Arts, Faculty of
Music, School of
DSpace
UBCV
Jensen, Mikyla
Master of Arts - MA
University of British Columbia
This thesis presents the results of a measurement study, focusing on tempo fluctuations at cadential boundaries that feature evaded and/or deceptive cadences. It investigates the most common ways performers approach evaded (EC) and deceptive (DC) cadences as defined by Caplin (1998) and Schmalfeldt (2011). Can performers’ microtiming, measured in inter-onset- intervals (IOIs), inform phrase segmentation? More specifically, do performers’ microtiming profiles predict whether such a cadence will function as end of previous material or the start of new material? In modern theory, cadences are defined as phrase endings; however, both ECs and DCs require a repetition of the cadential approach to a more conclusive cadence (i.e., IAC or PAC). For each of the following pieces approximately twenty recordings featuring evaded and deceptive cadences were examined and compared: (1) Scarlatti’s Sonata in D Major, K. 492; (2) Beethoven’s Piano Sonata in Ab Major, Op. 26, IV; and (3) Chopin’s Etude in Eb, Op. 10, No. 6. Based on studies showing phrase-end lengthening in both music and speech (e.g., Todd 1994), it is hypothesized that a deceleration at an EC or DC may indicate an ending, while an acceleration may indicate a new beginning. Considering only the point of view of the performers, the results do not show absolute agreement between performers as to how each cadence is approached, both in terms of acceleration or deceleration and the proportion of speed increase or decrease. However, the majority of performers decelerate into deceptive cadences.
Comparison of Performed Tempo Changes at Deceptive and Evaded Cadences by Mikyla Jensen B.Mus., The University of Regina, 2015 M.Mus., The University of Manitoba, 2017 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, Emphasis Theory) The University of British Columbia (Vancouver) April 2020 © Mikyla Jensen, 2020 ii The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, a thesis entitled: Comparison of Performed Tempo Changes at Deceptive and Evaded Cadences submitted by Mikyla Richelle Jensen in partial fulfilment of the requirements for the degree of Master of Arts in Music, Emphasis Theory Examining Committee: Dr. Ève Poudrier, Assistant Professor, Faculty of Music, UBC Supervisor Dr. John Roeder, Chair of Music Theory Division, Professor, Faculty of Music, UBC Supervisory Committee Member iii Abstract This thesis presents the results of a measurement study, focusing on tempo fluctuations at cadential boundaries that feature evaded and/or deceptive cadences. It investigates the most common ways performers approach evaded (EC) and deceptive (DC) cadences as defined by Caplin (1998) and Schmalfeldt (2011). Can performers’ microtiming, measured in inter-onset-intervals (IOIs), inform phrase segmentation? More specifically, do performers’ microtiming profiles predict whether such a cadence will function as end of previous material or the start of new material? In modern theory, cadences are defined as phrase endings; however, both ECs and DCs require a repetition of the cadential approach to a more conclusive cadence (i.e., IAC or PAC). For each of the following pieces approximately twenty recordings featuring evaded and deceptive cadences were examined and compared: (1) Scarlatti’s Sonata in D Major, K. 492; (2) Beethoven’s Piano Sonata in Ab Major, Op. 26, IV; and (3) Chopin’s Etude in Eb, Op. 10, No. 6. Based on studies showing phrase-end lengthening in both music and speech (e.g., Todd 1994), it is hypothesized that a deceleration at an EC or DC may indicate an ending, while an acceleration may indicate a new beginning. Considering only the point of view of the performers, the results do not show absolute agreement between performers as to how each cadence is approached, both in terms of an acceleration or deceleration and the proportion of speed increase or decrease. However, the majority of performers decelerate into deceptive cadences. iv Lay Summary This paper examines tempo fluctuations at evaded and deceptive cadences that are featured in Analysing Classical Form by William Caplin (1998) and “Cadential Processes: The Evaded Cadence and the One More Time Technique” by Janet Schmalfeldt (2011). Approximately twenty recordings are examined and compared for each of the following pieces: (1) Scarlatti’s Sonata in D Major, K. 492; (2) Beethoven’s Piano Sonata in Ab Major, Op. 26, IV; and (3) Chopin’s Etude in Eb minor, Op. 10, No. 6. The results do not show absolute agreement between performers as to how each evaded cadence is approached (through either acceleration or deceleration ), and the proportion of speed increase or decrease. However, a majority of performers decelerate at deceptive cadences . v Preface This thesis is original, unpublished, independent work by the author, M. Jensen. vi Table of Contents Abstract .......................................................................................................................................... iii Lay Summary ................................................................................................................................ iv Preface ............................................................................................................................................. v Table of Contents .......................................................................................................................... vi List of Tables ............................................................................................................................... viii List of Figures ............................................................................................................................... ix Acknowledgements ........................................................................................................................ xi 1. Introduction ................................................................................................................................ 1 1.1 Formal Analysis .................................................................................................................. 1 1.1.1 Evaded and Deceptive Cadences ................................................................................... 2 1.2 Performance Analysis ......................................................................................................... 7 1.2.1 Issues in Performance Analysis ..................................................................................... 7 1.2.2 Analyzing Recordings .................................................................................................. 11 1.2.3 Tempo Fluctuations in Performance ............................................................................ 12 1.3 Current Study ................................................................................................................... 15 2. Methods .................................................................................................................................... 16 2.1 Source Materials ............................................................................................................... 16 2.1.1 Selection Criteria for Musical Examples ..................................................................... 16 2.1.2 Selected Excerpts ......................................................................................................... 17 2.1.3 Selection Criteria for Recordings ................................................................................. 23 2.2 Data Collection and Procedure ........................................................................................ 24 2.3 Measures and Analysis ..................................................................................................... 25 3. Results ...................................................................................................................................... 30 3.1 Scarlatti’s Sonata in D Major, K. 492 ............................................................................. 31 3.1.1 Timing Profiles ............................................................................................................ 32 3.1.2 Cadential Approach ..................................................................................................... 36 3.3 Beethoven’s Sonata in Ab Major Op. 26, Movement IV ............................................... 42 3.2.1 Categories of Timing Profiles ...................................................................................... 44 3.2.2 Cadential Approach ..................................................................................................... 46 3.2 Chopin’s Etude Op. 10, No. 6 .......................................................................................... 53 3.2.1 Timing Profiles ............................................................................................................ 56 3.1.2 Cadential Approach ..................................................................................................... 59 4. Discussion ................................................................................................................................ 65 4.1 Comparison of Timing Profiles Across Examples ......................................................... 65 4.2 Comparison of Cadential Approach Across Examples ................................................. 65 vii 4.3 Phrase Structure ............................................................................................................... 69 5. Conclusion ................................................................................................................................ 72 5.1 Summary Findings ............................................................................................................ 72 5.2 For Further Research ....................................................................................................... 73 viii List of Tables TABLE 2.1 ALL ANALYZED CADENCES. .......................................................................................... 18 TABLE 2.2 COMPARISON OF RAW AND NORMALIZED IOIS IN TWO RECORDINGS OF SCARLATTI’S SONATA IN D MAJOR, K. 492, MM. 35A-35B. ......................................................................... 26 TABLE 3.1 LIST OF RECORDINGS FOR SCARLATTI’S SONATA IN D MAJOR, K. 492, MM.30A-44B. .. 32 E 3.2 EIGHT POSSIBLE APPROACHES INTO THE DECEPTIVE AND EVADED CADENCES IN SCARLATTI’S SONATA IN D MAJOR K. 492, MM. 30A-44B. .......................................................................... 36 TABLE 3.3 SUMMARY OF CADENTIAL APPROACHES FOR SCARLATTI’S SONATA IN D MAJOR, K. 492, MM. 30A-44B. ........................................................................................................................ 42 TABLE 3.4 LIST OF RECORDINGS FOR BEETHOVEN’S SONATA IN AB MAJOR, OP. 26, IV, MM.40A-38B. ....................................................................................................................................... 44 TABLE 3.5 EIGHT POSSIBLE APPROACHES INTO THE EVADED AND DECEPTIVE CADENCES IN BEETHOVEN’S SONATA IN AB MAJOR, OP. 26, IV, MM. 42A-46A. ......................................... 47 TABLE 3.6 SUMMARY OF CADENTIAL APPROACHES FOR BEETHOVEN’S SONATA IN AB MAJOR, OP. 26, IV, MM. 40A-48B. ............................................................................................................. 52 TABLE 3.7 LIST OF RECORDINGS FOR CHOPIN’S ETUDE OP. 10, NO. 6, MM. 47A-51B. ................... 55 TABLE 3.8 FOUR POSSIBLE APPROACHES INTO THE EVADED CADENCES IN CHOPIN’S ETUDE OP. 10, NO. 6, MM. 47A-51B. .............................................................................................................. 60 TABLE 3.9 SUMMARY OF CADENTIAL APPROACHES FOR CHOPIN’S ETUDE, OP. 26, NO. 6, MM. 47A-51B. ....................................................................................................................................... 64 TABLE 4.1 SUMMARY OF ACCELERATION/DECELERATION INTO EVADED AND DECEPTIVE CADENCES ACROSS ALL EXCERPTS. .......................................................................................................... 66 ix List of Figures FIGURE 1.1 EXAMPLE OF DECEPTIVE CADENCE (DC). ...................................................................... 3 FIGURE 1.2 EXAMPLE OF EVADED CADENCE (EC). ........................................................................... 3 FIGURE 2.1 SCARLATTI SONATA IN D MAJOR, K. 492, MM. 30-44. ................................................ 20 FIGURE 2.2 BEETHOVEN SONATA IN A♭ MAJOR, OP. 26, IV, MM. 41-48. ....................................... 22 FIGURE 2.3 CHOPIN ETUDE OP. 10, NO. 6, MM. 47-51. .................................................................. 23 FIGURE 2.4 COMPARISON OF KOOPMAN AND WATANABE’S APPROACH INTO THE EVADED CADENCE, IN SCARLATTI SONATA IN D MAJOR, K. 492, MM. 35A-36B. ................................. 26 FIGURE 3.1 TIMING PROFILE A FOR SCARLATTI’S SONATA IN D MAJOR, K. 492, MM. 30A-44B. ... 33 FIGURE 3.2 TIMING PROFILE B FOR SCARLATTI’S SONATA IN D MAJOR, K. 492, MM. 30A-44B. ... 33 FIGURE 3.3 TIMING PROFILE C FOR SCARLATTI’S SONATA IN D MAJOR, K. 492, MM. 30A-44B. ... 34 FIGURE 3.4 TIMING PROFILE D FOR SCARLATTI’S SONATA IN D MAJOR, K. 492, MM. 30A-44B. ... 34 FIGURE 3.5 SCARLATTI SONATA IN D MAJOR, K. 492, ACCELERATION INTO INITIAL DC, MM. 30A-31B. ....................................................................................................................................... 37 FIGURE 3.6 SCARLATTI SONATA IN D MAJOR, K. 492, DECELERATION INTO INITIAL DC, MM. 30A-31B. ....................................................................................................................................... 38 FIGURE 3.7 SCARLATTI SONATA IN D MAJOR, K. 492, ACCELERATION INTO FIRST EC, MM. 35A-36B................................................................................................................................................ 38 FIGURE 3.8 SCARLATTI SONATA IN D MAJOR, K. 492, DECELERATION INTO FIRST EC, MM. 35A-36B................................................................................................................................................ 39 FIGURE 3.9 SCARLATTI SONATA IN D MAJOR, K. 492, ACCELERATION INTO SECOND EC, MM. 39A-40B. ....................................................................................................................................... 