the listener forward as the A phrase is repeated for the first time.   The only positive BUR for beat 2 in the A section is Outlier V12, located in measure 8.  In a way, this is not surprising, as the outlier refers to one of the times when beat 2 is divided into two eighth notes, not the more unequal . The positive BUR gives the second eighth note anacrustic function, emphasizes beat 3 as a low-level beginning, rather than previous measures which placed more emphasis (through the phenomenal accents on the  figure) on beat 2.  This is likely due to measure 8’s function.  Rather than continuing the A phrase, measure 8 ends it and leads into the first B section. UBR Outlier Z13 arises in measure 4 (second time) when the offbeat eighth note of beat 1 is shorter than onbeat eighth note of beat 2.  In this case, the ratio occurs because the offbeat eighth of beat 1 is short, providing anacrustic function into beat 2.   Outlier X12 represents a higher BUR for beat 3 of measure 5 (second time). This means that the onbeat eighth note of beat 3 is longer than the offbeat eighth note that                                                           135 Hasty defines a beginning as “a potential for duration” (Meter as Rhythm, 78), or “the making present of an event.” (74). 68  follows it.  This puts a slight durational accent on beat 3, reinforcing the notion of 3 as a lower-level beginning, which makes sense as beat 3 begins the alternate-foot skip-change step.  Measure 5 (second time) is the first measure of the last A phrase in the whole performance, so emphasizing the step pattern in this measure may help engage dancers as the A section ends and the B section is about to begin. Section B Measure 12, which concludes the first B phrase, provides an important structural boundary.  The downbeat eighth note of measure 12 (the first time) lasts 186 ms, so compared with the 128 ms eighth notes that precede and follow it, this eighth has a strong durational accent.  This lengthening helps provide a brief sense of pause, marking this measure as a structural boundary, and suggesting that the high A is the goal of the ascent in m. 11.  It also produces a particularly negative UBR value for beat 1, Outlier W15.      Outlier Y14 occurs on beat 4 of m. 11 (second time).  Its high BUR indicates that the two eighth notes on beat 4 have a more unequal long-short division, similar to swung jazz eighth notes.  Just as in swung eighths, the second eighth note takes on a strong anacrustic function, providing strong forward momentum into m. 12 (second time), the measure that leads into the very last four bar phrase.  The BUR for Outlier X14 is significantly lower than the other BURs for beat 2 of the B section.  In fact, the beat division is more similar to many of the ratios for beat 2 of the A section.  This is because X14 occurs in measure 12 (second time), which includes the figure from the A section.  Like other performers, Cassel uses this figure to help mark the phrase ending just before the last phrase of the performance.  This extreme ratio results in a skewed UBR for beat 2 as well, Outlier X15.  This excitingly extreme division not only 69  catches the listener’s ear, but also harks back to the A section, simultaneously achieving cohesion between sections and emphasizing the structural significance of measure 12 (second time), the last measure before the final phrase of the performance. Outlier Z15 takes place in the first measure of the very last phrase: m. 13 (second time).  Z15 is the only positive UBR outlier on beat 4 of the B section.  It is not clear how this outlier functions in a musical context, so it is possible that Cassel’s microtiming, in this case, was random rather than musically driven.   Performance: Bruce Macgregor The recording used for analysis can be found at: https://www.youtube.com/watch?v=FfwReZUXgAI  Like Cassel, Macgregor is one of the performers who may have influenced – or at least been heard by – some of the others.  With three solo albums and an active role in popular Celtic groups like Blazin’ Fiddles and Cliar, Macgregor is a leader of the Scottish music scene.  He is also the host of BBC Scotland’s programme “Travelling Folk” and is a founding member of the fiddle school “Blazin’ in Beauty”, so it is possible that the other artists may be familiar with his discourse on traditional fiddle as well as his performing abilities.136 The most notable thing about Macgregor’s performance is that it includes the A section only.  This is likely due to the recording’s source: a video tutorial about how to bow the  figure, which is characteristic of the A section.  Macgregor is also the only                                                           136 “Biography,” Bruce MacGregor Official Website, last modified 2014, accessed February 12, 2014, http://www.brucemacgregor.co.uk/about/ 70  performer to place the  rhythm on beat 1.  He only does this once, in measure 12, but its surprising presence on the downbeat, combined with outliers X17 and Y18 (as we shall see), clearly emphasizes measure 12, the last measure before the final phrase.  FIGURE 16: Transcription   FIGURE 17: log(BUR) in Section A FIGURE 18: log(UBR) in Section A  71    Macgregor decelerates noticeably in the last measure, resulting in several outliers which are caused by the tempo decrease.  Outliers W17, Y17, Z17, and Z18 occur in the last measure, and can therefore be discounted from the analysis.    A BUR/UBR analysis of this performance yields interesting results, despite the omission of the B section.  All the BUR means, regardless of beat, are negative.  Therefore, on a whole, Macgregor plays every beat with a short-long division, resulting in a sort of sub-metrical syncopation throughout.  This is a feature unique to Macgregor’s performance and does not occur in any of the other analyzed recordings.  The short-long division is especially exaggerated on the  figure on beat 2.    Similarly, all of Macgregor’s UBR means are positive, another unique characteristic (though Blair has positive UBR means on three beats of the A section, and one UBR mean which is zero).  This indicates that in the A section, the first eighth of most beats is shorter than the eighth which precedes it, which again corresponds to a short-long division.  This seems to correlate with Iyer’s theory that in groove-based music, musicians have an individual way of relating to the pulse.  In other words, one of the hallmarks of this style may be the individual performer’s personal groove.   As in the previously discussed performances, the BUR is by far the most unequal on the beats when the characteristic  figure occurs, ranging from -0.61979 to -0.22185.  A value of -0.61979 represents a division which is even more extreme than a ratio of an eighth note to a quarter note.  Concomitantly, the UBR of the last half of beat 1 and the first half of beat 2 is also extremely unequal.  The most extreme of these UBRs occurs in measure 4, where there is a UBR of 0.588832.  Similarly, the one time this motive occurs on 72  beat 1, the resulting BUR is extreme.  This out-of-place occurrence of the figure provides an interesting feature in the tune.  As previously mentioned, the strong accent of the  figure could act as a sort of downbeat displacement for new listeners, or a sort of backbeat accent for more familiar listeners.137  Putting the  on beat 1 means that the downbeat is shifted back to its true place, or alternatively (if the listener hears beat 2 as a backbeat), the backbeat is displaced to beat 1.  Either way, this measure clearly subverts the listener’s expectations, placing great emphasis on this measure.  The emphasis serves to enhance measure 4’s status as the very first structural boundary, the end of the first phrase.  It is worth noting that although the lengths of the sixteenths in both Cassel’s and MacGregor’s recordings are very similar (in fact there are many occurrences of sixteenths lasting exactly. 046ms), the BUR in these situations is much more extreme in the MacGregor reel, as the IOI for the following eighth note tends to be much longer than in Cassel’s interpretation.  This gives MacGregor’s rendition of this figure a stronger durational accent, which enhances the backbeat effect. In this performance of the piece, this backbeat is not only stronger, but it is even more solidly established since the performer loops the A section, meaning that the listener never goes more than a measure without this familiar figure and its accompanying accent on beat 2.  Moving the  figure to beat 1 in measure 12 takes the listener by surprise.  This may be a way to incite more listener interest and engagement as the performance comes to a close.                                                               137 In the video, Macgregor taps his heel on the tactus, beats 1 and 3, and raises his knee sharply on the backbeats 2 and 4.  It seems possible an accented beat 2/backbeat effect would still influence the groove of the tune, even if claps or foot taps take place on the tactus itself. 73  Both the BUR and UBR become more even in the last four measures of the piece.  It is possible that this is a preparation for the potential but absent B section - a section which omits the  figure that is responsible for many of the most extreme inequalities in beat division.  It is also possible that in this relatively short performance, Macgregor only firmly established his desired groove in the last four measures. The third quarter-note beat of each measure is often the most equally divided beat of the measure.  There is more variation in this trend, but in general, the last two quarter-note beats of each measure tend to be more equally divided than the first two.  As discussed in “Generic Observations”, this relative equality of beat division in the latter half of the measure may be intended to compensate for the varied inequality of beat 2, thus distinguishing the groove of a reel from that of a strathspey by incorporating more even divisions of the beat. X18 takes place in m. 9, a significant structural boundary as it begins the repeat of the A section.  With a value of 0.30103, X18 is the highest UBR value in the entire performance, indicating that the offbeat eighth of beat 1 is much longer than the first eighth of the second beat.  In this case, the ratio is due to the brevity of the sixteenths in the  figure on beat 2.  