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Fluctuating and suspended meter in selected passages from Arnold Schoenberg’s Das Buch der hangenden… Evdokimoff, Thomas William 1997

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FLUCTUATING AND SUSPENDED METER IN SELECTED PASSAGES FROM ARNOLD SCHOENBERG'S DAS B UCH DER HANGENDEN GARTEN, OPUS 15 by THOMAS WILLIAM EVDOKIMOFF B.Mus., The University of British Columbia, 1993 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS in THE FACULTY OF GRADUATE STUDIES (School of Music) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA October 1997 © Thomas William Evdokimoff, 1997 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of -my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of The University of British Columbia Vancouver, Canada Date DE-6 (2/88) ABSTRACT 11 This thesis explores Arnold Schoenberg's use of meter in Das Buck der hangenden Garten, Opus 15. The thesis works from the premise that Schoenberg treats meter in a manner analogous to that usually associated with pitch material: meter is motivic in nature, and can be subjected to developmental techniques. The concepts of fluctuating meter and suspended meter are developed, and used to describe the music; these concepts are derived from an analogy with Schoenberg's own terms schwebende Tonalitat and aufgehobene Tonalitat (fluctuating and suspended tonality). Selected excerpts from the song cycle are analyzed. The analyses focus on issues of meter, although some pitch analysis is used to complement the discussion. iii TABLE OF CONTENTS Abstract ii Table of Contents iii List of Examples iv List of Tables vii List of Figures viii Acknowledgments ix Introduction 1 Chapter 1 Schoenberg's Early Metrical Developments: Towards a Practice of Fluctuating Meter 5 Chapter 2 Suspended Meter in Schoenberg's Das Buck der hangenden Garten 37 Chapter 3 An Examination of Fluctuating and Suspended Meter in the Piano Introduction to the First Song 61 Concluding Remarks 86 Selected Bibliography 89 LIST OF EXAMPLES Example 1.1 Brahms, String Quartet No. 3 in Bb Major (Opus 67), mm. 1-4. Example 1.2 Brahms, String Quartet No. 3 in Bb Major (Opus 67), mm. 8-9. Example 1.3 Brahms, String Quartet No. 3 in Bb Major (Opus 67), mm. 63-65. Example 1.4 Brahms, String Quartet No. 3 in Bb Major (Opus 67), mm. 96-97 and mm. 101-103. Example 2.1 Brahms, Abenddammerrung (Opus 49 No. 5), mm. 1-2. Example 2.2 Brahms, Abenddammerrung (Opus 49 No. 5), mm. 21-22. Example 2.3 Brahms, Abenddammerrung (Opus 49 No. 5), mm. 43-45. Example 3.1 Schoenberg, Madchenfruhling, mm. 1-15. Example 3.2 Schoenberg, Madchenfruhling, mm. 27-30. Example 3.3 Schoenberg, Madchenfruhling, mm. 40-43. Example 4.1 Schoenberg, Nicht Doch!, mm. 6-8. Example 4.2 Schoenberg, Nicht Doch!, m. 60. Example 4.3 Schoenberg, Nicht Doch!, mm. 65-66. V Example 5 Schoenberg, Opus 15 No. 15. 33 Example 6 Schoenberg, Opus 15 No. 4, mm. 9-12. 34 Example 7.1 Schoenberg, Opus 15 No. 13, mm. 10-13. 35 Example 7.2 Untitled 36 Example 8 Schoenberg, Opus 15 No. 11, mm. 1-4. 54 Example 9.1 Schoenberg, Opus 15 No. 2, mm. 1-3. 55 Example 9.2 Untitled 55 Example 9.3 Untitled 55 Example 9.4 Untitled 55 Example 10.1 Schoenberg, Opus 15 No. 3, mm. 1-4. 56 Example 10.2 Untitled 57 Example 10.3 Untitled 57 Example 11.1 Schoenberg, Opus 15 No. 4, mm. 1-2. 58 Example 11.2 Untitled 58 Example 11.3 Untitled 59 Example 11.4 Untitled 59 Example 11.5 Untitled 59 Example 12.1 Schoenberg, Opus 15 No. 10, mm. 1-4. 60 Example 12.2 Untitled 60 Example 12.3 Untitled 60 Example 13 Schoenberg, Opus 15 No. 1, mm. 1-8. 