39 FIGURE 3.10 SCARLATTI SONATA IN D MAJOR, K. 492, DECELERATION INTO SECOND EC, MM. 39A-40B. ....................................................................................................................................... 40 FIGURE 3.11 SCARLATTI SONATA IN D MAJOR, K. 492, ACCELERATION INTO FINAL PAC, MM. 43A-44B. ....................................................................................................................................... 40 FIGURE 3.12 SCARLATTI SONATA IN D MAJOR, K. 492, DECELERATION INTO FINAL PAC, MM. 43A-44B. ....................................................................................................................................... 41 FIGURE 3.15 TIMING PROFILE C FOR BEETHOVEN’S SONATA IN AB MAJOR, OP. 26, IV, MM. 40A-48B. ....................................................................................................................................... 45 FIGURE 3.16 BEETHOVEN SONATA IN A♭ MAJOR, OP. 26, IV, ACCELERATION INTO INITIAL EC, MM. 41A-42B. ................................................................................................................................ 48 FIGURE 3.17 BEETHOVEN SONATA IN A♭ MAJOR, OP. 26, IV, DECELERATION INTO INITIAL EC, MM. 41A-42B. ................................................................................................................................ 49 FIGURE 3.18 BEETHOVEN SONATA IN A♭ MAJOR, OP. 26, IV, ACCELERATION INTO FIRST DC, MM. 43A-44B. ................................................................................................................................ 49 FIGURE 3.19 BEETHOVEN SONATA IN A♭ MAJOR, OP. 26, IV, DECELERATION INTO FIRST DC, MM. 43A-44B. ................................................................................................................................ 50 FIGURE 3.20 BEETHOVEN SONATA IN A♭ MAJOR, OP. 26, IV, ACCELERATION INTO SECOND DC, MM. 45A-46B. ........................................................................................................................ 50 FIGURE 3.21 BEETHOVEN SONATA IN A♭ MAJOR, OP. 26, IV, DECELERATION INTO SECOND DC, MM. 45A-46B. ................................................................................................................................ 51 x FIGURE 3.22 BEETHOVEN SONATA IN A♭ MAJOR, OP. 26, IV, ACCELERATION INTO FINAL PAC, MM. 47A-48B. ................................................................................................................................ 51 FIGURE 3.23 BEETHOVEN SONATA IN A♭ MAJOR, OP. 26, IV, DECELERATION INTO FINAL PAC, MM. 47A-48B. ................................................................................................................................ 52 FIGURE 3.24 TIMING PROFILE A FOR CHOPIN’S ETUDE OP. 10, NO. 6, MM. 47A-51B. ................... 56 FIGURE 3.25 TIMING PROFILE B FOR CHOPIN’S ETUDE OP. 10, NO. 6, MM. 47A-51B. .................... 56 FIGURE 3.26 TIMING PROFILE C FOR CHOPIN’S ETUDE OP. 10, NO. 6, MM. 47A-51B. .................... 57 FIGURE 3.27 TIMING PROFILE D FOR CHOPIN’S ETUDE OP. 10, NO. 6, MM. 47A-51B. ................... 57 FIGURE 3.28 CHOPIN ETUDE OP. 10, NO. 6, ACCELERATION INTO FIRST EC, MM. 47A-48B. .......... 61 FIGURE 3.29 CHOPIN ETUDE OP. 10, NO. 6, DECELERATION INTO FIRST EC, MM. 47A-48B. .......... 61 FIGURE 3.30 CHOPIN ETUDE OP. 10, NO. 6, ACCELERATION INTO SECOND EC, MM. 48A-49B. ...... 62 FIGURE 3.31 CHOPIN ETUDE OP. 10, NO. 6, DECELERATION INTO SECOND EC, MM. 48A-49B. ...... 62 FIGURE 3.32 CHOPIN ETUDE OP. 10, NO. 6, ACCELERATION INTO FINAL PAC, MM. 50A-51B. ....... 63 FIGURE 4.1 TEMPO CHANGE AT THE FINAL PERFECT AUTHENTIC CADENCE FOR THE SCARLATTI SONATA IN D MAJOR, K. 492, MM. 43A-44B; BEETHOVEN SONATA IN A♭ MAJOR OP. 26, IV, MM. 47A-48B; AND CHOPIN ETUDE OP. 10, NO. 6, MM. 50A-51B. .......................................... 68 FIGURE 4.2 PHRASE STRUCTURE ANALYSIS OF SCARLATTI’S SONATA IN D MAJOR, K. 492, MM. 26-44........................................................................................................................................... 70 FIGURE 4.3 PHRASE STRUCTURE ANALYSIS OF BEETHOVEN’S SONATA IN AB MAJOR, OP. 26, IV, MM. 28-48. ............................................................................................................................. 71 FIGURE 4.4 PHRASE STRUCTURE ANALYSIS OF CHOPIN’S ETUDE, OP. 10, NO. 6, MM. 41-53. ........ 72 xi Acknowledgements I would like to thank Dr. Alan Dodson for beginning this research with me and teaching me how to use Sonic Visualiser. I would also like to thank my advisor, Dr. Ève Poudrier, and second reader, Dr. John Roeder, for strengthening my writing and mentoring me through this process. I would like to thank both of my parents for their continued support throughout my master’s degree. 1 1. Introduction What are the most common ways performers approach evaded and deceptive cadential boundaries as defined by Caplin (1998) and Schmalfeldt (2011)? Can performers’ microtimings inform phrase boundaries? More specifically, do performers’ microtiming profiles influence whether a cadential boundary will be perceived as a segment ending or beginning? These research questions are equally relevant in the fields of music theory, music performance, and music psychology. Although these questions deal with formal functions and boundaries in music, and how the performer may interpret, understand, and segment melodic and harmonic material, one must first understand the complicated relationship between these fields and how this study may benefit from considering the perspective of each. In the past, studies in performance analysis have favoured the theorist over the performer and have often not considered the role of music psychology. In order to address these questions, I will analyze musical recordings through the mapping of tempo fluctuations between each onset of sound. This way, I am focusing my research on performances that represent the performers’ intended presentation of the formal structure, without imposing my own analysis of the score 1.1 Formal Analysis Formal analysis is the study of “how standard patterns of repeated material appear in works; how different sections of a work are organized into themes; and how the themes themselves break down into smaller phrases and motives” (Caplin, 1998). In modern theory, a phrase is a series of events (a segment) that concludes with a formulaic pattern called a cadence. The two most traditional types of phrase structures in tonal music are the period and the sentence. A period contains two phrases, the antecedent (ending with an IAC or HC) and the 2 consequent (ending with a more conclusive cadence such as a PAC). A sentence contains one phrase that can be divided into the presentation (divided into a repeating two-measure motive) and the continuation (ending with a conclusive cadence such as a HC, IAC or PAC). In both instances, there is a distinct relationship between the less conclusive cadence (or lack thereof) and a final conclusive cadence (at the end of the consequent or continuation phrase). Therefore, a period represents a pattern of 4 + 4 grouping of measures, whereas, a sentence presents a 2 + 2 + 4 grouping of measures. However, their endings are both signalled by a cadence. Composers can expand these phrases in different ways through the use of ECs and DCs. 1.1.1 Evaded and Deceptive Cadences The EC and DC can present a challenge for the performer of how best to convey the musical structure of a piece. Meant to literally evade the cadential arrival of tonic harmony and surprise the listener with a change of mode, these two cadences expand the traditional four-measure or eight-measure phrase length classical musicians have come to expect. A basic DC is most often the defined as cadential motion from the dominant (V) to the submediant (vi/VI) in lieu of the arrival of tonic harmony (I/i). The EC is the cadential motion of the dominant (V) that does not resolve; for example, V--I⁶ or dominant harmony followed by a repetition of melodic material leading up to the expected authentic cadence (IAC, PAC). Examples of the DC and EC can be found in Figures 1.1 and 1.2 3 Figure 1.1 Example of deceptive cadence (DC). Dominant harmony (V) moving to the submediant harmony (vi). Figure 1.2 Example of evaded cadence (EC). Dominant harmony (V) in third inversion, moving to tonic harmony (I) in first inversion. Arguably, both performers and analysts recognise the hierarchical ranking of cadence type in tonal music, with each cadence type judged for the level of closure it achieves. The “ranking” of these cadences from strongest sense of closure to least amount of closure would be: 1. Perfect Authentic Cadence (PAC) 2. Imperfect Authentic Cadence (IAC) 3. Half Cadence (HC) 4. Deceptive Cadence (DC) 5. Evaded Cadence (EC) The DC ranks higher than the EC as it does afford some closure; however, with a mode change (to vi or substitute iv ⁶). The EC avoids closure completely. 4 If we base the structure of a piece on its cadential boundaries, then exactly how obvious is it to the performer to group a DC or EC with the preceding material, when its purpose is most often to expand the phrase by requiring the re-attempt at cadential closure, provided by the PACs? Are the EC and DC the end of the primary segment or the beginning of the subsequent segment? Two of the most well-known music theorists of the modern era, with regard to their work on formal structures and cadences, are Janet Schmalfeldt (1992, 2011) and William Caplin (1998). Although theorists and performers usually have a general understanding of what comprises the typical harmonic progressions of both a DC and EC, there is still some debate as to whether one should view them as the end of the proceeding musical segment or the start of a new material. Caplin defines the EC as “The failure of an implied authentic cadence to reach its goal harmony. The event appearing in place of the final tonic groups with the subsequent unit and (usually) represents the beginning of a new cadential progression.” (1998, 254) Schmalfeldt defines an EC as “a technique that eighteenth-century composers developed within numerous genres for multiple purposes: for motivating text repetitions, for highlighting the soloist's secondary-key cadential area within the aria and the concerto, in general for extending and invigorating secondary-key materials, and for generating varied reprises as well as extensive codas.” (1992, 1) Schmalfeldt also believes that the EC and the “one more time technique” (a term coined by Schmalfeldt) often present together. She defines the “one more time technique:” This convention begins to appear around the second decade of the eighteenth century in isolated works by Rameau and Alessandro Scarlatti, becomes established over a broad range of genres in the music of such diverse composers as Hasse, Sammartini, Galuppi, Stamitz, C.P.E. Bach, and J.C. Bach, serves as a hallmark in the music of Domenico Scarlatti and Mozart, continues to be much exploited by late eighteenth- and nineteenth-century composers in general, 5 resurfaces in twentieth-century neoclassical works and popular music (especially of the vaudeville and Broadway types), and survives today as an improvisatory tradition adopted when performers wish to repeat the approach to the final cadence "one more time. (1992, 1-2) In her article, Schmalfeldt states that “The performer who tries to effect absolute rhythmic and voice-leading continuity [at an evaded cadence] may be making a big mistake. Instead... the composer asks the performer to treat that harmony not as an ending, or goal, but rather only as the basis of a new beginning…” (1992, 9) She also states that “A genuine evaded cadence has no melodic or harmonic closure; therefore, it has no ending. Instead, it has a distinct beginning, with the material in place of the PAC.” (2011, 11). Caplin and Schmalfeldt agree that DCs and ECs do not represent a single event, rather but a series of events. In a DC, the final even is altered from the expected tonic (I/i) harmony to the submediant (VI/vi). In an EC we hear all the events of an authentic cadence (tonic (T)-predominant (PD)-dominant (D)-tonic (T)) except the “final tonic” which is replaced by another event that begins the next musical segment. Therefore, this event is simultaneously an ending (lacking tonic arrival) of the previous group and the beginning of the next segment. Does Caplin interpret the evaded cadence as the failed ending and the material after it representing the new beginning? There is a definite ambiguity as to where the boundary points of this event are. Is it the EC, itself, as Schmalfeldt suggests, or the material directly following the evaded cadence, as posed by Caplin? This will be directly discussed with reference to how the use of the “one-more-time” technique also affects the placement of the new beginning. The DC may imply more of a sense of boundary and closure with the resolution of the leading-tone, as part of the dominant (V) harmony, to the tonic, as part of the submediant harmony (vi/VI). However, it requires the “one-more-time” technique where tonic harmony (I) is finally achieved. The boundaries are even more ambiguous due to the surprising resolution of the 6 initial DC, followed by a direct repetition of the same material. Caplin defines it as a “variant of the authentic cadential progression in which the final tonic is replaced by a related harmony (usually VI).” (1989, 254) Schmalfeldt states: “As with the evaded cadence, the progression that leads to a deceptive cadence begins by promising a perfect authentic cadence; but rather than withholding the goal harmony, the deceptive cadence substitutes a deceptive goal — the submediant.” (1992, 7) Traditionally, the DC features the harmonies I--ii--V--vi, where the submediant harmony (vi) replaces the expected tonic harmony (I) of a perfect authentic cadence (PAC) which utilizes the harmonic progression I--ii--V--I. Schmalfeldt and Caplin seems to propose that a deceptive cadence should be segmented with the material that comes before it - as an alternate ending. However, it creates less closure with the change of mode and the rising harmony. An interesting point to consider is how neither the EC nor the DC actually end a phrase as formalized in music-theoretical analysis; therefore, referring to them as cadences would be misleading. Instead, they are harmonic events that require internal expansion of the phrase (through repetition of the cadential progression) in order to achieve closure through an authentic cadence (IAC or PAC). This study addresses how performers understand these two ambiguous pattern of events. Is and EC or DC a segment beginning, ending, or not present any boundary at all? Beginnings and endings in music consist of different dynamic qualities, either bringing a process to a goal or initiating a new process. These qualities manifest in performance timings through acceleration or deceleration at ECs and DCS as well as in the shaping of dynamics (loudness). In order to consider how a DC or EC should be segmented, one can listen to multiple recordings of the same 7 ambiguous cadential moments and analyze how performers have traditionally portrayed the musical structure. 