It makes sense that Macgregor would mark the start of the repeat with an exaggeration of the established groove, dividing the  even more extremely than previously.   The only other two outliers, X17 and Y18, both occur in measure 12.  Measure 12 is notable due to its incorporation of the  figure (typically found on beat 2 only) on beat 1.  It seems logical that this subversion of expectations would be accompanied by an outlier 74  in the beat ratios, but rather than a positive UBR for beat 2 (which would result from a long eighth in the  figure followed by a shorter eighth on the downbeat of 2), Y18 occurs—the sole negative UBR for beat 2.  It is possible that without the phenomenal accent attributed to beat 2 from the  figure, the established backbeat requires that beat 2 be accented in some other way.  In this case, the eighth-note downbeat of beat 2 is surprisingly long, giving beat 2 a durational accent and resulting in a negative UBR for beat 2.  This results in X17, which, while still a negative value, is the highest BUR for beat 2.  Performance: Farquhar MacRae The recording used for analysis can be found here: http://www.tobarandualchais.co.uk/fullrecord/79631/1 starting at 2:13.  Farquhar MacRae was the only performer fluent in Gaelic, and therefore the one with the most intimate knowledge of the accentuation in the sung port-a-beul from which this fiddle tune stems.  MacRae’s groove is likely strongly influenced by the original Gaelic lyrics or even his distinction of speaking Gaelic as a first language.  However further research is needed to determine whether the specifics of MacRae’s performance are individual interpretive elements or more universal indications of a Gaelic-speaking player.  From a rhythmic standpoint, MacRae’s performance is distinctive because he is the only player to omit the A section’s  motive.  MacRae also plays the tune very fast (around 129BPM, accelerating to 166BPM for the very last repeat of the B section), so the lack of sixteenth notes may reflect the difficulty in vocalizing such a fast rhythm in the sung port-a-75  beul, especially considering that the sixteenth notes, as played by other performers, as sometimes as short as 46ms.   FIGURE 19: TRANSCRIPTION  Please note: Though m. 17 begins the A phrase, this measure was not included in the analysis as the tempo had already deteriorated significantly and the performance ends in the next bar.           76  FIGURE 20: log(BUR) in Section A  FIGURE 21: log(UBR) in Section A   FIGURE 22: log(BUR) in Section B   FIGURE 23: log(UBR) in Section B   Overall, MacRae’s performance has a much smaller range of BUR and UBR values than other performances.  He divides the beat not only more evenly on average, but also much more consistently, perhaps due to the quick tempo.  It is also worth noting that almost all of the UBR and BUR values fall within the upper limit of Butterfield’s estimate for just-noticeable BUR or UBR differences.138  Unlike the other performances, where certain subdivisions would be heard as swung or, in some cases, even as dotted rhythms, MacRae’s performance sounds like even eighths (with a few exceptions).  I suspect this is due to                                                           138 According to Buttefield, a BUR differential below the range of ±0.1–0.2 (or ±0.04–0.08 on the log scale) is inaudible, meaning that a BUR below this range cannot be distinguished from a (equal) BUR of 0.  Butterfield, “Why Do Jazz Musicians Swing Their Eighth Notes?” 8.   77  MacRae being the only Gaelic-speaking player – in fact, Gaelic was MacRae’s mother tongue.  Considering MacRae was lauded as an embodiment of traditional Gaelic life139, it is reasonable to assume that MacRae was familiar with the port-a-beul for which this tune is derived, and that he likely knew the Gaelic lyrics.  Perhaps the tune is sung more evenly, so as to facilitate the comprehension of the words.  More research would be needed to determine whether the remarkable evenness of MacRae’s performance is an individual interpretation, or influenced by his knowledge of the Gaelic language. One striking difference between MacRae’s performance and the others is the lack of the distinctive  “cut” rhythmic figure on beat 2. Instead he plays just two notes on that beat. However, they are unequal; indeed, the majority of the BURs for beat 2 of the A section are negative, and the most extreme values in MacRae’s performance can be found in the BURs for beat 2 of the A section (indicated in black in Figure 20).  These values are quite comparable to other performances’ BURs for the  figure.  Some of the outliers can be understood to relate to this figure. For instance, UBR outlier Y21, which occurs in m. 6, represents a division where the offbeat eighth of beat 1 is much longer than the eighth note value directly on beat 2.  Beat 2 contains the equivalent of the   figure.  Outlier Z22 actually encompasses two almost identical data points, one occurring in measure 12 (first time) and one occurring in measure 12 (second time).  Both these measures are identical to measures 13 and 29 of Cassel’s performance, which represents the same structural point in the tune.   As I noted in Cassel’s analysis, beat 2 of this measure is an approximation of the  figure, and thus has a very unequal division.                                                             139 Martin Macdonald, “Farquhar MacRae," The Herald Scotland, September 12, 2000, accessed February 5, 2014, http://www.heraldscotland.com/sport/spl/aberdeen/farquhar-MacRae-1.218830 78  A section MacRae’s performance has only one outlier – V20 - which can be regarded as musically insignificant due to its placement in the first measure.  Almost all of the outliers for the A section occur during the repeat of A, meaning that MacRae plays the first iteration of A in more strict adherence to the established trends, likely to help establish a steady groove for the listener.  Besides the aforementioned Y21, the only other outlier during the first occurrence of the A section is outlier Y20. Melodic function seems to be a consideration for outlier Y20, which occurs in m. 8 (first time), the measure that ends the first A section and is followed by the very first iteration of the B section. Y20 a ratio of -0.097, a short-long division of beat 4 more substantial than the corresponding BUR in the previous (and first) statement of this measure, -0.052 on beat 4.  Since the m. 4 ratio indicates nearly equal eighths I believe it gives an effect of a half cadence (F# resolving to E, with an F# pickup into the next phrase) whereas, the stronger short-long division in m. 8 might be heard as a cadence on the tonic (F# being embellished with an E).  This gives the A phrases an antecedent-consequent relationship, firmly establishing the A as a separate and resolved entity from the B section which follows. Aside from the absence of the figure, there are some distinctive trends in MacRae’s microtiming. In the A section, all BURs for beat 3 and beat 1 are positive, which denotes a long-short division of the beat, in which case the shorter, offbeat eighth note would be heard as an anacrusis, likely for the purposes of emphasizing beat 2 even further. There are only two exceptions, both on beat 1, in measure 6 (second time) and measure 8 (second time).  Neither of these bars contains the characteristic  figure on beat 2.  79  However the negative values are so close to 0 that they would likely be perceived as equal divisions by listeners, and so do not really disrupt the trend.  Another consistency in the A section is that all UBRs for beat 2 are positive (no doubt due to the unevenness of the second beat figure), and all UBRs for beat 1 (aside from one outlier) are positive as well.  However the positive UBRs for beat 1 are so low that the divisions would likely be heard as equal.  The sole negative UBR for beat 1 is Outlier X21, which occurs in measure 8 (second time), which is the last, cadential measure of the final A section. Another outlier, W20, is present in this measure as well.  W20 represents one of the few negative BURs for beat 1 of the A section.  These two anomalies subtly reverse the established trends of the A section, changing the expected ratio of long-short to a slight short-long ratio.  They both occur at a significant structural boundary, helping to signal the final closure for the section. They may also prime the listener for the subtle switch in groove which arrives with Section B, discussed below It seems that in most of the measures with the uneven second beat figure the last three eighth notes act similarly as an extended anacrusis towards the next downbeat. Outlier Z21 occurs in m. 1 (second time), the first measure of the return of the A section.  It specifies that the offbeat eighth of beat 3 is much shorter than the downbeat eighth note of beat 4.  This outlier is markedly deviant from the other data points, especially considering that its nearest neighbouring data point occurs in the first measure,  when tempo is still being established.  The extreme shortness of the offbeat eighth of beat 3 gives it stronger anacrustic function, and beat 4 as a whole also acts an anacrusis.  Driving almost the entire second half of the measure toward the next downbeat infuses significant motional energy into the beginning of the sectional repetition. Outlier X20 occurs on beat 3 of m. 3 (second 80  time).  Its relatively high BUR means that this beat 3 has as strong long-short division.  This is the third measure of the first A phrase, meaning it is the last measure of the phrase the characteristic figure on beat 2.  It is possible that the long eighth note on beat 3 acts as a sort of grouping boundary between the second beat figure and the moving eighths which follow into the next phrase.  The durational accent it assigns to beat 3 acts almost as a rhythmic cadence, effectively casting the rest of m. 3 (second time) as an extended pickup to m. 4 (second time). Some outliers seem to clarify melodic function.  For instance, outlier Z20 occurs on beat 4 of m. 6 (second time).  This means that the E eighth note on beat 4 is shorter than the offbeat F# eighth note which follows it.  Measure 6, like measure 2, is the second measure of the A phrase, and MacRae plays two versions of this measure throughout the piece:  m. 2 m. 2 (second time)  The last variation above is present in m. 6 (second time).  