77 Example 14 Untitled 78 Example 15.1 Untitled 79 Example 15.2 Untitled 79 vi Example 15.3 Untitled 80 Example 16.1 Untitled 81 Example 16.2 Untitled 82 Example 16.3 Untitled 82 Example 17 Untitled 83 Example 18.1 Untitled 84 Example 18.2 Untitled 85 Vll LIST OF TABLES Table 1 Untitled Table 2 Unititled 64 69 LIST OF FIGURES Figure 1 Necker Cube 61 ACKNOWLEDGMENTS ix I would like to thank my principal advisor, Dr. Richard Kurth, for his generous support, suggestions, direction, advice, and time throughout this project. I would also like to thank Dr. John Roeder for taking the time to read this thesis and for his comments. INTRODUCTION In 1937, nearly three decades after completing his setting of Stefan George's Das Buck der hangenden Garten, Opus 15 (1907-1910), Arnold Schoenberg wrote: I was inspired by the poems of Stefan George, the German poet, to compose music to some of his poems and, surprisingly, without any expectation on my part, these songs showed a style quite different from everything I had written before. And this was only the first step on a new path, but one beset with thorns. It was a first step towards a style which has since been called the style of 'atonality'.1 Over the years much debate and analysis has been generated by Das Buck der hangenden Garten. In general, atonal analysis and tonal analysis have constituted opposing approaches to this music, and to other works from the same time period, most notably the Three Piano Pieces, Opus 11. In the Opus 15 song cycle there is much to support both tonal and atonal types of musical coherence. The opening seven measures of the work, to be 1 Arnold Schoenberg, "How One Becomes Lonely," Style and Idea: Selected Writings of Arnold Schoenberg, Leonard Stein ed., trans. Leo Black (London: Faber & Faber, 1975), 49. Books and essays specifically treating Opus 15 include: Albrecht Dumling, Die fremden Klange der hangenden Garten (Mtinchen: Kindler, 1981); David Lewin, "Toward the Analysis of a Schoenberg Song (Opus 15 No. XI)," Perspectives of New Music 12 (1973-1974): 43-86; Allen Forte, "Concepts of Linearity in Schoenberg's Atonal Music: A Study of the Opus 15 Song Cycle," Journal of Music Theory 36.2 (Fall 1992): 285-381. Two articles that take contrasting approaches to Schoenberg's so-called "atonal" music are: Allen Forte, "The Magical Kaleidoscope: Schoenberg's First Atonal Masterwork, Opus 11, No.l," Journal of the Arnold Schoenberg Institute 5/2 (1981): 127-168; and Will Odgen, "How Tonality Functions on Schoenberg's Opus 11, No. 1," Journal of the Arnold Schoenberg Institute 5/2(1981): 169-181. examined in detail in Chapter 3, seem to defy any type of traditional tonal analysis, yet the fifth song, Saget mir, is full of tonal allusions.3 The cycle responds in part to both types of analysis, but at the same time, neither approach seems completely fitting; the music eludes any attempt at a comprehensive explanation of its harmonic make-up by any one system of analysis. This elusive nature of the music seems appropriate for the chosen text. Schoenberg chose to set the second part of George's three-part Symbolist work, in which the main character enters a metaphorical world of "Hanging Gardens." David Michael Hertz describes the poems of George's Das Buck der hangenden Garten as " displaying] a Symbolist voice in their command of ambiguity, in their systematized negation of direct discourse, in their consistent negation of expected combinations of signifiers, and in their creation of the interacting vibrations of semantically ambiguous symbols."4 Hertz draws a parallel between George's "ambiguous" poetry and Schoenberg's "subjective" music, which is in contrast to the "objectivism" of classical tonality.5 Schoenberg explores the metaphorical world of George's symbolist poems with his own ideas of extended chromaticism and so-called atonality. 3 For example, the vocal line outlines the key of B major/minor in mm. 1-2. The piano supports B in m. 2 with the progression VI-V-I, where the VI chord is notated enharmonically and has an added seventh and sixth, and where the dominant chord is in second inversion with its fifth flattened. The final tonic chord is sounded with the leading tone from the dominant chord left unresolved. The final measures of the song close with three statements of D-G in the bass. The accompanying harmonies for the last two statements suggest a V-I cadence in the key of G. ^ David Michael Hertz, The Tuning of the Word: The Musico-literary Poetics of the Symbolist Movement (Carbondale and Edwardsville: Southern Illinois University Press, 1987), 135. iDia. The ambiguity and negation Hertz reads in George's poems can be found in Schoenberg's music, in which tonality is referred to, but is often "suspended," and sometimes even