1.2 Performance Analysis Relevant sources pertaining to the field of performance analysis fall into three categories: 1. Issues in performance analysis 2. Analyzing recordings 3. Microtiming in performance 1.2.1 Issues in Performance Analysis Performance analysis involves the combination of performance, music theory, and music psychology. The first psychologist to make the connection between music and psychology was Carl Seashore in “The Psychology of Music. II. Approaches to the Experimental Psychology of Music” (1936) in which he describes how pitch, dynamic, time, and timbre can be studied empirically in terms of how we (as the performers, listeners, or analysts) interpret frequency, intensity, duration, and form. As someone who comes from a background in music performance and teaches others to perform music, I constantly iterate that one must understand the music that they play. The first person to explore this idea in length was Joel Lester in “Performance and Analysis: Interaction and Interpretation” in The Practice of Performance: Studies in Musical Interpretation (1995) where he argues that “analyses are assertions about a piece, not a particular rendition of it.” In other words, why is it more relevant to examine the score versus an actual performance of the music? The less-considered notion of analyzing unique moments of a performer’s rendition of a well-known composition and why they may have chosen to perform these in a certain way, is 8 often overlooked by the analyst. When one approaches the analysis of performance, should it not begin with the performance itself rather than an analysis of the score? Most recently, Dodson defines performance analysis as the close study of one or more specific performances or recordings (2019). Early publications in the field of performance analysis (i.e., Berry, 1989; Narmour 1998) have often been unable to attain a balanced relationship between the role of the analyst and that of the performer. They focus on the analysts’ findings, often disregarding the opinions of the performer completely. Moreover, if a performer’s opinion is considered, it is almost always secondary to the analysis. In general, most publications that deal with the dichotomy of performance versus analysis introduce their work by summarizing the many ways in which past publications have failed to find an equal balance between performer and theorist. Rather, they present the realization of the theorist's ideal performance, and why performers should perform the piece a certain way. For example, John Rink’s review of Berry’s Musical Structure and Performance (1910), places a critical eye to the work of Meyer, Cone, Narmour, Dunsby, and Schmalfeldt, who are all well-known and respected theorists in their respective fields, and who set a standard for how performance analysis is to be conducted 319-339). Rink highlights the imbalance between the theorist and performer, drawing the reader’s attention to how analysts insist on using phrases such as “the performer must,” or “the performer has to.” On the other hand, as Dunsby, who often favours the analyst in his writing, puts it: Understanding and trying to explain musical structure is not the same kind of activity as understanding and communicating music. There is a genuine overlap between these poles of activity, but it cannot be a complete overlap. (1989, 7). 9 With such differences between the two fields, a difficult relationship is often thrust forward into a variety of ways of thinking as to which method of said overlap promotes an equal partnership between analyst and performer. Nicholas Cook’s Beyond the Score: Music as Performance (2013) discusses the dichotomy of performance and analysis at length, addressing most relevant sources on the subject. His description of a “theorist’s analysis” is the complete disregard of all emotional or expressive elements of performance that instead emphasizes the projection of formal structure (often based on Schenkerian analysis). (2013, 2) This format of creating an instruction manual on the performance of classical music results in the one-way relationship of the theorist informing the performer what to do. For example, although Janet Schmalfeldt attempts to play both the role of the analyst and performer in her 1985 article “On the Relation of Analysis to Performance: Beethoven's "Bagatelles" Op. 126, Nos. 2 and 5,” the “voice” of the performer seems irrelevant and agrees with everything the analyst says, without providing any of her own insight into the piece. Therefore, one finds oneself asking what is more important, one’s ability to highlight the formal structure of a piece or the resulting presentation of those formal structures by performers? If listening to a performance can provide just as much, if not more, insight into the musical structure., it would seem questionable to allow the analyst’s opinion to be hierarchically more significant. As Cook states: “There is no suggestion that, where a performer does something that doesn’t make sense in theoretical terms, it might be the theory that is at fault.” (10) To explain why the performer has seemingly played a secondary role to the analyst, Cook points to the fact that the performer’s analysis lies more in an oral tradition, that is, passed on from teacher to student and created through the need to justify the reasoning to perform a particular piece a certain way (for example, “there is a dissonant harmony which sounds wrong 10 unless you stress the downbeat and decelerate into it”) Cooks argues that when compared to a theorist’s approach, the performer's analysis occurs in real-time, and insists that the performer adheres to one particular interpretation of successive transitions that is music. (15-16) Cook states that “transitions are places where meaning is both concentrated and open to performers’ intervention.” (15-16) The real-time response of the performer is present in both the through process and physical embodiment of the reproduction of sound – each performer establishing their own voice within another’s composition, based on unknown influences and past experiences. (18) Although this style of analysis is much less common than the theorist’s approach, one must consider how there are typically hundreds of performances compared to a small number of theoretical analyses on the subject that are readily available today. Bethany Lowe (2003) argues that performance and analysis can only find common ground through the study of how one interprets the music. Therefore, by understanding how both the performer and analyst interpret the piece, one can compare their performance analyses and gain a greater understanding of all opinions. This puts this particular analysis in disagreement with Wallace Berry’s Musical Structure and Performance (1989), that favours the opinion of the theorist. In particular, his notion that “The purely spontaneous, unknowing and unquestioned impulse is not enough to inspire convincing performance...” (Berry, 220). Instead, taking Lowe’s model, by recognizing the moments where performers have a “spontaneous impulse” and then returning to the score to understand why they may have chosen to approach that moment in a certain way may highlight the inspiration behind the performer’s interpretation of the piece. Therefore, instead of limiting analyses to a particular piece, one can apply it instead, to a particular rendition of said piece. (Lester, 1995) Why is a theorist’s analysis more relevant than a performer’s interpretation? Both 11 generally have years of experience in their respective fields and feel confident in the research decisions they make about the way they present their materials (either through a published paper, or recorded performance). Does one have a tendency to place more trust in that of the theorist because they have written down their perspective, research ideas, methods, and proof? Yet, a performer goes through the same process of learning their music, considering what method is best to approach more difficult sections of the piece, and their own personal reasoning, or “proof,” of why they present the piece in a certain way. Within the field of performance analysis, one must consider the many ways a performer might attempt to convey the musical structure of a piece and how that relates to the way theorists typically define and recognize structural boundary points, such as cadences. Especially those cadences like the EC that are more unexpected, resulting in an expanded phrase, lack of closure, or elision of boundary points. 1.2.2 Analyzing Recordings Cook emphasizes the definition of performance analysis as the “analysis of performances, whether live or recorded.” (2013, 1) However, most of the literature focuses on recorded music, because it allows for an equally balanced relationship between the analyst and performer, thus avoiding what Cook calls the “theorist’s analysis” and the “performer’s analysis,” as discussed above (2013, 1). It also addresses the issue raised by Janet Schmalfeldt: Whereas the analyst's verbal medium requires a final commitment to a presently held view, the performer's non-verbal "view" must never be taken as final within a live performance. Just one false move-a finger placed too heavily (or too lightly) on the key, an arm motion that misses its target-can force the performer to adjust the fine points of his strategy; suddenly new decisions must be made, and with these, a new "view" may be born. (1985, pg. 25) 12 In opposition, Lydia Goehr, in “The Perfect Performance of Music and the Perfect Musical Performance” argues that recordings are not spontaneous and ruin the “human” element in the music, which is audible in live performances in the form of small mistakes. However, recordings allow one to recognize historical tradition and the evolution of performance style. For example, early recordings in the early 1900s often take more liberties in rhythm, tempo, timbre, and dynamic level (Day, 2000; Philip, 2003). Studies completed by Day (2000) and Philip (2003) provide an explanation of this phenomenon, based on how the recording industry placed higher demands on more modern recordings for precision and their ability to be repeated. Taruskin (1995) cites modernism as the cause, whereas, Daniel Leech-Wilkinson (2009) discusses the change of aesthetic in the postwar era. Interestingly, Bruno Repp (1992a, 1992b, 1998, 1999a, 1992b) advocates that the liberties still exist in modern recordings; however, they are the result of student vs. professional musician’s recordings (1997 study of performances of Schumann’s Traümerei) and how students are less-likely to take risks, in comparison to established, professional musicians. As Narmour puts it, “...commercial recordings, … are, after all, not just convenient products for home entertainment but also primary source documents for the study of performance in our century” (Narmour, 318). Many theorists insist on listening to the music first before examining the score, as not to allow the score to influence what they may or may not actually hear in the music as apparent structural boundaries. Moreover, before learning a piece, performers will typically listen to multiple recordings of the piece. 1.2.3 Tempo Fluctuations in Performance Performances by highly skilled musicians have innumerable departures from mechanical regularity, many of them related to grouping (Dodson, 2008). Past studies in grouping tempo 13 fluctuations can be found in the fields of performance analysis, cognition, psychology, and music theory. The first to consider the presentation of musical phrases was Neil McAngus Todd, in his 1985 article “A model of expressive timing in tonal music.” By presenting a series of parabolic equations to represent performers’ timings of grouping structures in three pieces (the Adagio from Mozart K. 331, Haydn’s Sonata no. 59, and Chopin’s Trois Nouvelles Etudes No. 3), he showed that performers tend to accelerate at the start of the phrase and decelerate at the end of the phrase. Furthermore, the phrase itself maintains a steady tempo which only varies when the phrase comes to a cadential formula. He bases his research on the previous findings of Seashore (1936) who recognised musicians are most likely to lengthen notes and slow down at the end of a musical phrase. This was explored further by Black, Tosi, Singh, & Takefuta in their 1966 study of how pausing in speech is a direct correlation to grouping techniques. Therefore, the longer the period of pause in both speech and music, the more important the structural boundary and grouping (O’Malley, Kloker, & DaraAbrams, 1973). Bruno Repp’s research in the early 1990s provides evidence of how micro-level data can be interpreted in an infinite number of ways. Therefore, he believes that generalizations can only be made at the macro-level of analysis and boundary points (specifically, cadences); the more similar the boundary points are, the more similar the performances of the pieces will be. This is often presented by performers through what Cook calls their “structuralist interpretation” in which “...