The brevity of the E eighth note in this measure may indicate that the E serves only to ornament the F#.  This interpretation seems to be reinforced by the other variant of this passage, where MacRae sometimes omits the E altogether, suggesting the F# is a more important pitch.  B Section Comparing the mean UBRs of the A section with those of the B section, a subtle change of groove is evident. While MacRae tends to play long-short UBRs on the first two beats of each measure in the A section, and more negative UBRs on the next two beats, in 81  the B section he incorporates more negative UBRs on the first two beats of each measure and more positive UBRs on the last two. Indeed, all beat 3 UBRs are positive or equal.   Investigation of this trend reveals another noteworthy phenomenon.  In cases where beats 2 and 3 both comprise eighth notes, the combined rhythmic values for beat 2 (in the B section) are longer than the combined rhythmic values of beat 3.  In other words, beat 2 lasts longer than beat 3.   The sole exception to this trend occurs in m. 13 (second time), where beat 2 lasts slightly longer than beat 3.  A similar trend is not present in the A section of this performance, so it seems that this is unique to the groove of the B section.   Most beat 1s in Section B are divided nearly evenly, so the second, offbeat eighth note acts as a continuation.  This is in contrast to section A, where, to emphasize the surprisingly arrival of the second beat’s trademark unevenness, beat 1 is divided in a long-short division,  meaning that the second offbeat eighth note is likely heard as an anacrusis, providing emphasis for the second beat figure.  Strikingly, however, measure 12 of section B (first time) presents a positive BUR, outlier Y22 which is particularly exaggerated, perhaps because this is the first occurrence of the phrase.  In measure 12 (second time), beat 1 has a long-short division so as to give beat 2 emphasis through anacrusis.  This means that the on-beat eighth note of beat 1 is longer, creating a negative UBR (Z23) when compared with the eighth note before it.   In short, MacRae’s style is characterised by remarkably even subdivisions.  His variance from even eighths, though subtle, can have powerful effects on the listener.  Though he omits the  figure, a strong accent and unequal subdivision on beat 2 provide a similar effect.  Though MacRae’s eighths are the most equal, his nuances in 82  microtiming, combined with a gradual acceleration of tempo throughout the performance, provide a strong drive forward.  Conclusions and areas for future research Throughout this project, my goal has been to shed light on how the groove in Gaelic fiddle music is created and perceived.  I feel that my research provides more support for the belief that microtimings can help to create groove within a single instrument, without interacting with other musical lines.  Based on the inherent groove and swing associated with jazz music, I chose to apply a jazz methodology to this music.  This methodology proved a fruitful avenue of discovery, and in the future I think this methodology could be applied even further to other genres of music. My research provides more tangible support for ideas I had intuitively assumed.  Overall, the analysis seemed to indicate that groove can indeed be created in a solo performance through the use of microtimings.  I believe that the relative simplicity of the pitch material motivates performers to create interest using other means – specifically through microtimings in beat subdivisions.  Based on my analysis, it seems that the trends and variants in microtimings could help to engage the listener and create interest.  For example, Cameron plays an extreme version of the unequal figure in measure 3.  This outlier, or variant from the overall trend, may help orient the listener to the groove by over-emphasizing it.  Blair continues the A section groove by playing beat 2 of the B section with wide variation which is at times very unequal.  These manipulations of microtimings, whether deliberate or intuitive, may create a unique experience for the listener.  83  This research also supports my idea that microtimings and uneven subdivisions in this music exist to affect the groove of the tune, and that the groove of this style is partially constructed by the subdivision of each beat and how beat trends create expectation (which can be subverted by outliers).  In fact, the microtimings seem to be one of the key elements in the creation of groove in these performances.  The microtimings are what makes the music “out of time,” an essential characteristic in order to achieve groove.140   Because of their pivotal role in the creation of groove, it seems logical to surmise that the microtimings are a hallmark of this style of music. The data show some consistencies of microtimings across these performances. For example, all performances demonstrated extreme un-evenness on the second beat of the A section, suggesting this may be an essential feature of the tune itself.  Similarly, all the performers played beat 3 much more evenly, perhaps to differentiate the reel’s groove from that of a strathspey, which is characterized by highly inequal subdivisions throughout. These trends may be understood as elements of overall Gaelic style. On the other hand, the data show that there was a great deal of variation between performers, suggesting that each musician has a highly individual way of relating to the pulse. Macrae’s recording, apart from the uneven second beat figure, features surprisingly even eighths when compared with the other players.  Cassel plays the A section with mostly even (and consistent) UBRs, and has an overall subdivision pattern of long-short, short-long, long-short, long-short per measure.  Conversely, Macgregor plays his A section with a short-long subdivision on each beat.  Though a larger study of musicians would be needed for confirmation, I believe these contrasting trends among different performances may                                                           140 Keil and Feld, Music Grooves, 155. 84  indicate that one of the defining features of this style is the distinctive ways that individual performers approach the groove. Though microtiming research has already been explored, particularly in regards to the interaction between bass and percussion in jazz music, I feel that my focus on solo folk dance music adds to the current body of research.  There are countless groove-based folk musics around the world, and many of these may be based around a solo musical line.  This project suggests a possible approach to beginning to understand the groove of such musics.  Furthermore, this project could be expanded by investigating how the groove and trends in microtiming correlate to the physical motion that may accompany them.  The dance movements could be mapped using motion capture technology, an exciting new tool in music theory.141  In addition, our understanding of groove could be further augmented by exploring how it is affected by dynamic accents and ornamentation.  It is my hope that this paper will also provide some of the first steps into theoretical research of this type of music.  Many of my sources suggested a link between the Gaelic language and the stylistic nuance of puirt-a-beul, but there seems to be little idea as to the nature of this connection.  Further research could explore the connection between sung puirt-a-beul, and its instrumental interpretations by both Gaelic speakers and non-speakers.  This research could also be compared with a similar study on another form of puirt-a-beul, such as the strathspey, to better understand the differences and commonalities between dance forms.                                                           141 Marcelo Wanderley, "Motion Capture of Music Performances: Advantages and Limitions,” (Paper presented at Symposium on Empirical Methods for Music Theorists, McGill University, November 2, 2009), https://ddmal.music.mcgill.ca/events/symposium-on-empirical-methods-for-music-theorists 85  This genre has been studied for its cultural impacts but less so for its musical characteristics.  Exploring the unique groove of this music could aid in understanding other types of dance music, or understanding other types of Scottish folk music.  As the Gaelic language faces possible extinction, it is logical to assume that this music – which according to insiders relies so heavily on the Gaelic words – will vary more and more from its original roots.  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Journal of the Royal Musical Association 129, no. 2 (2004): 272 – 297.    91  Appendix Neil Cameron’s performance calculations Event onset Interonset Interval Measure Beat BUR (in log) BUR UBR (in log) UBR               0.05510204 0.131 1 1         0.185759637 0.104   1.5 0.100232652 1.2596     0.290249433 0.049   2     -0.05116 0.88888 0.33877551 0.068   2.25         0.406349206 0.116   2.5 0.003718964 1.0086     0.522448979 0.174   3     -0.17393 0.67 0.696598639 0.128   3.5 0.133538908 1.36     0.82430839 0.128   4     0 1 0.95201814 0.163   4.5 -0.10237291 0.79     1.114557823 0.174 2 1     -0.02836 0.93678 1.288707482 0.151   1.5 0.061565562 1.1523     1.439637188 0.093   2     0.210586 1.624 1.532517006 0.151   2.5 0.210853365 1.625     1.683446712 0.151   3     0.060698 1.15 1.834376417 0.128   3.5 -0.07058107 0.85     1.962086167 0.163   4     -0.10237 0.79 2.12462585 0.116   4.5 0.149219113 1.41     2.240725623 0.186 3 1     -0.20761 0.62 2.42648526 0.116   1.5 0.204119983 1.6     2.542585034 0.046   2     0.049218 1.12 2.589024943 0.058   2.25         2.647074829 0.186   2.5 -0.25181197 0.56     2.832834467 0.148   3     0.09861 1.254902 2.980861678 0.131   3.5 0.054344889 1.1333     3.111473922 0.151   4     0.089905 1.23 3.262403628 0.128   4.5 0.071882007 1.18     3.390113378 0.174 4 1     -0.13077 0.74 3.564263038 0.104   1.5 0.222716471 1.67     3.668752834 0.151   2     -0.16115 0.69 3.819682539 0.151   2.5 0 1     3.970612244 0.128   3     0.071882 1.18 4.098321995 0.104   3.5 0.089905111 1.23     4.202811791 0.174   4     -0.22185 0.6 4.376961451 0.104   4.5 0.222716471 1.67     4.481451247 0.163 5 1     -0.19382 0.64 4.643990929 0.128   1.5 