completely absent. Opus 15 may be a prime example of what Schoenberg called schwebende or aufgehobene Tonalitat.6 These ideas are generally conceived with respect to pitches and harmonies, but the effect of schwebende or aufgehobene Tonalitat is also created by meter and rhythm. In Opus 15, the written meters often seem to be more of a notational convenience than an indication of stress patterns or conventional meters. Despite the written meters, pulses continuously shift and accents are placed unexpectedly, helping conjure the suspended atmosphere of the Hanging Gardens. This thesis explores how meter fluctuates and is suspended in Schoenberg's music, by analogy with the fragile and suspended state of the gardens in George's poems. The thesis is ultimately geared toward the kind of detailed analysis of rhythmic and metric subtleties that will be offered in Chapter 3. Chapters 1 and 2 will set the stage by first considering basic features of fluctuating and suspended meter, and the general conditions under which they can arise. Chapter 1 introduces the idea of musical meter as motivic material that can be manipulated and developed, drawing examples from compositions by Brahms and Schoenberg. It then moves toward a definition of fluctuating meter and closes with some examples from Das Buch der hangenden Garten. Chapter 2 develops a definition of suspended meter using excerpts from five different songs in the cycle. Chapter 3 is an extensive analysis of the cycle's opening material (the piano introduction to the first song) with a " On schwebende and aufgehobene Tonalitat, see Schoenberg, "Concerning Fluctuating and Suspended Tonality" Theory of Harmony, trans. Roy E. Carter (Berkeley: University of California Press, 1978), 385-6, and Structural Functions of Harmony, ed. Leonard Stein (New York: W.W. Norton & Company Inc., 1969), 111. detailed examination of its fluctuating and suspended meter. The thesis closes with some brief general observations. Musical examples appear at the end of each chapter. CHAPTER 1 SCHOENBERG'S EARLY METRICAL DEVELOPMENTS: TOWARDS A PRACTICE OF FLUCTUATING METER This thesis works from the premise that Schoenberg treats meter in Das Buck der h&ngenden Garten in a manner that is analogous to the treatment of pitch material: that meter can be motivic in nature, and can be manipulated, or developed. But before diving directly into the Opus 15 song cycle, it is appropriate first to do three things: to explain some of the other underlying assumptions in this thesis; to establish Schoenberg's interest in meter as a compositional device; and to provide an explanation of what exactly is meant by fluctuating meter. After explicating this thesis's assumptions, four different works will be examined, two by Brahms and two early works by Schoenberg. Following their discussion, some general observations regarding the two composers' use of meter are made, and a definition of fluctuating meter is proposed. The chapter closes with three examples of fluctuating meter from Das Buck der h&ngenden Garten. 6 I A primary assumption in this thesis is that Schoenberg's approach to composition is one that is steeped in the history of western music up to his time. An innovator in the development of musical language, Schoenberg built on past conventions of harmony, meter, and Lieder, stretching their limits and boundaries rather than abandoning them. He describes his music from circa 1907-13 not so much atonal as an extended form of tonality. In a commentary on his Harmonielehre, Schoenberg writes: The Harmonielehre endowed me with the respect of many former adversaries...They had to acknowledge that none of the slurs they had cast on me could be justified. Far from having no background, or a poor one, I had, on the contrary, been brought up in the Brahmsian culture .... But just because I was so true to our predecessors I was able to show that modern harmony [circa 1911] was not developed by an irresponsible fool, but that it was the very logical development of the harmony and technique of the masters.1 Closely allied with tonal harmony are its conventions of meter. For the purposes of this thesis, meter will also be approached