[at] the expense of interpreting ‘expression’ - traditionally seen as the core of performer’ individuality…; performers introduce rubato and other deviations from the notated music, they claim, in order to project or bring out (in a word, to express) its underlying structure.” (242-243). This research was duplicated by Turner (2005, 2007) and Dahl (2007), in which no generalizations could be made about the pieces in question, other than their approach to 14 large-scale structure. However, in 1994 Repp proposed that the timing profiles (IOIs) of varied tempos can produce the same outcome of boundary measurements. Both fast and slow performance tempos produce the same overarching tempo fluctuations. Therefore, by normalizing the IOIs, one can ignore the impact of tempo on the overall presentation of formal structures and their cadential boundaries. A fast recording and a slow recording can produce the same magnitude of acceleration/deceleration at phrase boundaries. This is relevant to this study as the performances represent a wide variety of bass-line tempos that are compared, considering their tempo fluctuations at the boundary points of DCs and ECs. The only study to directly examine cadential approach is reported by Sears, Spitzer, McAdams, and Caplin’s 2018 article, which examined the feeling of expectancy listeners experience (both musicians and non-musicians) when approaching different types of cadences in the music of Mozart. They found the highest expectancy of closure when approaching tonic harmony, and the strongest feeling of expectancy for cadences arriving on tonic harmony through an authentic cadence (AC) (imperfect authentic cadence (IAC) or perfect authentic cadence (PAC)). The expectancy of closure dramatically lessened when the music approached dominant harmony at a boundary point (half cadence (HC)). The order from highest level of expectancy of closure to lowest of all other cadences was found to be as follows: PAC, IAC, DC, and EC. It is important to note that while this study addressed the way a listener approaches the EC and DC, it did not attempt to address the results from the performer’s point of view. This idea of hierarchical levels of cadential closure was echoed in Alan Dodson’s 2019 article examining Bach’s Invention in C Major, no. 1. Dodson found that three performers utilized the same patterns of approach at phrase endings with use of rubato and a more noticeable deceleration into the final PAC in comparison to the previous HCs, DCs, or EC. 15 Our review of the concepts of EC and DC suggests that theorists attribute more of a sense of ending – more closure – to DC than to EC, the last event of which serves to begin a group (the last event of the DC would be the tonic substitute vi; the last event of the EC would be the failed resolution to the tonic). The timing literature we have just surveyed suggests that performers tend to slow down when ending a group but accelerate when beginning. I hypothesis, therefore, that at the final onset of a DC, performers will tend to decelerate, whereas at the final onset of an EC, they will tend to accelerate. 1.3 Current Study This is an exploratory study which addresses performers’ tempo fluctuations at evaded and/or deceptive cadences. What are the most common ways performers approach evaded and deceptive cadential boundaries as defined by Caplin (1998) and Schmalfeldt (2011)? Can performers’ timing inform phrase segmentation by analysts? From the performer’s timing data alone, can we tell whether an EC or a DC is being performed? How does the performer interpret a cadence if it evades closure? By extracting performers’ timing fluctuations, one may begin to understand how ambiguous musical structure is interpreted and segmented. Given that two of the selected excerpts feature an example of Schmalfeldt's "one-more-time" technique, that is, a repetition of the phrase materials following the first failed cadence, one question that will be considered is the effect of this technique on performers' timing decisions. This paper does not address the increasingly popular study of performer intention and performance, studied in real-time performances, considering what was intentional and what was merely a “mistake” in the moment. As the performances studied are recorded, this study assumes that the performer’s intentions were both considered and realised in obtaining the “best possible recording” for publication. This paper also does not address the listener’s perspective as to what 16 way they may segment the ECs or DCs based on their interpretation of the presented material in the form of the musical recording. 2. Methods 2.1 Source Materials For this study multiple commercial recordings of segments from the 18th- and 19th-century Western art tradition were examined from the perspective of microtiming. In the discussion below, scores of the selected music segments are provided with a basic Roman numeral analysis that highlights each EC or DC. 2.1.1 Selection Criteria for Musical Examples Although there are many examples of ambiguous cadences in music from the late Baroque to early Romantic period, the musical excerpts selected for this exploratory study had to satisfy the following criteria: 1) Are discussed in one of two leading texts on formal structure: a) William Caplin’s Classical Form (1998) b) Janet Schmalfeldt’s “Cadential Processes: The Evaded Cadence and the One More Time Technique,” in The Journal of Musicological Research (1992) 2) Are written for solo piano 3) Include at least one Evaded Cadence (EC) or Deceptive Cadence (DC), but may contain multiple instances of one or both types 4) Feature a two-beat (or strong-weak) pattern at the measure level The two texts by Caplin and Schmalfeldt represent two of the most well-known publications pertaining to structural form and define the basic formal structure components of 17 music (including the EC and DC). The choice of compositions for the piano is directly related to the capabilities of the software Sonic Visualiser, which was used to extract onset times from each recording. If there is more than one instrument recorded, the spectrogram and waveform are very challenging to interpret. A piano produces sharper onset attacks, giving the analyst an advantage in extracting the location of each time point. The third criterion is related to the fact that ECs and DCs often occur more than once in an expanded phrase structure (for example, EC + EC + PAC in the “one-more-time technique), and often together (for example, DC + EC + PAC or EC + DC + PAC). It is relevant to consider that the performances contain both DCs and ECs in different positions throughout a phrase. Is a DC that occurs first in an ambiguous cadential passage performed differently than a DC that occurs after an initial EC? Is the second EC in a segment performed differently than the first EC? Finally, the two-beat (or strong-weak) beat pattern criterion has been chosen to maintain consistency across examples. Out of all possible examples, three pieces contained passages that fit all four criteria: (1) Domenico Scarlatti’s Sonata in D Major, K. 492; (2) Frederic Chopin’s Etude in Eb minor, Op. 10, No. 6; and (3) Ludwig van Beethoven’s Piano Sonata in Ab Major, Op. 26, movement IV. 2.1.2 Selected Excerpts Each recorded excerpt: 1) Begins one complete measure before the first EC or DC occurs 2) Ends with the complete measure of the arrival (tonic) chord of the PAC (i.e., the last tone heard in the measure of the tonic arrival chord) These segment boundaries were chosen in order to compare the timing patterns of each performer’s acceleration/deceleration into the EC/DC in comparison to both their base-line 18 tempo and their approach to the Perfect Authentic Cadence (PAC), where segmentation is more obvious due to a stronger sense of closure achieved. A list of analyzed cadences can be found in Table 2.1. Altogether, there are three DCs and five ECs. The Scarlatti and Beethoven excerpts feature both ECs and DCs, and all excerpts feature at least two ambiguous cadences. All three excerpts end with a PAC. Scarlatti Sonata in D Major, K. 492 Chopin Etude in Eb minor Beethoven Piano Sonata in A♭ Major, Op. 26, IV m. 31a DC m. 48a EC m. 42a EC m. 36a EC m. 49a EC m. 42b DC m. 40a EC m. 51a PAC m. 46b DC m. 44a PAC m. 48a PAC Table 2.1 All analyzed cadences. (EC = evaded cadence; DC = deceptive cadence; PAC = perfect authentic cadence). PACs were included in the analysis for comparison with DCs and ECs. The letters in this chart represent the chord changes, which do not always correspond with the notated downbeat (in the Beethoven excerpt in 2/4 time, for example, the letter a denotes a chord change on the first eighth-note of the bar , b on second chord on the second eighth-note, c on the third chord on the third eighth-note, and d on the final chord on the final eighth-note of the bar). Scarlatti’s Sonata in D Major, K. 492, was written for Queen Maria Barbara of Portugal and was most likely composed late in the composer’s life (1750s). It was published as part of the 12th volume of the Venice Essercizi (Boyd & Pagano, 2001). It adheres to what Ralph Kirkpatrick (1983), one of the recorded performers examined here, defines as the “basso continuo” style, indicating that the performer would be knowledgeable in the art of improvised accompaniment over a traditional bass line. However, in the recordings selected for this study, none of the performers added any improvised ornamentation or passage work that obscured the rhythmic presentation of the analyzed segment. They began notated ornamentation on the beat (rather than before it) so that the onset time of the ornamentation could be considered as the 19 onset time of the notated beat. Performers’ ornaments were mainly short mordents (both above and below the note) that began on the notated pitch and corresponded to two beats of 6/8 (dotted-quarter-note value), the rate at which the IOIs were extracted. The analyzed excerpt is from the opening movement in 6/8 time (mm. 31-44; 15 measures in length), which begins in A minor and then modulates to A major. The phrase from which the analyzed segment is extracted begins following a half cadence with dominant arrival in m. 26 (not shown). A DC ensues with a tonic substitute (iv⁶) arrival at m. 31a, followed by two ECs at mm. 36a and 40a. The ECs do not follow a traditional harmonic progression of the EC as previously discussed, rather they represent the failed resolution of the melodic, motivic, and rhythmic material. In other words, there may be tonic harmony, but it is a repetition of the cadential process of (T-PD-D), not a resolution. The melody leaps away from the leading tone (G#4) to A5, which initiates a rapid descending scale, and the bass fails to attack on the downbeat (an evasion technique dating back to the Renaissance by Zarlino in 1562). A Roman numeral analysis is presented as Figure 2.1 20 Figure 2.1 Scarlatti Sonata in D Major, K. 492, mm. 30-44. (EC = evaded cadence; DC = deceptive cadence; PAC = perfect authentic cadence). The “V-----” represents an expanded dominant harmony through the alternation of a root position dominant chord and a second-inversion ii⁰⁷ chord. (Ed. Gouin, 2013; adapted from Schmalfeldt, 1992, Ex. 1a, p. 4). 21 Beethoven’s Ab Major Sonata, Op. 26 (1800-1801) is dedicated to Prince Lichnowsky (1761-1814). The fourth movement, Allegro, is in 2/4 time and includes one EC (completed at m. 42b) followed by two DCs (with tonic substitute arrivals at mm. 44a and 46a), in the key of Eb major (established m. 30). The DCs are emphasized with fast, descending scalar passages utilizing the “one-more-time” technique, typically associated with the EC. The resolution (tonic) chord of the expected PAC is finally achieved at m. 48a. These DCs are unique, given how close they are to the EC, and how they are linked together into an intensifying larger gesture in which the each retake of the descending scaler passage (the sfz after each cadence) starts on a higher member of tonic (I) harmony (Eb5 in m. 42, G5 in m. 44, and Bb 5 in m. 46). Furthermore, the PAC is quite different than the PAC in the Scarlatti excerpt. In the Beethoven excerpt, the music following the PAC prolongs the cadential tonic, whereas, the music following the PAC in the Scarlatti excerpt moves on to a new thematic idea. Therefore, the approach to the final PAC in the Beethoven excerpt is less abrupt, most likely resulting in less of the traditional deceleration into the downbeat of m. 48. A Roman numeral analysis of the eight-measure excerpt (mm. 41-48) is presented as Figure 2.2. 22 Figure 2.2 Beethoven Sonata in A♭ major, Op. 26, IV, mm. 41-48. (EC = evaded cadence; DC = deceptive cadence; PAC = perfect authentic cadence). (Ed. Breitkopf and Härtel, 1970; adapted from Caplin, 1988, Ex. 8.5, p. 103). Chopin’s Etude Op. 10, No. 6, was originally published in 1833 (Paris), dedicated to Franz Liszt (1811-1886). (Michalowski, 2001) The piece is in 6/8 time and features two ECs (arriving mm. 48a and 49a), the second of which is an exact repetition of the first (representing what Schmalfeldt describes as the “one-more-time” technique). The examined segment is seven measures in length (mm. 47-51). Chopin utilizes the tonicized ♭II⁶ as the predominant (m. 47a), preceded by an enharmonically spelled IV chord in the key of ♭II (the B♭♭-D♭-F♭ chord as A-C#-E in m. 49b-50a). Both ECs utilize the same melody; however, the melodic descent to the final PAC deviates first to C#5 (from the IV/♭II chord) before arriving on tonic harmony at m. 51a. 23 Once again, the final PAC is different than the final PACs of the Scarlatti and Beethoven. Like the Beethoven, the final PAC of the Chopin excerpt is extended by a sustained tonic chord; however, it is not anacrustic to a thematic reprise, rather is the final harmonic arrival of the entire piece. Moreover, Chopin has specified a ritardando after the arrival of the PAC, which might bias the performers to refrain from decelerating until after the final PAC. A Roman numeral analysis is presented as Figure 2.3. Figure 2.3 Chopin Etude Op. 10, No. 6, mm. 47-51. (EC = evaded cadence; DC = deceptive cadence; PAC = perfect authentic cadence). (Ed. Scholtz, 1918; adapted from Schmalfeldt, 1992, Ex. 2, p. 8). 