0.103803721 1.27     92  Event onset Interonset Interval Measure Beat BUR (in log) BUR UBR (in log) UBR 4.77170068 0.046   2     -0.03621 0.92 4.818140589 0.093   2.25         4.911020408 0.104   2.5 0.127104798 1.34     5.015510204 0.163   3     -0.19382 0.64 5.178049886 0.116   3.5 0.146128036 1.4     5.294149659 0.174   4     -0.17393 0.67 5.468299319 0.128   4.5 0.133538908 1.36     5.59600907 0.139 6 1     -0.03581 0.92086 5.735328798 0.128   1.5 0.035789833 1.0859     5.863038548 0.046   2     -0.03581 0.92086 5.909478458 0.093   2.25         6.002358276 0.151   2.5 -0.03621217 0.92     6.153287981 0.139   3     0.037426 1.09 6.292607709 0.151   3.5 -0.03621217 0.92     6.443537414 0.139   4     0.037426 1.09 6.582857142 0.116   4.5 0.071882007 1.18     6.698956916 0.139 7 1     -0.08092 0.83 6.838276643 0.139   1.5 0 1     6.977596371 0.058   2     0 1 7.035646258 0.081   2.25         7.116916099 0.139   2.5 0 1     7.256235827 0.139   3     0 1 7.395555555 0.151   3.5 -0.03621217 0.92     7.54648526 0.174   4     -0.06048 0.87 7.72063492 0.116   4.5 0.176091259 1.5     7.836734693 0.151 8 1     -0.11452 0.76821 7.987664399 0.116   1.5 0.114510905 1.3017     8.103764172 0.151   2     -0.11452 0.76821 8.254693877 0.128   2.5 0.071882007 1.18     8.382403628 0.139   3     -0.03621 0.92 8.521723356 0.139   3.5 0 1     8.661043083 0.151   4     -0.03621 0.92 8.811972789 0.139   4.5 0.037426498 1.09     8.951292517 0.174 9 1     -0.09691 0.8 9.125442176 0.081   1.5 0.33243846 2.15     9.206712018 0.128   2     -0.20066 0.63 9.334421768 0.174   2.5 -0.13076828 0.74     9.508571428 0.128   3     0.133539 1.36 9.636281179 0.139   3.5 -0.03621217 0.92     9.775600907 0.151   4     -0.03621 0.92 9.926530612 0.163   4.5 -0.03151705 0.93     10.08907029 0.186 10 1     -0.05552 0.88 93  Event onset Interonset Interval Measure Beat BUR (in log) BUR UBR (in log) UBR 10.27482993 0.116   1.5 0.205055422 1.60345     10.39092971 0.139   2     -0.07857 0.8345 10.53024943 0.163   2.5 -0.06917318 0.85276     10.69278912 0.221   3         10.91337868 0.151   4         11.06430839 0.104   4.5 0.161368002 1.45     11.16879819 0.186 11 1     -0.25181 0.56 11.35455782 0.104   1.5 0.252853031 1.79     11.45904762 0.139   2     -0.12598 0.7482 11.59836735 0.163   2.5 -0.06920374 0.8527     11.76090703 0.128   3     0.104965 1.2734 11.88861678 0.104   3.5 0.090187488 1.2308     11.99310658 0.163   4     -0.25251 0.5591 12.15564626 0.104   4.5 -0.16115091 0.69     12.26013605 0.186 12 1     -0.16115 0.69 12.44589569 0.128   1.5 0.162265614 1.453     12.57360544 0.070   2     0.041393 1.1 12.64326531 0.046   2.25         12.68970522 0.163   2.5 -0.14772744 0.71166     12.8522449 0.151   3     0.033223 1.0795 13.0031746 0.116   3.5 0.114510905 1.3017     13.11927438 0.151   4     -0.11452 0.76821 13.27020408 0.174   4.5 -0.06048075 0.87     13.44435374 0.139 13 1     0.09691 1.25 13.58367347 0.128   1.5 0.037426498 1.09     13.71138322 0.128   2     0 1 13.83909297 0.116   2.5 0.041392685 1.1     13.95519274 0.151   3     -0.11351 0.77 14.10612245 0.116   3.5 0.113943352 1.3     14.22222222 0.163   4     -0.14874 0.71 14.3847619 0.128   4.5 0.103803721 1.27     14.51247166 0.116 14 1     0.041393 1.1 14.62857143 0.128   1.5 -0.04095861 0.91     14.75628118 0.151   2     -0.07058 0.85 14.90721088 0.174   2.5 -0.06048075 0.87     15.08136054 0.290   3         15.37160998 0.116   4         15.48770975 0.139   4.5 -0.08092191 0.83     15.62702948 0.151 15 1     -0.03621 0.92 15.77795918 0.116   1.5 0.113943352 1.3     15.89405896 0.174   2     -0.17393 0.67 16.06820862 0.104   2.5 0.222716471 1.67     94  Event onset Interonset Interval Measure Beat BUR (in log) BUR UBR (in log) UBR 16.17269841 0.139   3     -0.12494 0.75 16.31201814 0.128   3.5 0.037426498 1.09     16.43972789 0.151   4     -0.07058 0.85 16.5906576 0.139   4.5 0.037426498 1.09     16.72997732 0.139 16 1     0 1 16.86929705 0.128   1.5 0.037426498 1.09     16.9970068 0.163   2     -0.10237 0.79 17.15954649 0.139   2.5 0.068185862 1.17     17.29886621 0.151   3     -0.03621 0.92 17.44979592 0.104   3.5 0.161368002 1.45     17.55428571 0.163   4     -0.19382 0.64 17.7168254 0.139   4.5 0.068185862 1.17     17.85614512 0.139 17 1     0 1 17.99546485 0.093   1.5 0.174524978 1.4946     18.08834467 0.058   2     -0.13873 0.72656 18.14639456 0.070   2.25         18.21605442 0.128   2.5 0 1     18.34376417 0.139   3     -0.03621 0.92 18.4830839 0.174   3.5 -0.09691001 0.8     18.65723356 0.139   4     0.09691 1.25 18.79655329 0.151   4.5 -0.03621217 0.92     18.94748299 0.128 18 1     0.071772 1.1797 19.07519274 0.116   1.5 0.04273298 1.1034     19.19129252 0.070   2     -0.08166 0.8286 19.26095238 0.070   2.25         19.33061224 0.163   2.5 -0.06550155 0.86     19.49315193 0.128   3     0.103804 1.27 19.62086168 0.139   3.5 -0.03621217 0.92     19.76018141 0.163   4     -0.07058 0.85 19.92272109 0.128   4.5 0.103803721 1.27     20.05043084 0.128 19 1     0 1 20.17814059 0.139   1.5 -0.03621217 0.92     20.31746032 0.070   2     -0.07058 0.85 20.38712018 0.058   2.25         20.44517007 0.163   2.5 -0.10474325 0.7857     20.60770975 0.163   3     0 1 20.77024943 0.116   3.5 0.146128036 1.4     20.88634921 0.163   4     -0.14874 0.71 21.04888889 0.104   4.5 0.195899652 1.57     21.15337868 0.139 20 1     -0.12494 0.75 21.29269841 0.139   1.5 0 1     21.43201814 0.139   2     0 1 95  Event onset Interonset Interval Measure Beat BUR (in log) BUR UBR (in log) UBR 21.57133787 0.151   2.5 -0.03621217 0.92     21.72226757 0.128   3     0.071882 1.18 21.84997732 0.128   3.5 0 1     21.97768707 0.151   4     -0.07058 0.85 22.12861678 0.139   4.5 0.071882007 1.18     22.26793651 0.139 21 1     0 1 22.40725624 0.104   1.5 0.127104798 1.34     22.51174603 0.070   2     -0.16115 0.69 22.5814059 0.081   2.25         22.66267574 0.128   2.5 0.071882007 1.18     22.79038549 0.163   3     -0.10237 0.79 22.95292517 0.104   3.5 0.195899652 1.57     23.05741497 0.163   4     -0.19382 0.64 23.21995465 0.139   4.5 0.068185862 1.17     23.35927438 0.128 22 1     0.037426 1.09 23.48698413 0.139   1.5 -0.03621217 0.92     23.62630385 0.058   2     -0.03621 0.92 23.68435374 0.093   2.25         23.77723356 0.116   2.5 0.113943352 1.3     23.89333333 0.151   3     -0.11351 0.77 24.04426304 0.139   3.5 0.071882007 1.18     24.18358277 0.116   4     0.079181 1.2 24.29968254 0.151   4.5 -0.11350927 0.77     24.45061224 0.128 23 1     -0.03321 0.92638 24.578322 0.151   1.5 0.147728869 1.40517     24.7292517 0.070   2     0 1 24.79891156 0.046   2.25         24.84535147 0.174   2.5 -0.1760913 0.666667     25.01950113 0.163   3     0.02836 1.06748 25.18204082 0.116   3.5 0.147728869 1.40517     25.29814059 0.151   4     0 1 25.44907029 0.116   4.5 -0.11350927 0.77     25.56517007 0.128 24 1     0.071882 1.18 25.69287982 0.151   1.5 -0.07058107 0.85     25.84380952 0.128   2     0.071882 1.18 25.97151927 0.139   2.5 -0.03621217 0.92     26.110839 0.151   3     -0.03621 0.92 26.26176871 0.128   3.5 0.071882007 1.18     26.38947846 0.151   4     -0.07058 0.85 26.54040816 0.139   4.5 0.037426498 1.09     26.67972789 0.116 25 1     0.075547 1.19 26.79582766 0.139   1.5 -0.07572071 0.84     96  Event onset Interonset Interval Measure Beat BUR (in log) BUR UBR (in log) UBR 26.93514739 0.151   2     -0.03621 0.92 27.0860771 0.128   2.5 0.071882007 1.18     27.21378685 0.139   3     -0.03621 0.92 27.35310658 0.174   3.5 -0.09691001 0.8     27.52725624 0.139   4     0.09691 1.25 27.66657596 0.151   4.5 -0.03621217 0.92     27.81750567 0.139 26 1     0.037426 1.09 27.9568254 0.104   1.5 0.127104798 1.34     28.06131519 0.197   2     -0.27572 0.53 28.25868481 0.139   2.5 0.149219113 1.41     28.39800454 0.244   3         28.64181406 0.139   4         28.78113379 0.139   4.5 0 1     28.92045351 0.186 27 1     -0.12494 0.75 29.10621315 0.093   1.5 0.301029996 2     29.19909297 0.116   2     -0.09691 0.8 29.31519274 0.151   2.5 -0.11350927 0.77     29.46612245 0.163   3     -0.03152 0.93 29.62866213 0.139   3.5 0.068185862 1.17     29.76798186 0.128   4     0.037426 1.09 29.89569161 0.116   4.5 0.041392685 1.1     30.01179138 0.151 28 1     -0.11351 0.77 30.16272109 0.151   1.5 0 1     30.31365079 0.070   2     0 1 30.38331066 0.081   2.25         30.4645805 0.139   2.5 0.037426498 1.09     30.60390023 0.139   3     0 1 30.74321995 0.139   3.5 0 1     30.88253968 0.116   4     0.079181 1.2 30.99863946 0.197   4.5 -0.22914799 0.59     31.19600907 0.128 29 1     0.187521 1.54 31.32371882 0.104   1.5 0.089905111 1.23     31.42820862 0.116   2     -0.04576 0.9 31.54430839 0.128   2.5 -0.04095861 0.91     31.67201814 0.139   3     -0.03621 0.92 31.81133787 0.151   3.5 -0.03621217 0.92     31.96226757 0.151   4     0 1 32.11319728 0.151   4.5 0 1     32.26412698 0.151 30 1     0 1 32.41505669 0.104   1.5 0.161368002 1.45     32.51954649 0.186   2     -0.25181 0.56 32.70530612 0.151   2.5 0.089905111 1.23     97  Event onset Interonset Interval Measure Beat BUR (in log) BUR UBR (in log) UBR 32.85623583 0.244   3         33.10004535 0.139   4         33.23936508 0.163   4.5 -0.07058107 0.85     33.40190476 0.139 31 1     0.068186 1.17 33.54122449 0.104   1.5 0.127104798 1.34     33.64571429 0.163   2     -0.19382 0.64 33.80825397 0.128   2.5 0.103803721 1.27     33.93596372 0.128   3     0 1 34.06367347 0.163   3.5 -0.1049644 0.7853     34.22621315 0.151   4     0.033223 1.0795 34.37714286 0.151   4.5 0 1     34.52807256 0.151 32 1     0 1 34.67900227 0.116   1.5 0.114510905 1.3017     34.79510204 0.139   2     -0.07857 0.8345 34.93442177 0.104   2.5 0.125968963 1.3365     35.03891156 0.116   3     -0.04743 0.89655 35.15501134 0.151   3.5 -0.11350927 0.77     35.30594104 0.163   4     -0.03152 0.93 35.46848073 0.139   4.5 0.068185862 1.17     35.60780045          Jim Blair’s performance calculations Event onset Interonset Interval Measure beat BUR(log) BUR  UBR(log) UBR                 0.429354 0.209 mm. 1 1           0.638229 0.302   1.5 -0.15989 0.692       0.939938 0.046   2       0.415548 2.60344 0.986354 0.070   2.25           1.055979 0.325   2.5 -0.44743 0.35692       1.380896 0.128   3       0.404663 2.539 1.508542 0.104   3.5 0.089905 1.23       1.612979 0.209   4       -0.25181 0.56 1.821854 0.139   4.5 0.177103 1.5035       1.961104 0.128 mm. 2 1       0.03579 1.0859 2.08875 0.197   1.5 -0.18729 0.6497       2.286021 0.058   2       