with traditional definitions in mind. In particular, meter will be considered groupings of stress patterns. Stress patterns of pulses are generally classed into one of three different meters: duple, triple, and quadruple. Pulses are usually subdivided by groupings of two or three. Irregular meters are thought of as a mixture of simple and compound meters and considered as duple, triple, 5 or quadruple. For example, ^ is often a duple meter with asymmetrical pulses, usually grouped either 2+3 or 3+2 quarters. The conventions of metric notation will also be considered in the later analyses. In a conventional interpretation, notated meters ought to be considered to have precedence, and barlines ought to correspond to Arnold Schoenberg, "How One Becomes Lonely," Style and Idea, 50. accentuated attacks, for example. But, our interest in this study will be with moments when these conventions are circumscribed or even undermined, so that the notated meters and barlines, even though taken as an initial point of departure, may not always be confirmed as having their traditional senses. A final assumption in this thesis involves the nature of poetry and its setting: specifically, the notion that poetic meter and musical meter can be considered analogous.2 Schoenberg does pursue this analogy in Opus 15, primarily through a direct translation of the poetic foot into musical pulse. The following study in fluctuating and suspended meter shows, in part, the implications of this analogy; how Schoenberg uses poetic meter compositionally to affect the perception of musical meter and pulse. This study also shows how Schoenberg manipulates the conventions of meter, how he uses them and avoids them, stretches their boundaries, and undermines them. In Das Buch der hangenden Garten, Schoenberg pushes the boundaries of both nineteenth-century tonal harmony and meter to their breaking points, and sometimes beyond. II As already suggested, Schoenberg treats meter in Das Buch der hangenden Garten as compositional material that is malleable. Quite possibly, his interest in meter came in part from his study of Brahms. In The Early Works of Arnold Schoenberg, Walter Frisch presents Schoenberg's preliminary development as a composer as a three-stage 2 For a discussion on analogies between poetic and musical meter, see Barney Childs, "Poetic And Musical Rhythm: One More Time," Music Theory, Special Topics, edited by Richmond Browne (New York: Academic Press, Inc., 1981), 33-57. process. In the first of these stages, encompassing 1893 to 1897, Frisch describes the young composer as enveloped in a "Brahmsian Fog."3 Here he argues that Schoenberg's composition style is partly a result of assimilating some of Brahms's techniques. Frisch writes: Arnold Schoenberg would also in later years acknowledge his early admiration for Brahms.... His earliest compositions also bear proud witness to this phenomenon. In the years through 1897, Schoenberg's works fall squarely into three Brahmsian genres mentioned above: piano music, Lieder, and chamber music. From the point of view of style and technique, too, these works are very much enveloped in a Brahmsian Fog. 4 As Frisch notes, Brahms's String Quartet No. 3 in Bb Major (op. 67) is an example of how meter becomes intrinsically involved in the development of the music.5 The fact that meter will become a salient feature in the first movement of the work becomes apparent in the very first measure. Example 1.1 (page 21) is a reduction the opening four measures, Q an a a' structure built of two-measure units in g. In mm. 1-2, the tonic harmony falls on the strong part of beats one and two, while on the weak part of these beats the music moves to the subdominant harmony. In m. 1 the change to the subdominant harmony is accompanied by accents on the weak part of the beat. The gesture is repeated more emphatically in mm. 3-4 with the addition of the viola and cello, and the sforzandos. The accents (including the sforzandos) are of particular interest because they provide 3 Walter Frisch, "The Brahmsian Fog: A Context for early Schoenberg," The Early Works of Arnold Schoenberg 1893-1908 (California: University of California Press, 1993), 3-19. 