2.1.3 Selection Criteria for Recordings Nineteen to twenty five recordings for each excerpt were chosen for analysis, ranging from the early 1900s to 2019. All recordings were sourced from the Naxos Music Library, which allows the listener to access a list of all recordings available on the database for any specific piece of music, ordered by most popular to least popular. Overall, 20/42 available recordings of the Scarlatti Sonata, 19/156 available recordings of the Beethoven Sonata, and 20/787 recordings 24 available of the Chopin Etude were chosen to be analyzed. If the sound quality was too poor to extract accurate onset times (too much echo or poor recording quality with too much feedback or background noise, obscuring the arrival of each onset), the recording was excluded from the pool. If a recording was eliminated, it was replaced by the next most popular listed recording (number 21 on the list and so forth). By selecting approximately 20 of the most popular recordings, this study imitates how past studies completed by Repp (1995, 1997), utilized around 20-30 performers or recordings for analysis, arguing that that number will present enough of a variety whilst keeping the data collection process manageable. 2.2 Data Collection and Procedure The selected excerpts were extracted from the Naxos Music Library and converted to mp3 files using the software Audacity. I processed each mp3 file into a dataset consisting of a time point series, with each time point corresponding to the onset of a chord. The onset times were extracted by simultaneously viewing the waveform and spectrogram on the software Sonic Visualiser and adding the time points or “time instants layers” by manually tapping while listening to the recording. The accuracy of each time marker was then examined, utilizing the spectrogram and waveform, and time point locations were adjusted accordingly. Each time instants layer was edited three times before exporting time point series data to a Microsoft Excel spreadsheet for further calculations. The raw data Excel spreadsheets for each performer can be found at the permanent Google Drive link: https://drive.google.com/open?id=1UB6XOpxBtpb6WMhYTZEBXqSKg3nzt79c. 25 2.3 Measures and Analysis Diana Deutsch describes the many ways in which one can measure timing in a performance analysis study: “...measurements may refer to tempo, durations of sound events and groups of sound events, and of nonsound events (rests, other silent intervals), and further the asynchrony between different instruments supposed to perform at the same time.” (1999, 524) As the basis of this study is to observe segmentation patterns of performers through their accelerating/decelerating microtiming patterns for ambiguous cadences, the harmonic events are measured to highlight the cadential structure of the music segment in question. Duration of harmonic events was measured by calculating the inter-onset interval (IOI), that is, the time interval in milliseconds between one onset (chord change) and the subsequent onset. Because the selected excerpts feature different time signatures, the notated value associated with the rate of harmonic change also varied from excerpt to excerpt. The Beethoven excerpt is measured at the eighth-note level (four chords per bar in 2/4 time; note the descending scaler passages begin on the second eighth-note of the bar), and the Scarlatti and Chopin excerpts are measured at the dotted-quarter-note level (two chords per bar in 6/8 time). The harmonic beats, on which events occur, are notated with letters: the harmonic events in the Beethoven excerpt are labeled with the measure number and the letters a, b, c, and d, while those in the Scarlatti and Chopin excerpts, are labeled with the measure number and the letters a and b. Performances of a given excerpt differed in mean tempo. To allow for comparison across recorded performances, the IOI values were normalized. Normalization of IOIs was performed by dividing each IOI value by the mean tempo (average IOI) of the performance from which it was extracted. For example, Koopman’s mean IOI in his recording of the Scarlatti excerpt is 633 26 ms, whereas Watanabe's mean IOI is 626 ms. The mean IOI used for normalization was averaged from the IOIs extracted from the analyzed musical segment. Measure Koopman IOI (ms) Koopman Normalized IOI Watanabe IOI (ms) Watanabe Normalized IOI 35a 640 1.011 514 0.821 35b 660 1.043 578 0.924 36a 670 1.058 815 1.302 36b 508 0.803 731 1.168 Table 2.2 Comparison of raw and normalized IOIs in two recordings of Scarlatti’s Sonata in D Major, K. 492, mm. 35a-35b. (IOI = inter-onset-interval). These IOIs represent the predominant (m. 35a), dominant (m. 35b) and tonic arrival of the first EC (m. 36a). Figure 2.4 Comparison of Koopman and Watanabe’s approach into the evaded cadence, in Scarlatti Sonata in D Major, K. 492, mm. 35a-36b. (EC = evaded cadence). In Table 2.1 and Figure 2.4, m. 36a represents the arrival of the first EC in the Scarlatti excerpt. By graphing the changes in the IOIs, Figure 2.4 highlights how both Koopman and Watanabe execute a two-step deceleration into the arrival chord of the EC. The magnitude of the timing change is measured by subtracting the IOI at m. 36a by the IOI at m. 35a. Koopman’s 27 increase is 30 ms, whereas Watanabe presents an increase of 301 ms. Normalized to their respective mean tempos, Watanabe’s change in tempo represents a greater deviation than Koopman’s (a two-step deceleration by 48.1% as compared with 4.7% ). The change of IOI has been attributed prospectively, in that it is perceived at the onset of duration (of the arrival chord) and therefore is “at” the onset of the cadential chord and not “into” it. The resulting values allow the analyst to compare the magnitude of changes in duration (IOI) from one chord to another. The direction of the change, whether the specific IOI contributes to an acceleration or deceleration, is determined based on its relative value as compared with the preceding and following IOIs. In considering acceleration and deceleration into cadences, four IOIs were examined, corresponding to the two chords preceding the arrival chord (predominant and dominant), the arrival chord (tonic or tonic substitute), and the chord following the arrival chord. Three types of approach are possible: 1. “One-step” acceleration/deceleration that features a single shorter or longer IOI for the arrival chord of the cadence (DC, EC, PAC) with changes of direction for both the previous and following IOIs. 2. “Two-step” acceleration/deceleration that features two successive shorter or longer IOIs, with two possible starting points: a. Starting on the pre-dominant (two chords before the arrival chord), with a change in direction following the arrival chord of the cadence (DC, EC, PAC). b. Starting on the dominant (one chord before the arrival chord), and including the chord following the arrival chord. . 28 3. Full acceleration/deceleration (three successive shorter or longer IOIs) starting on the pre-dominant and ending with the chord following the arrival chord. The timing fluctuations were measured between the IOI of the arrival chord and the IOI at the start of the acceleration/deceleration in all cases. The magnitude of three fluctuations are provided in percentages of the mean tempo. Percentages are obtained by multiplying the difference between two normalized IOIs by 100. For example, given a normalized IOI series of 1.011 and 1.230, the difference is 1.230 - 1.011 = 0.219 * 100 = 21.9%. A small number of performers, in all three excerpts, accelerate or decelerate at a magnitude of equal to or less than five percent upon their approach (type 1, 2a, 2b, or 3 as described above) to the arrival chord of the cadence (EC, DC, PAC). These small events, or successive events, would not necessarily be audible to the listener (Fraisse, 1952) nor would they necessarily be felt by the performer, making these events less likely to be intentional accelerations/decelerations, and more to do with basic human error. As these changes in tempo are only recognised by a computer, any tempo change under five percent was considered to be “no change,” therefore slightly altering the results. I have decided to remain more sensitive in my considerations of acceleration/deceleration than past studies (8.6%; Madison & Merker, 2002) to consider a wider variety of tempo fluctuations at DCs and ECs. When considering the data in Table 2.1 and Figure 2.4, given the threshold for timing fluctuations (i.e., ≤ 5%) , the performance by Koopman would not be considered an audible deceleration. Once normalized, the overall tempo fluctuations of each performer’s IOI series were compared to one another using the dynamic time warping algorithm, and performances that presented a similar timing profile were grouped together. Therefore, the IOI series of all performers were compared in two ways: (1) the timing profile of the entire segment and (2) their 29 approach to various cadences (EC, DC, and PAC). The former is used to compare whether there are any trends in the tempo fluctuations outside of the cadential approach; therefore, highlighting the significance (or lack-there-of) of said ambiguous cadential boundaries. The dynamic time warping algorithm compares all points in one series against the corresponding points from all other series (as described by Petitjean, Forestier, Webb, Nicholson, Chen, & Keogh, 2016), with the square root (representing Euclidean distance) of the entire equation representing their overall likeness to each other. In this case, each series would represent a different performer’s successive IOIs associated with the same musical segment. The smaller the resultant number is, the more alike the two examples will be, where the value of 0 would represent two series that are the exact same. Generally, most series that are recognizably alike will have a Euclidean distance less than 2. For example, in the case of the two performances of mm. 35a-36b by Koopman and Watanabe, each series is comprised of four points, which we could label as a1 through a4 and b1 through b4, respectively; therefore, the equation would be: √(a1 – b1)2 +(a2 – b2)2+(a3 – b3)2+(a4 – b4)2 √(1.011 - 0.821)² + (1.043 - 0.924)² + (1.059 - 1.302)² + (0.802 - 1.168)² The result of the calculation is 0.493 which represents the Euclidean distance between the two series (two performances). Given the number is further away from 0, the two performances by Koopman and Watanabe result in IOI profiles that are relatively dissimilar (i.e., one corresponds to a much higher rate of deceleration into the EC in m. 36a). Following these calculations, the performances are grouped in clusters as to which are most alike. For example, group 1: performances A, B, C, D, group 2: performances E, F, G, A. In this case, B and C are most alike in group 1, F and G are most alike in group 2, but all performances in group 1 are very dissimilar to all performances in group 2. Furthermore, although A and D are least alike in 30 group 1, they are more alike than any performances listed in group 2. These calculations were made using the program TextWrangler and the programming language Python. 3. Results The results of all three excerpts are presented here in order of composition date: (1) Scarlatti, Sonata in D Major, K. 492; (2) Beethoven, Sonata in Ab major, Op. 26, IV, and (3) Chopin, Etude Op. 10 No. 6. For each excerpt, there are two comparisons made. The first relates to the timing profiles of the overall segment, in which different performers are categorized together based on likeness (measured in Euclidean distance) for the full IOI series. The purpose of this comparison is to acknowledge that performers may have different approaches to a cadence while maintaining similar timing profiles of melodic and harmonic events between the cadences. The second comparison highlights the similarities between performances when only considering their cadential approach (to DCs, ECs, or PACs) by either acceleration or deceleration (approach 1, 2a, 2b, or 3, as discussed above). Normalized graphs have the measure numbers and chords on the x-axis, while the normalized IOI values are represented on the y-axis. For a more visually precise comparison between graphs, all timing profile graphs and cadential approach graphs use the same y-axis scale (0.6-1.5 ms for the Scarlatti, 0.5-2.3 ms for the Beethoven, and 0.6-2.2 ms for the Chopin). Further comparisons of excerpts can be found in the discussion portion of this paper (section 4). For the purposes of this study, I hypothesized that, given the arrival of substitute tonic harmony (vi), the DC will have a higher sense of closure; therefore, the performers will tend to decelerate into the DC (leading to a segmentation of the cadence with the music that comes before it). This corresponds with Caplin’s (2018) ordering of cadences in terms of closure, in which the DC has a higher ranking of closure achieved than the EC, due to the proper resolution 31 of the leading tone in the dominant (V) to the tonic note in the submediant (vi, or iv ⁶ substitute as seen in the Scarlatti excerpt), rather than the evasion of proper resolution of the dominant in an EC. The performers may interpret the repeating melodic/harmonic material of the EC as a new beginning; therefore, I hypothesized that the performers will shorten/accelerate at the EC (segmenting the EC with the music that follows it). 3.1 Scarlatti’s Sonata in D Major, K. 492 The recordings of Scarlatti’s Sonata in D Major feature performances on either the harpsichord or the modern piano. The oldest is dated 1954 (Kirkpatrick); the most recent is dated 2018 (Taylor and Colli). The twenty excerpts that were analyzed for this study are listed in Table 3.1 along with the average tempo for the full performance. Performer Record Label Record Number Recording Date* Excerpt Start Time Belder, Pieter-Jan** Brilliant Classics BC94923 2012 .29 Black, Virginia CRD Records CRD3533 2015 .29 Bloch, Boris Ars Produktion ARS38506 2013 .28 Colli, Federico Chandos CHAN10988 2018 .26 Fadini, Emilia Stradivarius STR33618SD n/a .36 Grante, Carlos Music and Arts Programs of America CD-1294 2017 .31 Greilsammer, David Sony Classical 886444092814 2014 .21 Hantaï, Pierre** Mirare MIR9918D 2002 .24 Kamenz, Igor Naive V5399 2014 .31 32 Kipnis, Igor** Sony Classical 074645326429 1993 .27 Kirkpatrick, Ralph** SWR Classic Archive SWR10365 1954 .29 Klosiewicz, Wladyslaw** CD Accord CDACCORDACD055 1999 .29 Koopman, Ton** Capriccio C10212 1988 .30 Lewin, Michael Naxos 8.553067 1995 (1999) .25 Pinnock, Trevor** Linn Records CKD570 2015 .27 Taylor, Justin** Alpha ALPHA399 2018 .25 Watanabe, Yoshio** ALM Records ALCD-1096 2007 .26 Yates, Sophie** Chandos CHAN0635 1998 .29 **Yang, Joyce Harmonia Mundi HMU907405DI 2005 .30 Zacharias, Christian Warner Classics 0724355534354 n/a .26 Table 3.1 List of recordings for Scarlatti’s Sonata in D major, K. 492, mm.30a-44b. (bpm = beat per minute; beat = dotted-quarter note). *Release dates are provided in parentheses when they are different from the recording dates. ** Indicates the music was recorded on a harpsichord, rather than a modern piano. 