0.187239 1.539 2.344042 0.070   2.25           2.413667 0.279   2.5 -0.3384 0.45878       2.692167 0.279   3           98  Event onset Interonset Interval Measure beat BUR(log) BUR  UBR(log) UBR 2.970667 0.128   4           3.098313 0.197   4.5 -0.18709 0.65       3.295583 0.139 mm. 3 1       0.152288 1.42 3.434833 0.209   1.5 -0.17393 0.67       3.643708 0.046   2       0.143015 1.39 3.690125 0.104   2.25           3.794563 0.174   2.5 -0.0655 0.86       3.968625 0.128   3       0.133539 1.36 4.096271 0.151   3.5 -0.07058 0.85       4.247125 0.174   4       -0.06048 0.87 4.421188 0.151   4.5 0.060698 1.15       4.572042 0.116 4 1       0.113943 1.3 4.688083 0.197   1.5 -0.22915 0.59       4.885354 0.128   2       0.187521 1.54 5.013 0.186   2.5 -0.16115 0.69       5.198667 0.313   3           5.511979 0.290   4           5.802083 0.116 5 1           5.918125 0.197   1.5 -0.23001 0.58883       6.115396 0.046   2       0.230007 1.69827 6.161813 0.070   2.25           6.231438 0.128   2.5 -0.38722 0.41       6.359083 0.128   3       0 1 6.486729 0.162   3.5 -0.10231 0.790123       6.649188 0.116   4       0.146128 1.4 6.765229 0.162   4.5 -0.14874 0.71       6.927688 0.186 6 1       -0.06048 0.87 7.113354 0.162   1.5 0.060698 1.15       7.275813 0.046   2       0.146128 1.4 7.322229 0.070   2.25           7.391854 0.244   2.5 -0.32331 0.475       7.635542 0.267   3           7.902438 0.162   4           8.064896 0.139   4.5 0.068186 1.17       8.204146 0.128 7 1       0.037426 1.09 8.331792 0.197   1.5 -0.18709 0.65       8.529063 0.058   2       0.113943 1.3 8.587083 0.093   2.25           8.679917 0.151   2.5 0 1       8.830771 0.139   3       0.037426 1.09 8.970021 0.174   3.5 -0.09691 0.8       9.144083 0.128   4       0.133539 1.36 99  Event onset Interonset Interval Measure beat BUR(log) BUR  UBR(log) UBR 9.271729 0.139   4.5 -0.03621 0.92       9.410979 0.139 8 1       0 1 9.550229 0.116   1.5 0.079181 1.2       9.666271 0.151   2       0.133539 1.36 9.817125 0.244   2.5 -0.20761 0.62       10.06081 0.255   3           10.3161 0.325   4           10.64102 0.116 9 1           10.75706 0.139   1.5 -0.08092 0.83       10.89631 0.174   2       -0.09691 0.8 11.07038 0.118   2.5 0.167317 1.47       11.18813 0.138   3       -0.0655 0.86 11.32567 0.116   3.5 0.075547 1.19       11.44171 0.162   4       -0.11351 0.77 11.60417 0.186   4.5 -0.06 0.87096       11.78983 0.116 10 1       0.205055 1.60345 11.90588 0.151   1.5 -0.11452 0.76821       12.05673 0.151   2       0 1 12.20758 0.116   2.5 0.113943 1.3       12.32363 0.151   3       -0.11351 0.77 12.47448 0.104   3.5 0.161368 1.45       12.57892 0.139   4       -0.12494 0.75 12.71817 0.162   4.5 -0.0655 0.86       12.88063 0.139 11 1       0.068186 1.17 13.01988 0.116   1.5 0.079181 1.2       13.13592 0.162   2       -0.14874 0.71 13.29838 0.116   2.5 0.146128 1.4       13.41442 0.139   3       -0.08092 0.83 13.55367 0.128   3.5 0.037426 1.09       13.68131 0.139   4       -0.03621 0.92 13.82056 0.151   4.5 -0.03621 0.92       13.97142 0.162 12 1       -0.03054 0.9321 14.13388 0.128   1.5 0.102296 1.2656       14.26152 0.070   2       -0.07177 0.84768 14.33115 0.081   2.25           14.41238 0.220   2.5 -0.16115 0.69       14.63285 0.244   3           14.87654 0.267   4           15.14344 0.151 13 1           15.29429 0.128   1.5 0.071882 1.18       15.42194 0.174   2       -0.13668 0.73 15.596 0.104   2.5 0.222716 1.67       100  Event onset Interonset Interval Measure beat BUR(log) BUR  UBR(log) UBR 15.70044 0.128   3       -0.09151 0.81 15.82808 0.116   3.5 0.041393 1.1       15.94413 0.174   4       -0.17393 0.67 16.11819 0.174   4.5 0 1       16.29225 0.116 14 1       0.176091 1.5 16.40829 0.139   1.5 -0.08092 0.83       16.54754 0.151   2       -0.03621 0.92 16.6984 0.151   2.5 0 1       16.84925 0.139   3       0.03583 1.086 16.9885 0.128   3.5 0.03583 1.086       17.11615 0.116   4       0.041393 1.1 17.23219 0.151   4.5 -0.11351 0.77       17.38304 0.116 15 1       0.113943 1.3 17.49908 0.116   1.5 0 1       17.61513 0.136   2       -0.06753 0.856 17.75067 0.143   2.5 -0.02319 0.948       17.89363 0.128   3       0.049218 1.12 18.02127 0.139   3.5 -0.03579 0.9209       18.16052 0.128   4       0.03583 1.086 18.28817 0.139   4.5 -0.03621 0.92       18.42742 0.151 16 1       -0.03598 0.9205 18.57827 0.116   1.5 0.114611 1.302       18.69431 0.070   2       0 1 18.76394 0.081   2.25           18.84517 0.232   2.5 -0.31876 0.48       19.07725 0.244   3           19.32094 0.267   4           19.58783 0.139 17 1           19.72708 0.174   1.5 -0.09691 0.8       19.90115 0.070   2       0.093422 1.24 19.97077 0.070   2.25           20.0404 0.116   2.5 0.079181 1.2       20.15644 0.139   3       -0.08092 0.83 20.29569 0.174   3.5 -0.09691 0.8       20.46975 0.116   4       0.176091 1.5 20.58579 0.151   4.5 -0.11351 0.77       20.73665 0.139 18 1       0.037426 1.09 20.8759 0.197   1.5 -0.14874 0.71       21.07317 0.046   2       0.152288 1.42 21.11958 0.093   2.25           21.21242 0.174   2.5 -0.09691 0.8       21.38648 0.255   3           101  Event onset Interonset Interval Measure beat BUR(log) BUR  UBR(log) UBR 21.64177 0.162   4           21.80423 0.139   4.5 0.068186 1.17       21.94348 0.128 19 1       0.037426 1.09 22.07113 0.162   1.5 -0.10237 0.79       22.23358 0.070   2       0.029384 1.07 22.30321 0.081   2.25           22.38444 0.151   2.5 0 1       22.53529 0.128   3       0.071882 1.18 22.66294 0.116   3.5 0.041393 1.1       22.77898 0.151   4       -0.11351 0.77 22.92983 0.139   4.5 0.037426 1.09       23.06908 0.139 20 1       0 1 23.20833 0.139   1.5 0 1       23.34758 0.128   2       0.037426 1.09 23.47523 0.174   2.5 -0.13077 0.74       23.64929 0.290   3           23.9394 0.244   4           24.18308 0.139 21 1           24.32233 0.174   1.5 -0.09753 0.79885       24.4964 0.046   2       0.136721 1.37 24.54281 0.081   2.25           24.62404 0.151   2.5 -0.07572 0.84       24.7749 0.116   3       0.113943 1.3 24.89094 0.128   3.5 -0.04096 0.91       25.01858 0.128   4       0 1 25.14623 0.128   4.5 0 1       25.27388 0.139 22 1       -0.03621 0.92 25.41313 0.186   1.5 -0.12494 0.75       25.59879 0.046   2       0.164353 1.46 25.64521 0.081   2.25           25.72644 0.162   2.5 -0.10791 0.78       25.8889 0.267   3           26.15579 0.116   4           26.27183 0.174   4.5 -0.17393 0.67       26.4459 0.116 23 1       0.176091 1.5 26.56194 0.186   1.5 -0.20761 0.62       26.7476 0.058   2       0.127105 1.34 26.80563 0.081   2.25           26.88685 0.151   2.5 -0.03621 0.92       27.03771 0.116   3       0.113943 1.3 27.15375 0.139   3.5 -0.08092 0.83       27.293 0.139   4       0 1 102  Event onset Interonset Interval Measure beat BUR(log) BUR  UBR(log) UBR 27.43225 0.139   4.5 0 1       27.5715 0.104 24 1       0.127105 1.34 27.67594 0.128   1.5 -0.09151 0.81       27.80358 0.162   2       -0.10237 0.79 27.96604 0.174   2.5 -0.03152 0.93       28.1401 0.279   3           28.4186 0.267   4           28.6855 0.128 25 1.5 0 1       28.81315 0.128   2       -0.07058 0.85 28.94079 0.151   2.5 0.071882 1.18       29.09165 0.128   3       0.041393 1.1 29.21929 0.116   3.5 0 1       29.33533 0.116   4       -0.04096 0.91 29.45138 0.128   4.5 -0.13077 0.74       29.57902 0.174 26 1       0.176091 1.5 29.75308 0.116   1.5 -0.08092 0.83       29.86913 0.139   2       -0.03621 0.92 30.00838 0.151   2.5 0.071882 1.18       30.15923 0.128   3       0 1 30.28688 0.128   3.5 0.041393 1.1       30.41452 0.116   4       -0.07572 0.84 30.53056 0.139   4.5 -0.03621 0.92       30.66981 0.151 27 1       0.113943 1.3 30.82067 0.116   1.5 0 1       30.93671 0.116   2       0.049218 1.12 31.05275 0.104   2.5 -0.04576 0.9       31.15719 0.116   3       -0.04096 0.91 31.27323 0.128   3.5 -0.03621 0.92       31.40088 0.139   4       -0.03621 0.92 31.54013 0.151   4.5 0.071882 1.18       31.69098 0.128 28 1       0 1 31.81863 0.128   1.5 -0.03621 0.92       31.94627 0.139   2       -0.03621 0.92 32.08552 0.058   2.25           32.14354 0.093   2.5 -0.03152 0.93       32.23638 0.162   3           32.39883 0.267   4           32.66573 0.244 29 1           32.90942 0.139   1.5 -0.03621 0.92       33.04867 0.151   2       -0.03152 0.93 33.19952 0.162   2.5 0.240549 1.74       33.36198 0.093   3       -0.09691 0.8 103  Event onset Interonset Interval Measure beat BUR(log) BUR  UBR(log) UBR 33.45481 0.116   3.5 -0.08092 0.83       33.57085 0.139   4       0 1 33.7101 0.139   4.5 0 1       33.84935 0.139 30 1       0.037426 1.09 33.9886 0.128   1.5 0 1       34.11625 0.128   2       -0.03621 0.92 34.2439 0.139   2.5 0.130334 1.35       34.38315 0.104   3       -0.16115 0.69 34.48758 0.151   3.5 0.113943 1.3       34.63844 0.116   4       0 1 34.75448 0.116   4.5 -0.04096 0.91       34.87052 0.128 31 1       0.089905 1.23 34.99817 0.104   1.5 -0.09151 0.81       35.1026 0.128   2       0.041393 1.1 35.23025 0.116   2.5 0.049218 1.12       35.34629 0.104   3       0.049218 1.12 35.45073 0.093   3.5 -0.13668 0.73       35.54356 0.128   4       -0.07058 0.85 35.67121 0.151   4.5 0.037426 1.09       35.82206 0.139 32 1       0.037426 1.09 35.96131 0.128   1.5 0.042733 1.1034       36.08896 0.116   2       -0.07857 0.8345 36.205 0.058   2.25           36.26302 0.081   2.5 -0.09151 0.81       36.34425 0.197   3           36.54152 0.209   4           36.7504 0.267 33 1           37.01729 0.151   1.5 0.071882 1.18       37.16815 0.128   2       -0.03621 0.92 37.29579 0.058   2.25           37.35381 0.081   2.5 0.049218 1.12       37.43504 0.116   3       0.049218 1.12 37.55108 0.104   3.5 -0.19249 0.64197       37.65552 0.162   4       0.068186 1.17 37.81798 0.139   4.5 0.079181 1.2       37.95723 0.116 34 1       -0.04096 0.91 38.07327 0.128   1.5 -0.07058 0.85       38.20092 0.151   2       0.033424 1.08 38.35177 0.070   2.25           38.4214 0.070   2.5 0 1       38.49102 0.139   3           38.63027 0.232   4           104  Event onset Interonset Interval Measure beat BUR(log) BUR  UBR(log) UBR 38.86235 0.151   4.5 0.071882 1.18       39.01321 0.128 35 1       0.041393 1.1 39.14085 0.116   1.5 -0.17393 0.67       39.2569 0.174   2       0.09691 1.25 39.43096 0.046   2.25           39.47738 0.093   2.5 -0.0655 0.86       39.57021 0.162   3       0 1 39.73267 0.128   3.5 -0.03621 0.92       39.86031 0.139   4       0.093422 1.24 39.99956 0.112   4.5 -0.07058 0.85       40.11188 0.131 36 1       -0.02687 0.94 40.24325 0.139   1.5 0.079181 1.2       40.3825 0.116   2       -0.11351 0.77 40.49854 0.151   2.5 -0.03152 0.93       40.6494 0.162   3           40.81185 0.278   4           41.09035 0.255 37 1           41.34565 0.116   1.5 -0.07856 0.83453       41.46169 0.174   2       0.09691 1.25 41.63575 0.046   2.25           41.68217 0.093   2.5 0.127105 1.34       41.775 0.104   3       -0.04743 0.89655 41.87944 0.116   3.5 -0.07857 0.8345       41.99548 0.139   4       -0.06651 0.858 42.13473 0.162   4.5 0.146128 1.4       42.29719 0.116 38 1       -0.04096 0.91 42.41323 0.128   1.5 -0.10237 0.79       42.54088 0.162   2       0.103804 1.27 42.70333 0.058   2.25           42.76135 0.070   2.5 -0.03621 0.92       42.83098 0.139   3           42.97023 0.244   4           43.21392 0.128   4.5 -0.1623 0.68817       43.34156 0.186 39 1       0.205053 1.60344 43.52723 0.116   1.5 -0.14506 0.71604       43.64327 0.162   2       0.029384 1.07 43.80573 0.070   2.25           43.87535 0.081   2.5 0.071882 1.18       43.95658 0.128   3       0 1 44.08423 0.128   3.5 0.090152 1.2307       44.21188 0.104   4       -0.19382 0.64 44.31631 0.162   4.5 0.068186 1.17       105  Event onset Interonset Interval Measure beat BUR(log) BUR  UBR(log) UBR 44.47877 0.139 40 1       0 1 44.61802 0.139   1.5 0.125969 1.3365       44.75727 0.104   2       -0.16115 0.69 44.86171 0.151   2.5 0 1       45.01256 0.151   3           45.16342 0.290   4           45.45352 0.279 41 1           45.73202 0.139   1.5 0.078558 1.19828       45.87127 0.116   2       -0.11452 0.76821 45.98731 0.151   2.5 0.071772 1.1797       46.13817 0.128   3       0.089905 1.23 46.26581 0.104   3.5 -0.09151 0.81       46.37025 0.128   4       -0.07058 0.85 46.4979 0.151   4.5 -0.03152 0.93       46.64875 0.162 42 1       0.145072 1.3966 46.81121 0.116   1.5 0 1       46.92725 0.116   2       -0.11453 0.7682 47.04329 0.151   2.5 0.071772 1.1797       47.19415 0.128   3       -0.03621 0.92 47.32179 0.139   3.5 0.079181 1.2       47.46104 0.116   4       0 1 47.57708 0.116   4.5 -0.04096 0.91       47.69313 0.128 43 1       0 1 47.82077 0.128   1.5 0.041393 1.1       47.94842 0.116   2       0 1 48.06446 0.116   2.5 -0.04096 0.91       48.1805 0.128   3       0.041393 1.1 48.30815 0.116   3.5 -0.04096 0.91       48.42419 0.128   4       0 1 48.55183 0.128   4.5 0 1       48.67948 0.128 44 1       0 1 48.80713 0.128   1.5 0 1       48.93477 0.128   2       -0.13077 0.74 49.06242 0.081   2.25           49.14365 0.093   2.5 0.060698 1.15       49.23648 0.151   3           49.38733 0.267   4           49.65423 0.255 45 1           49.90952 0.151   1.5 0.114611 1.302       50.06038 0.116   2       -0.11351 0.77 50.17642 0.151   2.5 0.161368 1.45       50.32727 0.104   3       -0.09151 0.81 106  50.43171 0.128   3.5 0 1       50.55935 0.128   4       0.042749 1.10344 50.687 0.116   4.5 -0.07831 0.835       50.80304 0.139 46 1       -0.07831 0.835 50.94229 0.116   1.5 0 1       51.05833 0.116   2       -0.04278 0.9062 51.17438 0.128   2.5 0.042772 1.1035       51.30202 0.116   3       -0.14509 0.716 51.41806 0.162   3.5 0.193125 1.56       51.58052 0.104   4       0 1 51.68496 0.104   4.5 -0.09151 0.81       51.7894 0.128 47 1       0 1 51.91704 0.128   1.5 0 1       52.04469 0.128   2       0.041393 1.1 52.17233 0.000   2.5 0 1       52.17233 0.116   3       0.049218 1.12 52.28838 0.116   3.5 0 1       52.40442 0.104   4       -0.04576 0.9 52.50885 0.104   4.5 -0.08092 0.83       52.61329 0.116 48 1       -0.03621 0.92 52.72933 0.139   1.5 0 1       52.86858 0.151   2       0.113943 1.3 53.01944 0.151   2.25           53.17029 0.058   2.5 -0.22915 0.59       53.22831 0.058   3           53.28633 0.197   4           53.4836 0.290         Hanneke Cassel’s performance calculations Event onset Interonset Interval Measure Beat BUR (log) BUR  UBR (log) UBR 0.09288         0.406349 0.313        0.557279 0.151        0.754649 0.197 mm2 1           0.928798 0.174   1.5 0.054357666 1.13333334       0.975238 0.046   2       0.064458 1.16 1.079728 0.104   2.25           1.242268 0.163   2.5 -0.03621217 0.92       1.404807 0.163   3       0 1 1.578957 0.174   3.5 -0.03151705 0.93       1.741497 0.163   4       0.029384 1.07 107  Event onset Interonset Interval Measure Beat BUR (log) BUR  UBR (log) UBR 1.880816 0.139   4.5 0.068185862 1.17       2.054966 0.174 mm3 1       -0.10791 0.78 2.194286 0.139   1.5 0.096910013 1.25       2.240726 0.046   2       0.079181 1.2 2.310385 0.070   2.25           2.507755 0.197   2.5 -0.22914799 0.59       2.798005 0.290   3           2.960544 0.163   4           3.088254 0.128   4.5 0.103803721 1.27       3.239184 0.151 mm4 1       -0.07058 0.85 3.401723 0.163   1.5 -0.03151705 0.93       3.448163 0.046   2       0.146128 1.4 3.517823 0.070   2.25           3.680363 0.163   2.5 -0.14709324 0.7127       3.819683 0.139   3       0.069298 1.173 3.959002 0.139   3.5 0 1       4.121542 0.163   4       -0.06905 0.853 4.249252 0.128   4.5 0.103803721 1.27       4.388571 0.139 mm5 1       -0.03621 0.92 4.539501 0.151   1.5 -0.03621217 0.92       4.678821 0.139   2       0.037426 1.09 4.841361 0.163   2.5 -0.07058107 0.85       5.01551 0.174   3       0.033424 1.08 5.16644 0.151   3.5 0 1       5.30576 0.139   4       -0.03152 0.93 5.468299 0.163   4.5 -0.06905097 0.853       5.616327 0.148 mm6 1       0.042182 1.102 5.735329 0.119   1.5 0.09482038 1.244       5.781769 0.046   2       0.012837 1.03 5.851429 0.070   2.25           6.025578 0.174   2.5 -0.1739252 0.67       6.164898 0.139   3       0.09691 1.25 6.327438 0.163   3.5 -0.06905097 0.853       6.478367 0.151   4       0.033424 1.08 6.606077 0.128   4.5 0.071882007 1.18       6.768617 0.163 mm7 1       -0.10237 0.79 6.896327 0.128   1.5 0.103803721 1.27       6.954376 0.058   2       0 1 7.024036 0.070   2.25           7.174966 0.151   2.5 -0.07058107 0.85       7.453605 0.279   3           7.604535 0.151   4           108  Event onset Interonset Interval Measure Beat BUR (log) BUR  UBR (log) UBR 7.743855 0.139   4.5 0.037426498 1.09       7.906395 0.163 mm8 1       -0.07058 0.85 8.034104 0.128   1.5 0.103803721 1.27       8.301134 0.267   2           8.452063 0.151   3           8.591383 0.139   3.5 0.037426498 1.09       8.753923 0.163   4       -0.07058 0.85 8.893243 0.139   4.5 0.068185862 1.17       9.055782 0.163 mm9 1       -0.07058 0.85 9.195102 0.139   1.5 0.068185862 1.17       9.346032 0.151   2       -0.03621 0.92 9.473741 0.128   2.5 0.071882007 1.18       9.752381 0.279   3           9.914921 0.163   4           10.04263 0.128   4.5 0.103803721 1.27       10.34449 0.302 mm. 10 1           10.49542 0.151   2           10.62313 0.128   2.5 0.071882007 1.18       10.76245 0.139   3       -0.03621 0.92 10.90177 0.139   3.5 0 1       11.06431 0.163   4       -0.07058 0.85 11.20363 0.139   4.5 0.068185862 1.17       11.34295 0.139 mm. 11 1       0 1 11.47066 0.128   1.5 0.025305865 1.06       11.62159 0.151   2       -0.07058 0.85 11.7493 0.128   2.5 0.071882007 1.18       12.03955 0.290   3           12.20209 0.163   4           12.35302 0.151   4.5 0.033423755 1.08       12.51556 0.163 mm. 12 1       -0.03339 0.926 12.64327 0.128   1.5 0.103803721 1.27       12.8058 0.163   2       -0.09909 0.796 12.93351 0.128   2.5 0.103803721 1.27       13.08444 0.151   3       -0.06651 0.858 13.21215 0.128   3.5 0.071882007 1.18       13.37469 0.163   4       -0.10237 0.79 13.5024 0.128   4.5 0.103803721 1.27       13.68816 0.186 mm. 13 1       -0.16115 0.69 13.81587 0.128   1.5 0.204119983 1.6       13.86231 0.046   2       0.30103 2 13.94358 0.081   2.25           14.09451 0.151   2.5 -0.60205999 0.25       109  Event onset Interonset Interval Measure Beat BUR (log) BUR  UBR (log) UBR 14.37315 0.279   3           14.53569 0.163   4 0.103803721 1.27       14.6634 0.128   4.5           14.98848 0.453 mm. 14 1           15.13941 0.151   2           15.26712 0.128   2.5 0.071882007 1.18       15.40644 0.139   3       -0.03621 0.92 15.53415 0.128   3.5 0.025305865 1.06       15.68508 0.151   4       -0.02228 0.95 15.81279 0.128   4.5 -0.03151705 0.93       15.97533 0.163 mm. 15 1       0.103804 1.27 16.11465 0.139   1.5 -0.03621217 0.92       16.25397 0.139   2       0 1 16.4049 0.151   2.5 -0.03621217 0.92       16.70676 0.302   3           16.85769 0.151   4           17.00862 0.151   4.5 0 1       17.17116 0.163 mm. 16 1       -0.03152 0.93 17.31048 0.139   1.5 0.103803721 1.27       17.46141 0.151   2       -0.03621 0.92 17.58912 0.128   2.5 0.071882007 1.18       17.72844 0.139   3       -0.03621 0.92 17.86776 0.139   3.5 0 1       18.01868 0.151   4       -0.03621 0.92 18.16961 0.151   4.5 0 1       18.34376 0.174 mm. 17 1       -0.06048 0.87 18.48308 0.139   1.5 0.096910013 1.25       18.6224 0.139   2       0 1 18.78494 0.163   2.5 -0.07058107 0.85       18.92426 0.139   3       0 1 19.06358 0.139   3.5 0.149219113 1.41       19.22612 0.163   4       -0.14874 0.71 19.36544 0.139   4.5 0.068185862 1.17       19.50476 0.139 mm. 18 1       0 1 19.64408 0.139   1.5 0 1       19.69052 0.046   2       0.178977 1.51 19.73696 0.046   2.25           19.92272 0.186   2.5 -0.31875876 0.48       20.06204 0.139   3       0.113943 1.3 20.22458 0.163   3.5 0.037426498 1.09       20.37551 0.151   4       -0.03621 0.92 20.52644 0.151   4.5 0 1       110  Event onset Interonset Interval Measure Beat BUR (log) BUR  UBR (log) UBR 20.66576 0.139 mm. 19 1       0.037426 1.09 20.80508 0.139   1.5 0 1       20.86313 0.058   2       0.078457 1.198 20.92118 0.058   2.25           21.10694 0.186   2.5 -0.20760831 0.62       21.38558 0.279   3           21.54812 0.163   4           21.67583 0.128   4.5 0.103803721 1.27       21.83837 0.163 mm. 20 1       -0.10237 0.79 21.97769 0.139   1.5 0.068185862 1.17       22.02413 0.046   2       0.127105 1.34 22.08218 0.058   2.25           22.25633 0.174   2.5 -0.22184875 0.6       22.40726 0.151   3       0.060698 1.15 22.54658 0.139   3.5 0.037426498 1.09       22.69751 0.151   4       -0.03621 0.92 22.82522 0.128   4.5 0.071882007 1.18       22.98776 0.163 mm. 21 1       -0.10237 0.79 23.11546 0.128   1.5 0.103803721 1.27       23.26639 0.151   2       -0.07058 0.85 23.41732 0.151   2.5 0 1       23.56825 0.151   3       0 1 23.70757 0.139   3.5 0.037426498 1.09       23.8585 0.151   4       -0.03621 0.92 23.99782 0.139   4.5 0.037426498 1.09       24.13714 0.139 mm. 22 1       0 1 24.28807 