4 Ibid., 5. 5 Ibid., 11. the potential for reinterpreting the notated g meter in ways that are taken up later in the music. In particular, the accents present the potential for 3 regrouping the eighth-notes into 4, as shown in the example, a typical hemiola rhythm for the notated meter. This potential reinterpretation of the meter also suggests, perhaps more indirectly, the possibility for contrasting compound and simple meters. The accents also allow for another metric reinterpretation of the meter that shifts the barline to the right a quarter-note, also shown in the example. Though the metric reinterpretations suggested here are not explicitly expressed in mm. 1 and 3 3, we shall presently see that Brahms does explore the potential 4 through a hemiola figure. 3 In particular, the latent 4 meter of the opening gesture foreshadows mm. 8-16, where a shift to the simple triple meter occurs, delineating the B section of ternary structured first-theme group shown on the two staves in 6 3 Example 1.2. Brahms re-interprets the notated g meter as 4 through a hemiola figure, which he highlights with accents. The lower system of Example 1.2 re-notates the music to show the hemiola and the new meter. 6 3 The shift from g to 4 is initiated in m. 8 when the last three eighths in the second violin are grouped an eighth plus a quarter-note (1+2) with an accent applied to the quarter-note. Though Brahms does not notate a new time signature for the subsequent measures of this section, he does continue to use accents to stress the new quarter-note pulse and to support Q the new simple triple meter. In m. 17, the music moves back to the noted g meter, re-asserting itself as the primary meter of the first theme group. The second thematic area of the movement provides further metric 2 contrast with a change in meter to 4. Example 1.3 shows the second theme's opening. It is this meter's aspect as a simple duple meter that contrasts with the compound duple meter of the previous section, as Brahms keeps the duration of the pulse the same between them, a dotted 6 2 quarter-note of g equaling a quarter-note of 4. The exposition then closes 6 2 with a return to g, but not before this meter and the second theme's 4 meter are set against each other, beginning in m. 97 (see Example 1.4). Consequently, the potential for metric development latent in the accents of the opening measures is exploited throughout the movement, creating metric contrast analogous to the traditional contrast of key centres and motivic material in a sonata form. In the song Abendd&mmerung (op. 49, no. 5) Brahms uses meter in a 3 12 similar manner, contrasting the notated 4 with ^g in the piano part. In this case, however, the opening measures of the song clearly support the written meter, offering no hint of the change to come (Example 2.1). Except for mm. 21-24, this piano figuration serves as an accompaniment to the song's first 43 measures. Measures 21-22 are of particular interest because they briefly hint at the upcoming shift to a compound meter by a change in the piano figuration (see Example 2.2). The arpeggios are phrased in two groups of six sixteenth-notes, a compound duple pattern which momentarily undermines the integrity of the primary triple meter. 12 The actual shift to jg begins in the first beat of m. 44, where the right 3 hand obscures the 4 meter's pulse through the introduction of a new arpeggio pattern (see Example 2.3). The arpeggio, beginning with the fourth sixteenth-note of the measure, consists of a three sixteenth-note descending figure, which contradicts the quarter-note pulse of the notated meter (see the brackets on the example). The piano's new meter is established in m. 45 when the left hand adds a complementary pattern to the right hand, and continues through to m. 61. In these measures both 12 hands arpeggiate through four groups of three sixteenth-notes each, or jg. Though the piano figuration in m. 45 might imply a grouping of the vocal 6 3 line into g, it actually remains in 4 throughout this section, clearly 3 projecting 4 with the help of the stresses inherent in the text. In effect, the 3 12 vocal line and the piano