3.1.1 Timing Profiles The Scarlatti excerpts were divided into four distinct timing profiles (labelled A-D) according to their similarity as measured by the dynamic time-warping algorithm. These are presented as Figures 3.1-3.4. 33 Figure 3.1 Timing Profile A for Scarlatti’s Sonata in D Major, K. 492, mm. 30a-44b. (EC = evaded cadence; DC = deceptive cadence; PAC = perfect authentic cadence). Figure 3.2 Timing Profile B for Scarlatti’s Sonata in D Major, K. 492, mm. 30a-44b. (EC = evaded cadence; DC = deceptive cadence; PAC = perfect authentic cadence). 34 Figure 3.3 Timing Profile C for Scarlatti’s Sonata in D Major, K. 492, mm. 30a-44b. (EC = evaded cadence; DC = deceptive cadence; PAC = perfect authentic cadence). Figure 3.4 Timing Profile D for Scarlatti’s Sonata in D Major, K. 492, mm. 30a-44b. (EC = evaded cadence; DC = deceptive cadence; PAC = perfect authentic cadence). Profile A represents the performances with the most consistent tempos. Generally, these performances feature some successive fluctuations that involve more than one shortening/lengthening. For example, the Kipnis (mm. 31b-33a), Taylor, and Kirkpatrick (mm. 35 33b-34b) performances feature a sharp acceleration in mm. 33b-34b (expansion of dominant harmony through the alternation of the predominant ii⁰⁷), manifested as downward-sloping line segments on the graph during that time span. The performances in Profile B present a slight arch-shaped tempo profile, peaking with a very slight deceleration into m. 37a (the arrival of predominant harmony, IV, as the expansion of tonic harmony while approaching the second EC), with the tempos levelling off at both the start and end of the segment. Interestingly, there are only mostly minor changes in tempo (both acceleration and deceleration) outside of the cadences. For example, Lewin’s performance in mm. 37b-39a features a shorter chord at m. 37b, which corresponds to the descending 16th-note run of the predominant IV chord (within a tonic expansion I--IV--I), followed by a deceleration. The performances in Profile B present more stable tempos than the performances in Profile A. Profile C features more prominent tempo changes at the dotted-quarter-note level. Performers often produce a one-beat alteration in timing resulting in a more unpredictable IOI pattern. Other performances maintain successive tempo acceleration/deceleration for two beats, such as Pinnock in mm. 33a-34a. Finally, there is a levelling off at the end of the segment with several performances accelerating into or following the arrival chord of the PAC. Profile D presents a wide variety of timing patterns. For example, Yates’s elongation of the arrival chord at each of the three ambiguous cadences contrasts with her sharp shortening of m. 37b. However, there is a unique moment in mm. 33-34, where these performances feature more stability in tempo (what Schmalfeldt calls repetitive, dominant “plucking” arpeggiations) which contrasts with the timing fluctuations that surround it. 36 3.1.2 Cadential Approach Out of eight (23) possible approaches into the three ambiguous cadences, the majority of performers (15/20) chose to decelerate at the initial DC (as seen in Figure 3.5 and 3.6). Of those 15, seven decelerated into both of the ECs that followed. A summary of all performers’ approaches into each cadence is presented as Table 3.2. Performers with identical strategies are listed in the same column. Accelerates into Initial DC Decelerates into Initial DC Accelerates into 1st EC Decelerates into 1st EC Accelerates into 1st EC Decelerates into 1st EC Accelerates into 2nd EC Decelerates into 2nd EC Accelerates into 2nd EC Decelerates into 2nd EC Accelerates into 2nd EC Decelerates into 2nd EC Accelerates into 2nd EC Decelerates into 2nd EC Colli Hantaï Bloch Grante Black Fadini Kamenz Belder Klosiewicz Kirkpatrick Kipnis Koopman Greilsammer Yang Lewin Zacharias Pinnock Taylor Watanabe Yates Total: 2 Total: 1 Total: 1 Total: 1 Total: 4 Total: 2 Total: 2 Total: 7 Table 3.2 Eight possible approaches into the deceptive and evaded cadences in Scarlatti’s Sonata in D Major K. 492, mm. 30a-44b. (EC = evaded cadence; DC = deceptive cadence). Although there is a definite preference to decelerate into the initial DC, there were five performers that accelerated. Out of these five performances, two (Hantaï and Grante) had tempo 37 fluctuations of just over five percent (5.6% and 5.5%, just over the threshold of ≤ 5%). Only Colli had a substantial acceleration into the DC (18.3%); these approaches can be found in Figure 3.5 and 3.6. Thus, one could say the DC in the Scarlatti excerpt is treated as the end of previous material, rather than a beginning of new material. Figure 3.5 Scarlatti Sonata in D major, K. 492, acceleration into initial DC, mm. 30a-31b. (DC = deceptive cadence). 38 Figure 3.6 Scarlatti Sonata in D major, K. 492, deceleration into initial DC, mm. 30a-31b. (DC = deceptive cadence). Figure 3.7 Scarlatti Sonata in D major, K. 492, acceleration into first EC, mm. 35a-36b. (EC = evaded cadence). 39 Figure 3.8 Scarlatti Sonata in D major, K. 492, deceleration into first EC, mm. 35a-36b. (EC = evaded cadence). Figure 3.9 Scarlatti Sonata in D major, K. 492, acceleration into second EC, mm. 39a-40b. (EC = evaded cadence). 40 Figure 3.10 Scarlatti Sonata in D major, K. 492, deceleration into second EC, mm. 39a-40b. (EC = evaded cadence). Figure 3.11 Scarlatti Sonata in D major, K. 492, acceleration into final PAC, mm. 43a-44b. (PAC = perfect authentic cadence). 41 Figure 3.12 Scarlatti Sonata in D major, K. 492, deceleration into final PAC, mm. 43a-44b. (PAC = perfect authentic cadence). The simplicity of this piece, in terms of overall level of performance difficulty, may be a factor in the results for the two ECs. It allows the performer to be very rhythmically accurate, maintaining the dotted-quarter-note pulse. However, given that the second EC is a direct repetition of the first, and maintains the driving dotted-quarter-note beat throughout, the performers might find it easier to maintain a steady tempo rather than accelerate into the ECs. Furthermore, representative of the late-Baroque era, there would naturally be less rubato present in the performances to apply appropriate Historically Informed Practice (HIP). This is evident in a number of performances presenting “no change” (≤ 5% fluctuation) into the ECs. Considering the nature of the EC and the “one-more-time” technique, the initial ambiguous cadence (the DC) would present more of the element of surprise, thwarting one’s expectation of tonic harmony. The approaches to the two ECs are also modified repetitions of the approach to the initial DC. Yet, 50% of the performances decelerate at the two ECs. The summary of the cadential approaches for the Scarlatti sonata are presented in Table 3.3. The 42 PAC features the most stability in cadential approach with 50% of the performances featuring no change over the ≤ 5% threshold. Position and Type of Cadence Acceleration Deceleration No Change Initial DC 5/20 (25%) 15/20 (75%) - First EC 7/20 (35%) 10/20 (50%) 3/20 (15%) Second EC 9/20 (45%) 10/20 (50%) 1/20 (5%) PAC 5/20 (25%) 5/20 (25%) 10/20 (50%) Table 3.3 Summary of cadential approaches for Scarlatti’s Sonata in D Major, K. 492, mm. 30a-44b. (EC = evaded cadence; DC = deceptive cadence; PAC = perfect authentic cadence). No change is any tempo change that is ≤ 5%. Overall, there are 14 performances that were not included in Figures 3.5-3.12, because their performance featured acceleration/deceleration ≤ 5%, as per the threshold (Pinnock and Grante accelerating and Koopman decelerating at the first EC; Taylor accelerating at the second EC; Bloch, Greilsammer, Colli, Klosiewicz, Yates, Zacharias, Yang, Koopman accelerating, and Pinnock and Fadini decelerating at the final PAC). These statistics confirm or make clear that the segmentation of the DC as an apparent ending (as 75% of the performers lengthened/decelerated into the DC), seems even more convincing when considering how it is the only cadence where all performers presented a tempo change of over 5% (shown by a dash in the “No Change” column). 3.3 Beethoven’s Sonata in Ab Major Op. 26, Movement IV For the excerpt from Beethoven’s Sonata, nineteen recordings were analyzed and compared. The oldest is dated 1932-34 (Schnabel); the most recent is dated 2018 (Williams). A summary of performers and their recording information can be found in Table 3.4. 43 Performer Record Label Record Number *Recording Date Excerpt Start Time (s) Benz, Robert Thoroton CTH2058 1992 0.29 Biss, Jonathan Onyx ONYX4082 2012 0.29 Brendel, Alfred Brilliant Classics BC95315 2013 0.32 Chochieva, Zlata Piano Classics PCL0068 2014 Costa, Sequeria Claudio Records CB5575-2 2013 0.34 Gilels, Emill Orfeo C883132B 1976 (2013) 0.25 Gulda, Friedrich Orfeo C808109L 1953-57 0.26 Harrison, Andri Joël Gramola Records Gramola99139 2017 0.30 Jumppanen, Paavali Ondine ODE1280-2D 2015 0.25 Kempff, Wilhelm Deutsche Grammophon 28947903147 1965 (2012) 0.32 Kuerti, Anton Analekta FL24010 n/a 0.35 Michelangeli, Arturo Benedetti Music and Arts Programs of America CD-1036 1998 0.30 Nodaira, Ichiro Live Notes WWCC-7416 2002 0.30 Richter, Sviatoslav Decca 28947586197 2007 0.24 44 Schiff, Andras ECM Records 28947658757 2007 0.32 Schnabel, Artur Naxos Historical 8.110756 1932-34 (2003) 0.24 Sheppard, Craig Romeo Records Romeo7233-41 2005 0.28 Varjon, Denes Capriccio C51123 1988 0.30 Willems, Gerard ABC Records 28948143399 2017 0.29 Williams, Llyr Signum Classics SIGCD527 2018 0.32 Table 3.4 List of recordings for Beethoven’s Sonata in Ab Major, Op. 26, IV, mm.40a-38b. (bpm = beat per minute; beat = eighth-note). *Release dates are provided in parentheses when they are different from the recording dates. 3.2.1 Categories of Timing Profiles For the Beethoven sonata there are only three distinct timing profiles (labelled A-C). These are presented as Figures 3.13-3.15. Figure 3.13 Timing Profile A for Beethoven’s Sonata in Ab Major, Op. 26, IV, mm. 40a-48b. (EC = evaded cadence; DC = deceptive cadence; PAC = perfect authentic cadence). 45 Figure 3.14 Profile B for Beethoven’s Sonata in Ab Major, Op. 26, IV, mm. 40a-48b. (EC = evaded cadence; DC = deceptive cadence; PAC = perfect authentic cadence). Figure 3.15 Timing Profile C for Beethoven’s Sonata in Ab Major, Op. 26, IV, mm. 40a-48b. (EC = evaded cadence; DC = deceptive cadence; PAC = perfect authentic cadence). Profile A begins with IOIs that fall within an approximate range of 2%; the segment ends with a wider range of IOIs (approximately 6%). All performances are quite varied. 46 The performances in Profile B gradually become more varied as the segment progresses, with the passage between the second DC and the final PAC featuring larger and more frequent spikes of both shortening (of the dominant (V)) and lengthening (of the tonic (I)). Costa and Schiff, in Profile C are very different than all performances in Profiles A and B. Overall, their tempos are more stable (including at the final PAC), featuring more significant shortening/lengthening at, or around, the ambiguous cadences (DC and EC). 3.2.2 Cadential Approach Overall, there are eight possible approaches to the cadences (DC, EC, PAC), presented in Table 3.5. Accelerates into the Initial EC Decelerates into the Initial EC Accelerates into 1st DC Decelerates into 1st DC Accelerates into 1st DC Decelerates into 1st DC Accelerates into 2nd DC Decelerates into 2nd DC Accelerates into 2nd DC Decelerate s into 2nd DC Accelerates into 2nd DC Decelerate s into 2nd DC Accelerates into 2nd DC Decelerates into 2nd DC Schiff Brendel Kuerti Gulda Nodaria Giels Schnabel Harrison Varjon Kempff Costa Michelangeli Willems 47 Scheppard Benz Williams Jumppanen Biss Richter Total: 1 Total: 0 Total: 1 Total: 2 Total: 1 Total: 0 Total: 1 Total: 13 Table 3.5 Eight possible approaches into the evaded and deceptive cadences in Beethoven’s Sonata in Ab Major, Op. 26, IV, mm. 42a-46a. (EC = evaded cadence; DC = deceptive cadence). A large majority of the performers (13/19) decelerated at all three cadences. One possible reason for this preferred approach relates to the structural make-up of the “one-more-time” technique, as coined by Schmalfeldt. By nature, the “one-more-time” technique features at least one direct repetition of cadential preparation (consisting of the progression from predominant harmony to dominant harmony). In this case, Beethoven repeats the cadential build-up three times, only changing the first melody note to a higher chord tone (by the interval of a third), and the arrival chord from I--I⁶ to vi--I⁶. When listening to the movement for the first time, listeners would be surprised by the initial evaded cadence in place of the anticipated PAC. The first DC may retain that element of surprise with the new arrival chord (vi); however, the second DC is likely to be less surprising. Therefore, the performers’ tempo strategies would reflect these perceptions by a greater magnitude of deceleration into the initial DC, in comparison to the 48 second DC. This would reflect the element of greater surprise upon the presentation of the initial DC, that is lessened in the consequent DC. There may also be an articulative reasoning behind the deceleration at all three cadences. Given the arrival chord (vi) of the DC is at the end of the slur, the next onset features a large leap in the left hand and a sforzando that requires a little extra preparatory time to be effective, the second onset would come a little later than we would expect from the preceding tempo. Figure 3.16 Beethoven Sonata in A♭ major, Op. 26, IV, acceleration into initial EC, mm. 41a-42b. (EC = evaded cadence). 49 Figure 3.17 Beethoven Sonata in A♭ major, Op. 26, IV, deceleration into initial EC, mm. 41a-42b. (EC = evaded cadence). Figure 3.18 Beethoven Sonata in A♭ major, Op. 26, IV, acceleration into first DC, mm. 43a-44b. (DC = deceptive cadence). 50 Figure 3.19 Beethoven Sonata in A♭ major, Op. 26, IV, deceleration into first DC, mm. 43a-44b. (DC = deceptive cadence). Figure 3.20 Beethoven Sonata in A♭ major, Op. 26, IV, acceleration into second DC, mm. 45a-46b. (DC = deceptive cadence). 51 Figure 3.21 Beethoven Sonata in A♭ major, Op. 26, IV, deceleration into second DC, mm. 45a-46b. (DC = deceptive cadence). Figure 3.22 Beethoven Sonata in A♭ major, Op. 26, IV, acceleration into final PAC, mm. 47a-48b. (PAC = perfect authentic cadence). 