0.151   1.5 -0.03621217 0.92       24.33451 0.046   2       0.161368 1.45 24.39256 0.058   2.25           24.56671 0.174   2.5 -0.22184875 0.6       24.72925 0.163   3       0.029384 1.07 24.85696 0.128   3.5 0.103803721 1.27       25.0195 0.163   4       -0.10237 0.79 25.15882 0.139   4.5 0.068185862 1.17       25.33297 0.174 mm. 23 1       -0.09691 0.8 25.46068 0.128   1.5 0.133538908 1.36       25.49551 0.035   2       0.139879 1.38 25.55356 0.058   2.25           25.73932 0.186   2.5 -0.30103 0.5       26.01796 0.279   3           26.16889 0.151   4           26.30821 0.139   4.5 0.037426498 1.09       111  Event onset Interonset Interval Measure Beat BUR (log) BUR  UBR (log) UBR 26.45914 0.151 mm. 24 1       -0.03621 0.92 26.59846 0.139   1.5 0.037426498 1.09       26.88871 0.290   2           27.03964 0.151   3           27.17896 0.139   3.5 0.103803721 1.27       27.35311 0.174   4       -0.16115 0.69 27.48082 0.128   4.5 0.161368002 1.45       27.62014 0.139 mm. 25 1       0 1 27.74785 0.128   1.5 0 1       27.88717 0.139   2       -0.03574 0.921 28.04971 0.163   2.5 -0.06905097 0.853       28.32834 0.279   3           28.47927 0.151   4           28.61859 0.139   4.5 0.037426498 1.09       28.90884 0.290 mm. 26 1           29.03655 0.128   2           29.19909 0.163   2.5 -0.10237291 0.79       29.35002 0.151   3       0.033424 1.08 29.50095 0.151   3.5 0 1       29.65188 0.151   4       0 1 29.80281 0.151   4.5 0 1       29.94213 0.139 mm. 27 1       0 1 30.06984 0.128   1.5 0.037426498 1.09       30.20916 0.139   2       -0.03621 0.92 30.34848 0.139   2.5 0 1       30.63873 0.290   3           30.80127 0.163   4           30.94059 0.139   4.5 0.068185862 1.17       31.10313 0.163 mm. 28 1       -0.06905 0.853 31.23084 0.128   1.5 0.103803721 1.27       31.38177 0.151   2       -0.06651 0.858 31.52109 0.139   2.5 0.037426498 1.09       31.67202 0.151   3       -0.03621 0.92 31.79973 0.128   3.5 0.071882007 1.18       31.97388 0.174   4       -0.13077 0.74 32.1132 0.139   4.5 0.176091259 1.5       32.28735 0.174 mm. 29 1       -0.22915 0.59 32.40345 0.116   1.5 0.230448921 1.7       32.44989 0.046   2       0.045323 1.11 32.50794 0.058   2.25 -0.19382003 0.64       32.67048 0.163   2.5           32.98395 0.313   3           112  Event onset Interonset Interval Measure Beat BUR (log) BUR  UBR (log) UBR 33.13488 0.151   4           33.26259 0.128   4.5 0.071882007 1.18       33.57605 0.313 mm. 30 1           33.71537 0.139   2           33.8663 0.151   2.5 -0.03621217 0.92       34.00562 0.139   3       0.033424 1.08 34.14494 0.139   3.5 0 1       34.31909 0.174   4       0.037426 1.09 34.45841 0.139   4.5 0.096910013 1.25       34.60934 0.151 mm. 31 1       -0.03621 0.92 34.73705 0.128   1.5 0.071882007 1.18       34.87637 0.139   2       -0.03621 0.92 35.01569 0.139   2.5 0 1       35.31755 0.302   3           35.48009 0.163   4           35.6078 0.128   4.5 0.103803721 1.27       35.77034 0.163 mm. 32 1       -0.10237 0.79 35.89805 0.128   1.5 0.103803721 1.27       36.02576 0.128   2       0 1 36.1883 0.163   2.5 -0.10237291 0.79       36.33923 0.151   3       0.033424 1.08 36.46694 0.128   3.5 0.071882007 1.18       36.62948 0.163   4       -0.10237 0.79 36.75719 0.128   4.5 0.103803721 1.27       36.93134 0.174 mm. 33 1       -0.13077 0.74 37.04744 0.116   1.5 0.176091259 1.5       37.19837 0.151   2       -0.11351 0.77 37.37252 0.174   2.5 -0.06048075 0.87       37.51184 0.139   3       0.09691 1.25 37.66277 0.151   3.5 -0.03621217 0.92       37.82531 0.163   4       -0.03152 0.93 38.0459 0.221   4.5 -0.13667714 0.73        Bruce Macgregor’s performance calculations Event onset Interonset interval measure beat BUR (log) BUR  UBR(log) UBR 0.557279         1.044898 0.488        1.277098 0.232 mm. 1 1      1.451247 0.174  1.5 0.124939 1.333333    1.532517 0.081  2    0.062148 1.153846 113  Event onset Interonset interval measure beat BUR (log) BUR  UBR(log) UBR 1.602177 0.070  2.25      1.799546 0.197  2.5 -0.11651 0.764706    1.985306 0.186  3    0.026329 1.0625 2.147846 0.163  3.5 0.057992 1.142857    2.298776 0.151  4    0.032185 1.076923 2.461315 0.163  4.5 -0.03218 0.928571    2.635465 0.174 mm. 2 1    -0.02687 0.94 2.809615 0.174  1.5 0 1    2.856054 0.046  2    0.221849 1.666667 2.914104 0.058  2.25      3.111474 0.197  2.5 -0.27621 0.529412    3.274014 0.163  3    0.084321 1.214286 3.448163 0.174  3.5 -0.02996 0.933333    3.588209 0.140  4    0.094654 1.243523 3.750023 0.162  4.5 -0.06275 0.865471    3.900952 0.151 mm. 3 1    0.030242 1.072115 4.075102 0.174  1.5 -0.06215 0.866667    4.133152 0.058  2    0.177791 1.505882 4.190748 0.058  2.25      4.364626 0.174  2.5 -0.17711 0.665102    4.527891 0.163  3    0.02735 1.065 4.681088 0.153  3.5 0.027643 1.065719    4.829751 0.149  4    0.013051 1.030506 4.98068 0.151  4.5 -0.00657 0.984976    5.13161 0.151 mm. 4 1    0 1 5.293175 0.162  1.5 -0.02957 0.934175    5.427959 0.135  2    0.078706 1.198688 5.597664 0.170  2.5 -0.10005 0.794228    5.746939 0.149  3    0.05571 1.136868 5.889615 0.143  3.5 0.019635 1.046249    6.031179 0.142  4    0.003395 1.007849 6.188118 0.157  4.5 -0.04478 0.902037    6.315828 0.128 mm. 5 1    0.089506 1.228871 6.513197 0.197  1.5 -0.18906 0.647059    6.559637 0.046  2    0.276206 1.888889 6.617687 0.058  2.25      6.803447 0.186  2.5 -0.24988 0.5625    6.942766 0.139  3    0.124939 1.333333 7.105306 0.163  3.5 -0.06695 0.857143    7.233016 0.128  4    0.104735 1.272727 7.372336 0.139  4.5 -0.03779 0.916667    7.523265 0.151 mm. 6 1    -0.03476 0.923077 114  Event onset Interonset interval measure beat BUR (log) BUR  UBR(log) UBR 7.685805 0.163  1.5 -0.03218 0.928571    7.743855 0.058  2    0.191886 1.556 7.790295 0.046  2.25      7.964444 0.174  2.5 -0.22185 0.6    8.115374 0.151  3    0.062148 1.153846 8.254694 0.139  3.5 0.034762 1.083333    8.370794 0.116  4    0.079181 1.2 8.544943 0.174  4.5 -0.17609 0.666667    8.684263 0.139 mm. 7 1    0.09691 1.25 8.846803 0.163  1.5 -0.06695 0.857143    8.904853 0.058  2    0.146128 1.4 8.962902 0.058  2.25      9.125442 0.163  2.5 -0.14613 0.714286    9.276372 0.151  3    0.032185 1.076923 9.415692 0.139  3.5 0.034762 1.083333    9.543764 0.128  4    0.036557 1.087819 9.694331 0.151  4.5 -0.07027 0.850602    9.845261 0.151 mm. 8 1    -0.00105 0.997596 9.99619 0.151  1.5 0 1    10.1239 0.128  2    0.072551 1.181818 10.27483 0.151  2.5 -0.07255 0.846154    10.41415 0.139  3    0.034762 1.083333 10.55347 0.139  3.5 0 1    10.69279 0.139  4    0 1 10.85533 0.163  4.5 -0.06695 0.857143    11.01787 0.163 mm. 9 1    0 1 11.20363 0.186  1.5 -0.05799 0.875    11.25007 0.046  2    0.30103 2 11.29651 0.046  2.25      11.47066 0.174  2.5 -0.27679 0.5287    11.60998 0.139  3    0.09691 1.25 11.76091 0.151  3.5 -0.03476 0.923077    11.90023 0.139  4    0.034762 1.083333 12.05116 0.151  4.5 -0.03476 0.923077    12.16726 0.116 mm. 10 1    0.113943 1.3 12.34141 0.174  1.5 -0.17609 0.666667    12.38785 0.046  2    0.221849 1.666667 12.4459 0.058  2.25      12.63166 0.186  2.5 -0.24988 0.5625    12.77098 0.139  3    0.124939 1.333333 12.91029 0.139  3.5 0 1    13.038 0.128  4    0.037789 1.090909 115  Event onset Interonset interval measure beat BUR (log) BUR  UBR(log) UBR 13.20054 0.163  4.5 -0.10474 0.785714    13.31664 0.116 mm. 11 1    0.146128 1.4 13.49079 0.174  1.5 -0.17609 0.666667    13.53723 0.046  2    0.176091 1.5 13.60689 0.070  2.25      13.76943 0.163  2.5 -0.14752 0.712    13.89714 0.128  3    0.104735 1.272727 14.05968 0.163  3.5 -0.10474 0.785714    14.199 0.139  4    0.066947 1.166667 14.36154 0.163  4.5 -0.06695 0.857143    14.41959 0.058 mm. 12 1    0.104735 1.272727 14.48925 0.070  1.125      14.61696 0.128  1.5 0 1    14.75628 0.139  2    -0.03779 0.916667 14.90721 0.151  2.5 -0.03476 0.923077    15.04653 0.139  3    0.034762 1.083333 15.19746 0.151  3.5 -0.03476 0.923077    15.32517 0.128  4    0.072551 1.181818 15.49932 0.174  4.5 -0.1347 0.733333    15.62703 0.128 mm. 13 1    0.134699 1.363636 15.80118 0.174  1.5 -0.1347 0.733333    15.84762 0.046  2    0.221849 1.666667 15.90567 0.058  2.25      16.07982 0.174  2.5 -0.22185 0.6    16.23075 0.151  3    0.062148 1.153846 16.35846 0.128  3.5 0.072551 1.181818    16.48617 0.128  4    0 1 16.6371 0.151  4.5 -0.07255 0.846154    16.77642 0.139 mm. 14 1    0.034762 1.083333 16.92927 0.153  1.5 -0.04027 0.911437    16.99297 0.064  2    0.060827 1.150341 17.06215 0.069  2.25      17.2176 0.155  2.5 -0.06811 0.85485    17.34531 0.128  3    0.085345 1.217152 17.48463 0.139  3.5 -0.03779 0.916667    17.60073 0.116  4    0.079181 1.2 17.78649 0.186  4.5 -0.20412 0.625    17.9142 0.128 mm. 15 1    0.162727 1.454545 18.06358 0.149  1.5 -0.06809 0.854888    18.11156 0.048  2    0.148879 1.408896 18.16961 0.058  2.25      18.32934 0.160  2.5 -0.17794 0.663827    116  18.45927 0.130  3    0.089665 1.229319 18.61079 0.152  3.5 -0.06675 0.857528    18.75011 0.139  4    0.036455 1.087565 18.88943 0.139  4.5 0 1    19.01714 0.128 mm. 16 1    0.037789 1.090909 19.17968 0.163  1.5 -0.10474 0.785714    19.28417 0.104  2    0.191886 1.555556 19.44671 0.163  2.5 -0.19189 0.642857    19.57442 0.128  3    0.104735 1.272727 19.74857 0.174  3.5 -0.1347 0.733333    19.86467 0.116  4    0.176091 1.5 20.12009 0.255  4.5 -0.34242 0.454545    20.35229 0.232          Farquhar MacRae’s performance calculations Event onset Interonset Interval Measure Beat BUR (log) BUR  UBR (log) UBR 0.092833333 0.302        0.394541666 0.139        0.533791666 0.162 1 1           0.69625 0.130   1.5 0.096798643 1.250       0.82625 0.114   2       0.058230636 1.143 0.9399375 0.128   2.5 0 0.891       1.067583333 0.128   3       0 1.000 1.195229166 0.116   3.5 0.041392683 1.100       1.311270833 0.139   4       -0.079181245 0.833 1.450520833 0.128   4.5 0.037788562 1.091       1.578166666 0.128 2 1       -3.40234E-09 1.000 1.7058125 0.116   1.5 0.04139269 1.100       1.821854166 0.093   2       0.096910007 1.250 1.9146875 0.174   2.5 -0.273001269 0.533       2.08875 0.232   3           2.320833333 0.146   4           2.466333333 0.129   4.5 0.052834751 1.129       2.595166666 0.120 3 1       0.030093664 1.072 2.715375 0.115   1.5 0.019787826 1.047       2.830229166 0.098   2       0.06809055 1.170 2.928416666 0.123   2.5 -0.099537489 0.795       3.051895833 0.123   3       0.00338375 1.008 3.174416666 0.117   3.5 0.018480193 1.043       3.291833333 0.120   4       -0.00869686 0.980 