52 Figure 3.23 Beethoven Sonata in A♭ major, Op. 26, IV, deceleration into final PAC, mm. 47a-48b. (PAC = perfect authentic cadence). The summary of the cadential approaches for the Beethoven sonata are presented in Table 3.6. Position and Type of Cadence Acceleration Deceleration No Change Initial EC 3/19 (16%) 15/19 (79%) 1/19 (5%) First DC 2/19 (11%) 16/19 (84%) 1/19 (5%) Second DC 4/19 (21%) 15/19 (79%) - PAC 1/19 (5%) 18/19 (95%) - Table 3.6 Summary of cadential approaches for Beethoven’s Sonata in Ab Major, Op. 26, IV, mm. 40a-48b. (EC = evaded cadence; DC = deceptive cadence; PAC = perfect authentic cadence). No change is any tempo change that is ≤ 5%. Overall, there were two instances of acceleration/deceleration under the ≤ 5% threshold (Brendel accelerating into the DC and Kuerti accelerating into the first DC). The most similar cadential approach is a deceleration at the final PAC, represented by 95% (18/19) of the 53 performances (as seen in Figure 3.23). This agrees with the findings of previous studies (beginning with Seashore, 1936) in which there is a tendency to lengthen, or decelerate, at the ends of phrases. For both DCs, performers have a clear preference (over 80%) to decelerate; therefore, suggesting a segmentation of the DC with the music that precedes it (an apparent ending). On the other hand, there is also a preference to decelerate into the initial EC (74%); therefore, categorizing the EC as an ending (segmenting the EC with the music preceding it). 3.2 Chopin’s Etude Op. 10, No. 6 The challenge of analysing the recordings of Chopin’s Etude, Op 10, No. 6 is a direct result of the extremely diverse approaches to the piece, with regard to the marked andante tempo. Although the average tempo of all 24 recordings is 108 bpm (beat = quarter-note) (SD = 36), individual tempos range from 76 bpm (Cherkassky and Bonino) to 210 bpm (Katz). A possible explanation for this may be stylistic, i.e., related to the piece having been composed during the romantic period (ca. 1830-1900). During this time, composers wrote music that represents emotions and feelings of the individual, resulting in more rhythmic freedom in performance as attested by the constant presence of rubato and extreme chromaticism (Hudson, 1994). More simply put, as an etude, some performer will understand this piece as a technical study of how to execute fast, middle-voiced figuration; others see it more as a compositional etude in a difficult key with a wide range of chromatic modulations, creating a beautiful harmonic tapestry. Given his extremely fast tempo, Katz (2017) in particular seems to be disregarding the marked andante. He may be focussing on the technical challenges of the figuration rather than the extreme chromatic modulations a slower tempo would emphasize. 54 The oldest recording is dated 1928-50 (Backhaus); the most recent recordings are dated 2018 (Brailowsky and Chernika). The 25 recordings of the Chopin Etude, Op 10, No. 6 that were analyzed for this study are listed in Table 3.7. Performer Record Label Record Number Recording Date Excerpt Start Time (s) Anda, Géza Orfeo C824102B 1965 (2010) 2.57 Ashkenazy, Vladimir Decca 00028946625026 2000 (2010) 3.01 Backhaus, Wilhelm IDIS IDIS6559 1928-50 (2008) 2.23 Badura- Skoda, Paul Music and Arts Programs of America CD-1230 1956 (2009) 2.23 Berzins, Gints Pavane Records ADW7312 1994 2.37 Biret, Idil Naxos 8.550364 1990 (1999) 2.32 Bonino, Gianmaria Cantus Records CANTUS9635 2017 3.36 Borac, Luiza AVIE AV2161 2008 (2009) 2.37 Brailowsky, Alexander RCA Records 88644680007 2018 2.11 Browning, John RCA Records 886446381978 1997 (2017) 2.18 Cherkassky, Shura Naxos Classical Archives 9.80022 1955 (2001) 3.16 Chernicka, Tatiana Ars Produktion ARS38548 2018 3.11 55 Chiu, Frederic Harmonia mundi HMU907201DI 1997 3.50 Chochieva, Zlata Piano Classics PCL0068 2014 2.53 Di Bin, Sebastian Centaur CRC3588 2017 3.27 Giuiano, Philippe Mirare MIR234D n/a 2.19 Katz, Amir Orfeo C922171A 2017 1.21 Kurashima, Yuki Triton OVCT-00097 2013 2.26 Lympany, Moura Erato 825646015863 2006 3.07 Manikonian, Vardan Phaia Music CAL9220 2016 2.51 Otey, Orlando CD Baby B001HEIKEG 2007 3.07 Perahia, Murray Sony Classical 884977129496 2004 (2011) 1.45 Schirmer, Ragna Berlin Classics 0017602BC 2003 (2010) 3.08 Shaboyan, Sona OEHMS Classics OC713 2008 3.08 Tomassi, Giorgia Warner Classics 724357277952 2003 2.17 Table 3.7 List of recordings for Chopin’s Etude Op. 10, No. 6, mm. 47a-51b. (bpm = beat per minute; beat = dotted-quarter note). *Release dates are provided in parentheses when they are different from the recording dates. 56 3.2.1 Timing Profiles The performances of Chopin’s Etude represent four distinct timing profiles (labelled A-D). These are presented as Figures 3.24-3.27. Figure 3.24 Timing Profile A for Chopin’s Etude Op. 10, No. 6, mm. 47a-51b. (EC = evaded cadence; PAC = perfect authentic cadence). Figure 3.25 Timing Profile B for Chopin’s Etude Op. 10, No. 6, mm. 47a-51b. (EC = evaded cadence; PAC = perfect authentic cadence). 57 Figure 3.26 Timing Profile C for Chopin’s Etude Op. 10, No. 6, mm. 47a-51b. (EC = evaded cadence; DC = deceptive cadence; PAC = perfect authentic cadence). Figure 3.27 Timing Profile D for Chopin’s Etude Op. 10, No. 6, mm. 47a-51b. (EC = evaded cadence; PAC = perfect authentic cadence). Profile A presents the performances that are most alike. The performers apply only minor fluctuations in tempo whilst achieving a small, gradual deceleration to the final dominant harmony (arriving m. 50b). The moment of most variation is mm. 49-50, where the ♭II harmony 58 is present in the third repetition of the cadential material, following the new melodic descent from E♭5 in m. 45. The performers' tempo fluctuations in Profile B present a visual two-beat, long-short, chord pattern of the dominant (V) to the predominant (♭II), supporting the idea of predominant expansion through passing dominant harmony (E♭3s in the left hand), where the ♭II is acting as a group beginning. There is also a more substantial (especially when compared to the performances in Profile A) deceleration at the dominant harmony on m. 50b. In fact, the almost perfect diagonal in Badura-Skoda’s performance from mm. 47b-50b represents a steady deceleration through the phrase expansion resulting from the two ECs that culminates on the dominant of the final PAC. Profile C presents the most substantial, although less graduated, overall deceleration to the final dominant harmony (m. 50b). There is no gradual acceleration/deceleration, rather, all performers allow for two sudden moments of tempo stability: (1) mm. 46a-47b before the onset phrase expansion, and (2) in mm. 49b-50a with the melodic descent from C#5 featuring predominant harmony (the direct opposite approach of that presented by the performances in Profile A). Although Timing Profile D represents the two most unique performers. Anda’s performance features an initial acceleration into dominant harmony (m. 48b), followed by a constant deceleration into the final instance of dominant harmony (m. 50b). On the other hand, Ashkenazy is the only performer to have an overall gradual deceleration that peaks at m. 50a, the final presentation of ♭II harmony before the phrase is completed. He may have chosen to emphasize the last moment of extended chromatic harmony before the more traditional harmonic conclusion. 59 3.1.2 Cadential Approach For the most part, all IOI’s in Chopin’s Etude, for all performances, remain flat until approaching one of the ambiguous structural boundaries (ECs). However, there are many recordings that produce very distinctive shapes of mapped IOIs due to extreme accelerations or decelerations in tempo. All performances (except for Ashkenazy) feature a deceleration at m. 50b (final dominant harmony) before a sharp acceleration at m. 51a (arrival of the tonic harmony of the PAC, as shown in Figure 3.32). On the other hand, the approaches into the more ambiguous ECs are more varied. Overall, there were four possible types of approach to the ECs, which are listed in Table 3.8. Accelerates into 1st EC Decelerates into 1st EC Accelerates into 2nd EC Decelerates into 2nd EC Accelerates into 2nd EC Decelerates into 2nd EC Backhaus Anda Kurashima Badura Berzins Ashkenazy Otey Biret Brailowsky Browning Bonino Lympany Cherkassky Borac Schirmer Chernika Di Bin Shaoyan Chiu Tomassi Chochieva Giuiano 60 Katz Manikanian Perahia Total: 7 Total: 11 Total: 2 Total: 5 Table 3.8 Four possible approaches into the evaded cadences in Chopin’s Etude Op. 10, No. 6, mm. 47a-51b. (EC = evaded cadence). The Chopin excerpt only contains two ECs. However, the complexity of the piece, compared to the Scarlatti, is evident in the use of chromatic harmonies (such as ♭II) and dense texture. The majority of the performers accelerate at the first EC (13/25) and decelerate at the second EC (16/25). Therefore, the first EC may be considered a beginning (segmented with the music that follows it), whereas, the second EC may be considered an ending (segmented with the music that precedes it). These approaches are summarized in Figures 3.28-3.32. 61 Figure 3.28 Chopin Etude Op. 10, No. 6, acceleration into first EC, mm. 47a-48b. (EC = evaded cadence). Figure 3.29 Chopin Etude Op. 10, No. 6, deceleration into first EC, mm. 47a-48b. (EC = evaded cadence). 62 Figure 3.30 Chopin Etude Op. 10, No. 6, acceleration into second EC, mm. 48a-49b. (EC = evaded cadence). Figure 3.31 Chopin Etude Op. 10, No. 6, deceleration into second EC, mm. 48a-49b. (EC = evaded cadence). 63 Figure 3.32 Chopin Etude Op. 10, No. 6, acceleration into final PAC, mm. 50a-51b. (PAC = perfect authentic cadence). Considering that the feeling of “surprise,” felt during the first EC where the expectation of the PAC is suddenly averted, would be lessened the second time the EC occurs, one might predict the opposite approach of deceleration and then acceleration to be more plausible, unless the performer is trying to create more surprise by decelerating into the second EC as if it was the final PAC. The more substantial the deceleration, the more significant emphasis of the moment of cadential arrival (Seashore, 1936). Furthermore, there is a change in melodic approach to the final PAC, rather than another direct repetition, making it stand out as the hierarchically more substantial event. This may have prompted some performers to close-off the segment with the two ECs, and then start again toward the final PAC, consistent with the acceleration/deceleration pattern of both ECs. However, perhaps it is merely the goal of performers to “never do the same thing twice” that is at play here. For example, this can also be observed with drastic changes in dynamics (the first time forte; the second time piano) creating an “echo effect.” Considering the 64 > 5% threshold for timing fluctuations, the summary of the cadential approach in Chopin’s Etude can be found in Table 3.9. Position and Type of Cadence Acceleration Deceleration No Change First EC 13/25 (52%) 1/20 (4%) 11/25 (44%) Second EC 4/25 (16%) 16/25 (64%) 5/25 (20%) PAC 24/25 (96%) - 1/25 (4%) Table 3.9 Summary of cadential approaches for Chopin’s Etude, Op. 26, No. 6, mm. 47a-51b. (EC = evaded cadence; PAC = perfect authentic cadence). No change is any tempo change that is ≤ 5%. There are 17 accelerating/decelerating approaches that are under the ≤ 5% threshold (Manikonian, Chiu, Ashkenazy, Chernika and Chochieva accelerating into the first EC; Badura, Otey, Bonino, Kurashima, Borac, and Di Bin decelerating into the first EC; Biret accelerating into the second EC; Berzins, Brailowsky, Kurashima, and Otey decelerating into the second EC; and Brailowsky accelerating into the final PAC). As noted previously, the majority of performers prefer to accelerate into the initial EC and then decelerate into the second EC, suggesting an interpretation of the first EC as a beginning and the second as an ending. Interestingly, the performers’ preferred approach to the final PAC completes the pattern of acceleration - deceleration - acceleration. It is the opposite of what one might expect, as it is most common to conclude a phrase with lengthening/deceleration. Considering this is the only excerpt with only two ambiguous cadences, in which the second is a direct repetition, and the final PAC is a decorated repetition, a pattern of alternation may have felt natural to the performer. On the other hand, if the approach to the final PAC has intentionally been made more substantial by the 65 composer (with the change in melodic material) one may suggest how the opposite pattern of deceleration - acceleration - deceleration would be more expected. 4. Discussion 4.1 Comparison of Timing Profiles Across Examples Chopin’s Etude proved to have the most similar timing profiles, while the profiles for the Scarlatti and Beethoven examples were more varied. It is important to consider, with regards to the Beethoven and Scarlatti examples, that there are four boundary points (one EC, two DCs, and one PAC for the Beethoven; one EC, two DCs, and one PAC for the Scarlatti ), compared to three boundary points in Chopin’s Op. 10, No. 6 (two EC’s and one PAC). Repp, in his 1998 study, proposes that the larger the number of structural boundaries, the more similar the timing of recordings. Furthermore, he suggests that the more boundary points there are, the more likely multiple recordings will contain more similarities, when comparing IOI’s. This study proposes the opposite results are true - the more structural boundaries (cadences) there are, the less-alike the timing profiles are. However, considering Repp is mainly addressing cadences like the HC and PAC, the earlier statement could be amended to highlight that when examining ambiguous cadential boundaries - the more ambiguous cadences, the less-alike the timing profiles will be. 4.2 Comparison of Cadential Approach Across Examples While the results indicate eight different possible approaches for both the Scarlatti and Beethoven examples, and four possible approaches for the Chopin example, one can see how all performers, across all recorded excerpts, approach the ambiguous cadences (DC, EC) in Table 4.1. It also lists the where the cadence is within the entire excerpt (i.e., first or second position). 66 Position and Type of Cadence Acceleration Deceleration No Change First DC 7/39 (18%) 31/39 (79%) 1/39 (3%) Second DC 4/19 (21%) 15/19 (79%) - First EC 23/64 (36%) 26/64 (41%) 15/64 (23%) Second EC 13/45 (29%) 26/45 (58%) 6/45 (13%) Table 4.1 Summary of acceleration/deceleration into evaded and deceptive cadences across all excerpts. (EC = evaded cadence; DC = deceptive cadence). The “first” DC includes both the Initial DC (followed by an EC) and the first of two DCs. The “first” EC includes both the initial EC (followed by a DC) and the first of two ECs. The DC, whether in initial or second position, features a consistent pattern of deceleration among the majority (79%) of performers. These results are consistent with the hypothesis of the DC being segmented with the material preceding it as an apparent ending. However, all performances present a variety of acceleration/deceleration patterns of approach at the ECs. Therefore, the results of this study are not consistent with the hypothesis that the EC can be grouped with the material that follows it. However, there are some performers who, in these excerpts, make a consistent distinction between the DCs and ECs (Scarlatti: Grante, Black, Kirkpatrick, Yang, and Zacharias (5/20); Beethoven: Kuerti, Gulda, and Schnabel (3/19)). The Chopin features two ECs and Backhaus, Berzins, Brailowsky, Lympany, Schirmer, Shaoyan, Tomassi, Badura, Di Bin, Borac, Bonino, and Biret (12/20) accelerate into the initial EC and decelerate into the second EC. It is interesting, that the Chopin, that only contains one type of ambiguous cadence (EC), is most consistent in tempo fluctuations at each EC. It is possible the consistency of the having only one type of ambiguous cadence in the Chopin excerpt alleviates not only further phrase expansion but allows the performer to simply vary the way they play a repeating cadential progression. 67 Seashore (1936) and other researchers found that there is typically a lengthening (deceleration) at the end of a phrase, especially in the case of more conclusive cadences (i.e., IAC or PAC). However, the majority (44%) of the performers in the selected excerpts from Scarlatti, Beethoven, and Chopin accelerated at the final PAC of the phrase. Therefore, these findings contradict Seashore’s. Considering the presence of multiple ambiguous cadences, the performer may be attempting to accelerate at the final PAC by finally achieving the tonic harmony closure that has been evaded, or substituted for such a long, expanded phrase. However, one must consider that while 96% of the Chopin recordings feature an acceleration at the final PAC, 95% of the Beethoven recordings feature a deceleration at the final PAC (50% of the Scarlatti recordings feature no change that is above the threshold of ≤ 5% at the PAC). These differences can be attributed to the very different nature of all three PACs, as discussed in previously in selected excerpts. Considering there were 25 recordings analyzed of the Chopin excerpt, and 19 analyzed of the Beethoven excerpt, the higher number of Chopin recordings would influence the overall comparisons across examples. Therefore, the tempo change at the final PAC would be better presented as a bar graph, as shown in Figure 4.1. 68 Figure 4.1 Tempo change at the final perfect authentic cadence for the Scarlatti Sonata in D major, K. 492, mm. 43a-44b; Beethoven Sonata in A♭ major Op. 26, IV, mm. 47a-48b; and Chopin Etude Op. 10, No. 6, mm. 50a-51b. Possible reasons for the varied approach at the PAC across examples are directly related to the make-up of each PAC, as discussed previously, and the type of ambiguous cadences within the excerpt (DC, EC, or both). The PACs are all unique; in the Scarlatti excerpt, the music following the PAC moves on to a new thematic idea; in the Beethoven excerpt, the music following the PAC prolongs the cadential tonic; in the Chopin excerpt, there is a marked rallentando, after the arrival chord of the PAC. In comparison, the DCs and ECs utilize the “one-more-time technique, involving repetition of similar material. Therefore, one can expect more varied tempo fluctuations at the PAC of each excerpt. Furthermore, the Scarlatti and Beethoven excerpts feature both DCs and ECs leading up to the final PAC, whereas, the Chopin only has two ECs. A further break down of the phrase structure can be found in Phrase Structure (4.3). 69 4.3 Phrase Structure The Scarlatti, Beethoven, and Chopin excerpts featuring ECs and DCs all represent a type of phrase expansion. All of these excerpts can be defined in terms of classical structure analysis (as coined by Caplin); however, they also showcase a departure from the standard phrase structure that results from the use of ECs and DCs. Caplin defines phrase expansion as “An internal lengthening of the constituent members of a formal function” (1998, 254). The standard period structure consists of a four-measure antecedent phrase (ending with a weaker cadence; for example, a HC), followed by a four-measure consequent phrase (ending with a more conclusive cadence; for example, a PAC). Instead of following this structural outline, Scarlatti, Beethoven and Chopin all present expanded consequent phrases. The opening of the Scarlatti sonata presents a repetition of a four measure T-PD-D-T phrase (I--IV6--V--I) ending with a PAC, at mm. 4a and 8a. However, the third phrase is expanded through repetition and a modulation to the minor v key, A minor. It is within this new key that the DC and two subsequent ECs occur following a six-measure phrase that ends on a HC in A minor (arriving m. 26a). The phrase in question comprises 19 measures, and includes motivic repetition, a deceptive cadence, two evaded cadences, and the “one-more-time” technique. A summary can be found in Figure 4.2. The piece differs from the expected even-numbered phrases to create a 19-measure phrase in which the DC occurs on the 6th bar of the phrase, the ECs land on the 11th and 15th measures of the phrase, and the PAC arrives on m. 19a. By having the cadential boundaries on odd-number measures, rather than even-numbered measures (such as mm. 4 or 8), this excerpt is typical for “Italian” style barring (Rothstein, 2008). 70 HC DC *1 2 3 4 5 6 7 8 9 10 11 12 13 **20 21 22 23 24 25 26 27 28 29 30 31 32 Am Tonic Expansion - - - - - - - - - - - - - - - Plucking Am V-ii⁰ - - - - - - - - - - - - - - - - EC EC PAC 14 15 16 17 18 19 20 21 22 23 24 33 34 35 36 37 38 39 40 41 42 43 AM AM AM Figure 4.2 Phrase structure analysis of Scarlatti’s Sonata in D Major, K. 492, mm. 26-44. * indicates measure numbers within the phrase. ** indicates measure numbers within the piece. The bold measure numbers indicate where the IOI extraction began. The phrase from Beethoven’s sonata movement, from which the segment is extracted, begins in m. 28. Measure 28-29 are repeated in mm. 31-32, ending with a HC in the dominant key in m. 32. This dominant harmony is expanded for ten measures (through repetition in different registers). There is further expansion by an EC followed by two DCs (arriving mm. 42a, 44a, and 46a). Unlike the Scarlatti and Chopin examples, the Beethoven sonata maintains the cadential arrival on the even-numbered measures (that we heard in the opening period of four-measure phrases, with cadences arriving at mm. 4 and 8). However, the ambiguous cadences are emphasized by a large dominant expansion that obscures the sense of where closure should be anticipated. The phrase structure analysis is presented as Figure 4.3. 71 HC *1 2 3 4 5 6 7 8 9 10 11 28 29 30 31 32 33 34 35 36 37 38 V Expansion - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - EC DC DC PAC 12 13 14 15 16 17 18 19 20 21 39 40 41 42 43 44 45 46 47 48 E♭M E♭M E♭M E♭M - - - - - - - - - - Figure 4.3 Phrase structure analysis of Beethoven’s Sonata in Ab Major, Op. 26, IV, mm. 28-48. * indicates measure number within the phrase. ** indicates measure number within the piece. The bold measure number indicates where the IOI extraction began. Chopin’s Etude features an expanded, 11-measure, phrase based on the initial eight-measure period at the opening of the piece. Instead of having two four-measure phrases (the first ending with a HC, the second ending with an AC), Chopin utilizes two EC and the “one-more-time” technique so that the ECs arrive on mm. 49 and 50 of the second phrase, within the final period, creating a seven-measure answer phrase and an 11-measure period. The ambiguous cadences are further emphasized by the metric arrival of the all cadences (EC, DC, PAC) on odd-number measures, when they were originally presented in a basic period format of arrival on m. 4 and 8 (even-measure numbers). The phrase structure analysis is presented as Figure 4.4. 72 HC EC EC PAC *1 2 3 4 5 6 7 8 9 10 11 **41 42 43 44 45 46 47 48 49 50 51 ii Ebm Ebm Ebm Tonicization - ♭II - - - - Tonicization Figure 4.4 Phrase structure analysis of Chopin’s Etude, Op. 10, No. 6, mm. 41-53. * indicates measure numbers within the phrase. ** indicates measure numbers within the piece. The bold measure number indicates where the IOI extraction began. The phrase structure is relevant to this study, as part of a deeper understanding of how the original eight bar phrases (period structure) have been expanded to accommodate the multiple ambiguous cadences. Given the performers have already played the original eight-measure period, they would be forced to address how the newly expanded repetition of period structure would be segmented. 5. Conclusion 5.1 Summary Findings This study has explored the most ways performers change their tempo at evaded and deceptive cadential boundaries in excerpts from Scarlatti’s Sonata in D Major, K. 492, Beethoven’s Piano Sonata in Ab Major, Op. 26 movement IV; and Chopin’sEtude in Eb minor, Op. 10, No. 6. Assuming that a decrease of tempo is associated with segment endings and an increase of tempo with segment beginnings, we can understand performers’ tempo changes to indicate how they group of the EC and DC with preceding and following materials. Most of them decelerate at the DC, grouping it with the material that preceded it (an apparent ending). On the other hand, the performances show different tempo fluctuations at the ECs, within and across 73 performances. This highlights how the segmentation of the EC may be affected by other factors: (1) its placement in the phrase, (2) the number of other ambiguous cadences that surround it, and (3) the melodic/harmonic content of the phrase. Therefore, the data showed no consistent way to perform the EC, rather, it presents varied approaches in performance. The ambiguous cadential boundaries are always presented as part of a phrase expansion and are often a part of an extended phrase in which there are more than one ambiguous cadence. This adds further ambiguity to the segmentation of the formal structure, giving it its unique presentation in performance. The greater the number of ambiguous cadential boundaries, the less alike the performances of these phrases will be on both the micro and macro levels. 5.2 For Further Research This paper has analyzed recordings of ambiguous cadential boundaries. However, it is limited to the performer’s point of view. Recommended further studies would include: 1. Live versus recorded performance 2. The listener’s segmentation 3. Musicians versus non-musicians 4. Multiple theorists’ analysis, including amateur theorists versus professional theorists The reason that it would be interesting to study live recordings has to do with the difference between an edited performance and a one-take performance. The recordings in this study would have been re-recorded and edited to suit the performer’s preferred presentation of the formal structure, whereas, a one-take performance of the piece, which not be as well prepared, may involve in-the-moment decisions about formal structure segmentation, especially 74 at ambiguous boundary points The listener’s point of view is relevant on whether or not the segmentation, due to shortening/acceleration or lengthening/deceleration, is audible (most often in, in-line segmentation procedures). For example, Schmalfeldt and Caplin are unique listeners in that they analyze these excerpts as containing DCs and ECs and generalize them for others to understand and perceive. Although these events may be more ambiguous to the performer, through the internal expansion of the basic period structure, are the performers aware that they are segmenting specific ECs and DCs? Or are they merely segmenting musical events that Caplin and Schmalfeldt have defined as being either DCs or ECs? Musicians and non-musicians might differently segment the ambiguous cadential boundaries (presented individually or as a group). The comparison of musician and non-musicians is always relevant as musicians are trained to recognize cadential boundaries and may have learned to segment them in a certain way. In the case of successive ECs or DCs, musicians may come to expect them, rather than being surprised by them, due to their prior experience with the one-more-time technique. On the other hand, non-musicians approach the segmentation task without any background knowledge and can shed light into the more obvious changes in boundary segmentations. Regardless of the specific question surrounding ambiguous cadential boundaries, if we view music performance as the presentation of musical structure, it can shed light into the segmentation of any piece of music. Considering multiple theorists’ analysis would allow for a less biased analysis of all excerpts, considering the Roman numeral analyses present in this study were adaptations of their original analysis by Caplin and Schmalfeldt. Furthermore, when comparing amateurs to professionals allows the amateur to be less influenced by the professional analysis and feel more confident presenting their own interpretation of the analysis. 75 6. Bibliography Addessi, A. R. & Caterina, R. (2005) Analysis and Perception in Post-Tonal Music: An Example from Kurtág’s String Quartet Op. 1. Psychology of Music, 33, 94-116. 10.1177/0305735605048015. Beethoven, L.V. Sonata in A♭ Major, Op. 26, IV. Kalmus, E. F. (Eds.), Ludwig van Beethovens Werke, Serie 16: Sonaten für das Pianoforte, Nr.135. 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Thesis/Dissertation
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Music - Theory
Vancouver : University of British Columbia Library
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Comparison of performed tempo changes at deceptive and evaded cadences
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