117  Event onset Interonset Interval Measure Beat BUR (log) BUR  UBR (log) UBR 3.411625 0.139   4.5 -0.065368595 0.860       3.550875 0.128 4 1       0.037788562 1.091 3.678520833 0.122   1.5 0.018609777 1.044       3.8008125 0.110   2       0.04682749 1.114 3.910604166 0.116   2.5 -0.024044584 0.946       4.026645833 0.255   3           4.2819375 0.116   4           4.397979166 0.131   4.5 -0.052380985 0.886       4.528895833 0.124 5 1       0.022261846 1.053 4.653270833 0.115   1.5 0.034586337 1.083       4.768125 0.110   2       0.019577381 1.046 4.877916666 0.116   2.5 -0.024044584 0.946       4.993958333 0.135   3       -0.065987809 0.859 5.129041666 0.124   3.5 0.035868674 1.086       5.253416666 0.132   4       -0.026183423 0.941 5.385520833 0.126   4.5 0.018969064 1.045       5.511979166 0.116 6 1       0.037333494 1.090 5.628020833 0.116   1.5 0 1.000       5.7440625 0.085   2       0.13317728 1.359 5.829458333 0.166   2.5 -0.289651389 0.513       5.995833333 0.236   3           6.2314375 0.128   4           6.359083333 0.128   4.5 -0.001980179 0.995       6.4873125 0.115 7 1       0.045561538 1.111 6.602770833 0.111   1.5 0.018326704 1.043       6.713458333 0.098   2       0.052042376 1.127 6.811645833 0.128   2.5 -0.113950439 0.769       6.939291666 0.125   3       0.008084454 1.019 7.064583333 0.118   3.5 0.02458577 1.058       7.182979166 0.116   4       0.008722458 1.020 7.299020833 0.123   4.5 -0.023817466 0.947       7.421604166 0.121 8 1       0.005272339 1.012 7.542708333 0.115   1.5 0.02301233 1.054       7.6575625 0.113   2       0.006028662 1.014 7.770833333 0.120   2.5 -0.025063152 0.944       7.890833333 0.302   3           8.192541666 0.093   4           8.285375 0.116   4.5 -0.096910007 0.800       8.401416666 0.274 9 1           8.675625 0.112   2           8.7876875 0.127   2.5 -0.05441465 0.882       8.914708333 0.121   3       0.021912895 1.052 118  Event onset Interonset Interval Measure Beat BUR (log) BUR  UBR (log) UBR 9.035479166 0.109   3.5 0.046115573 1.112       9.144083333 0.104   4       0.016990022 1.040 9.248520833 0.120   4.5 -0.061078107 0.869       9.368729166 0.123 10 1       -0.011659116 0.974 9.492208333 0.116   1.5 0.026979732 1.064       9.60825 0.139   2       -0.079181245 0.833 9.7475 0.119   2.5 0.068400334 1.171       9.866458333 0.115   3       0.013910977 1.033 9.981666666 0.114   3.5 0.004737801 1.011       10.095625 0.116   4       -0.007867864 0.982 10.21166667 0.122   4.5 -0.02278291 0.949       10.33395833 0.121 11 1       0.003193086 1.007 10.45535417 0.111   1.5 0.040105201 1.097       10.56604167 0.133   2       -0.079753062 0.832 10.69904167 0.134   2.5 -0.002915424 0.993       10.8329375 0.121   3       0.042563285 1.103 10.95433333 0.111   3.5 0.040105201 1.097       11.06502083 0.119   4       -0.032587367 0.928 11.18433333 0.132   4.5 -0.043270651 0.905       11.31614583 0.148 12 1       -0.049938161 0.891 11.46402083 0.088   1.5 0.223565331 1.673       11.55239583 0.087   2       0.008895127 1.021 11.63897917 0.116   2.5 -0.127179659 0.746       11.75502083 0.249   3           12.00427083 0.105   4           12.10939583 0.141   4.5 -0.127705568 0.745       12.25045833 0.236 13 1           12.48608333 0.147   2           12.63277083 0.126   2.5 0.067533153 1.168       12.75833333 0.111   3       0.054761376 1.134 12.86902083 0.116   3.5 -0.020515381 0.954       12.9850625 0.139   4       -0.079181245 0.833 13.1243125 0.116   4.5 0.079181249 1.200       13.24035417 0.116 14 1       -3.74258E-09 1.000 13.35639583 0.123   1.5 -0.026979732 0.940       13.479875 0.130   2       -0.021443935 0.952 13.60960417 0.123   2.5 0.022470984 1.053       13.73279167 0.117   3       0.021530963 1.051 13.85002083 0.110   3.5 0.0284663 1.068       13.9598125 0.116   4       -0.024044576 0.946 14.07585417 0.116   4.5 -3.74258E-09 1.000       14.19189583 0.128 15 1       -0.041392683 0.909 119  Event onset Interonset Interval Measure Beat BUR (log) BUR  UBR (log) UBR 14.31954167 0.116   1.5 0.041392683 1.100       14.43558333 0.139   2       -0.079181245 0.833 14.57483333 0.128   2.5 0.037788562 1.091       14.70247917 0.116   3       0.041392683 1.100 14.81852083 0.116   3.5 -6.65386E-15 1.000       14.9345625 0.139   4       -0.079181245 0.833 15.0738125 0.116   4.5 0.079181249 1.200       15.18985417 0.116 16 1       -3.74257E-09 1.000 15.30589583 0.111   1.5 0.020515381 1.048       15.41658333 0.133   2       0 0.832 15.54958333 0.116   2.5 0.059237682 1.146       15.665625 0.104   3       0 1.111 15.7700625 0.128   3.5 -0.087150175 0.818       15.89770833 0.124   4       0.012001618 1.028 16.021875 0.131   4.5 -0.023680478 0.947       16.153 0.128 17 1       0.011678859 1.027 16.28064583 0.120   1.5 0.027127093 1.064       16.4005625 0.103   2       0.067538226 1.168 16.50320833 0.114   2.5 -0.045404764 0.901       16.61716667 0.128   3       -0.049260558 0.893 16.7448125 0.104   3.5 0.087150178 1.222       16.84925 0.139   4       -0.124938737 0.750 16.9885 0.128   4.5 0.037788562 1.091       17.11614583 0.116 18 1       0.041392683 1.100 17.2321875 0.116   1.5 3.74256E-09 1.000       17.34822917 0.093   2       0.096910007 1.250 17.4410625 0.151   2.5 -0.21085336 0.615       17.59191667 0.232   3           17.824 0.247   4   0.940       18.07095833 0.120 19 1           18.19116667 0.103   1.5 0.068064694 1.170       18.2939375 0.099   2       0.017699427 1.042 18.39260417 0.128   2.5 -0.111836192 0.773       18.52025 0.135   3       -0.024595123 0.945 18.65533333 0.111   3.5 0.086503189 1.220       18.76602083 0.110   4       0.003529199 1.008 18.8758125 0.122   4.5 -0.046827482 0.898       18.99810417 0.114 20 1       0.03065077 1.073 19.1120625 0.119   1.5 -0.018876894 0.957       19.23108333 0.117   2       0.006587306 1.015 19.3483125 0.135   2.5 -0.061566089 0.868       19.48339583 0.232   3           120  Event onset Interonset Interval Measure Beat BUR (log) BUR  UBR (log) UBR 19.71547917 0.116   4           19.83152083 0.133   4.5 -0.059237682 0.872       19.96452083 0.122 21 1       0.036454776 1.088 20.0868125 0.116   1.5 0.02278291 1.054       20.20285417 0.093   2       0.096910007 1.250 20.2956875 0.116   2.5 -0.096910007 0.800       20.41172917 0.128   3       -0.04139269 0.909 20.539375 0.116   3.5 0.04139269 1.100       20.65541667 0.128   4       -0.04139269 0.909 20.7830625 0.116   4.5 0.04139269 1.100       20.89910417 0.116 22 1       0 1.000 21.01514583 0.116   1.5 -0.000779003 0.998       21.13139583 0.104   2       0.047403695 1.115 21.235625 0.139   2.5 -0.125805937 0.749       21.374875 0.232   3           21.60695833 0.101   4           21.708125 0.138   4.5 -0.135954799 0.731       21.84647917 0.132 23 1       0.021035644 1.050 21.97829167 0.116   1.5 0.055342638 1.136       22.09433333 0.093   2       0.096910016 1.250 22.18716667 0.116   2.5 -0.096910016 0.800       22.30320833 0.128   3       -0.041392683 0.909 22.43085417 0.116   3.5 0.041392683 1.100       22.54689583 0.114   4       0.008901243 1.021 22.66058333 0.114   4.5 0 0.995       22.7748125 0.120 24 1       -0.022157565 0.950 22.89502083 0.132   1.5 -0.041392687 0.909       23.02725 0.123   2       0 1.074 23.1503125 0.116   2.5 0.025511778 1.061       23.26635417 0.255   3         0.455 23.52164583 0.104   4           23.62608333 0.104   4.5 0 1.000       23.73052083 0.255 25 1           23.9858125 0.116   2           24.10185417 0.116   2.5 -3.74259E-09 1.000       24.21789583 0.093   3       0.096910016 1.250 24.31072917 0.116   3.5 -0.096910016 0.800       24.42677083 0.139   4       -0.079181245 0.833 24.56602083 0.128   4.5 0.037788562 1.091       24.69366667 0.116 26 1       0.041392683 1.100 24.80970833 0.104   1.5 0.045757492 1.111       24.91414583 0.128   2       -0.087150175 0.818 121  Event onset Interonset Interval Measure Beat BUR (log) BUR  UBR (log) UBR 25.04179167 0.124   2.5 0.011273548 1.026       25.16616667 0.119   3       0.018047148 1.042 25.28547917 0.116   3.5 0.012071987 1.028       25.40152083 0.104   4       0.045757492 1.111 25.50595833 0.116   4.5 -0.045757492 0.900       25.622 0.109 27 1       0.025282479 1.060 25.73147917 0.123   1.5 -0.049173751 0.893       25.85408333 0.142   2       -0.063017837 0.865 25.99583333 0.125   2.5 0.054106674 1.133       26.12097917 0.116   3       0.032802434 1.078 26.23702083 0.116   3.5 -1.33077E-14 1.000       26.3530625 0.126   4       -0.036115475 0.920 26.47916667 0.110   4.5 0.058761359 1.145       26.5893125 0.134 28 1       -0.083851925 0.824 26.72291667 0.101   1.5 0.119532274 1.317       26.824375 0.100   2       0.007556271 1.018 26.92408333 0.134   2.5 -0.128980606 0.743       27.05827083 0.257   3           27.315375 0.117   4           27.43225 0.104   4.5 0.048865157 1.119       27.5366875 0.220 29 1           27.75716667 0.116   2           27.87320833 0.116   2.5 1.33077E-14 1.000       27.98925 0.116   3       3.74256E-09 1.000 28.10529167 0.133   3.5 -0.059237686 0.872       28.23829167 0.122   4       0.036454776 1.088 28.36058333 0.136   4.5 -0.046075511 0.899       28.4965625 0.131 30 1       0.01647744 1.039 28.62747917 0.104   1.5 0.09813847 1.254       28.73191667 0.116   2       -0.045757492 0.900 28.84795833 0.128   2.5 -0.041392683 0.909       28.97560417 0.104   3       0.087150175 1.222 29.08004167 0.104   3.5 0 1.000       29.18447917 0.128   4       -0.087150178 0.818 29.312125 0.116   4.5 0.04139269 1.100       29.42816667 0.104 31 1       0.045757488 1.111 29.53260417 0.116   1.5 -0.045757492 0.900       29.64864583 0.128   2       -0.041392683 0.909 29.77629167 0.128   2.5 -3.40235E-09 1.000       29.9039375 0.116   3       0.04139269 1.100 30.01997917 0.116   3.5 -3.74259E-09 1.000       30.13602083 0.139   4       -0.079181245 0.833 122  Event onset Interonset Interval Measure Beat BUR (log) BUR  UBR (log) UBR 30.27527083 0.116   4.5 0.079181245 1.200       30.3913125 0.116 32 1       3.74259E-09 1.000 30.50735417 0.116   1.5 -3.74259E-09 1.000       30.62339583 0.139   2       -0.079181245 0.833 30.76264583 0.116   2.5 0.079181245 1.200       30.8786875 0.104   3       0.045757492 1.111 30.983125 0.128   3.5 0 0.818       31.11077083 0.116   4       0.041392683 1.100 31.2268125 0.151   4.5 -0.113943349 0.769       31.37766667                                                                                                    

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