part together project a polymeter of 4 against ^g, all of which corresponds to a change in musical texture and key, contributing to the demarcation of the ternary song's middle section.6 Schoenberg's treatment of meter as a compositional device during his early Brahmsian period will now be briefly explored in two songs, Madchenfruhling and Nicht Doch!, both written in 1897, and both of which set the poetry of Richard Dehmel.7 Example 3.1 reproduces the opening measures of the song Madchenfruhling. Frisch notes that the "harmonic planning and control in Madchenfruhling are complemented by -actually, intrinsically linked to- Schoenberg's sophisticated treatment of meter and rhythm," and how Brahmsian techniques are "integrated into the ... musical idiom of Madchenfruhling. " 8 Our discussion will focus on some of the song's rhythmic and metric characteristics. 6 For an interesting exploration of how hemiola and other metric changes can be related to harmony, see David Lewin, "On Harmony and Meter in Brahms's Op. 76, No. 8", 19th-century Music TV (1981): 21-265. 7 For a chronology of Schoenberg's early songs see Frisch, The Early Works of Schoenberg, Table 2, 49. 8 Ibid., 70 and 72. In the piano accompaniment throughout the song, Schoenberg 3 explores various configurations of the g meter, which are primarily established by means of slur markings. There are four different groupings, and these either characterize formal sections within the song or delineate them. Hemiolas, for example, consistently mark the end of sections. La the first five measures of the song, the phrasing of the music establishes a pattern that foreshadows the first hemiola of mm. 10-11. The beaming of the notes and the slurs project a two sixteenth-note anacrusis followed by a group of four sixteenth-notes, the latter establishing the downbeat of the measure. This phrasing can be summarized as 2+4 sixteenths, in a weak-strong, short-long pattern. The second half of the pattern, four sixteenth-notes, corresponds to the duration of a pulse in the 3 hemiola, allowing for a smooth transition to the implicit ^ meter beginning in m. 10. The structure of the song's first section also helps prepare the hemiola. Following the music from the first measure, the 2+4 sixteenth-note pattern that opens the music is repeated four times. On the fourth repetition of this pattern (see mm. 4-6) its second part is extended to a full 3 measure of g plus four sixteenths, denoting the first half of a ten-measure structure. Notice that latent within these measures is the potential for hemiola, outlined by brackets below the piano right-hand on the example. (The slur across mm. 4-5 groups together eight sixteenth-notes; the lowest note in m. 5 (E4) presents the potential subdivision of this gesture into 4+4 sixteenth-notes, as well as the 2+6 division implied by the barlihe. If the latent 4+4 division is considered with the four sixteenth-note group of m. 6, mm. 4-6 might be said to have the latent potential for hemiola, even though the hemiola is not explicitly expressed.) The short-long phrasing resumes with the pick-up to m. 7. In m. 10, where the repetition of the extension from mm. 5-6 would be expected (this sense of anticipation preparing the listener for a metric change), the latent hemiola of mm.4-6 is realized, 3 temporarily shifting the meter to 4. This hemiola marks a cadence, thus bringing this section of music to a close. Later in the song (mm. 22-24, 40-43, and 44-46), hemiolas serve a similar cadential function. The second section of the song, mm. 13-21, is differentiated by the accompaniment's grouping (the first few measures are also shown in Example 3.1). In the piano right hand, each measure is phrased as a distinct unit, projecting a single pulse per measure and lacking the anacrusis characteristic of the previous section. As can be seen from mm. 13-14 in Example 3.1, the left hand sometimes projects a hemiola grouping against the right hand's dotted-quarter-pulse. The first half of the third section, mm. 27-30 (Example 3.2), is marked by the grouping of each measure into 2+2+2 sixteenths, effecting a very quick triple meter so that each measure has three slight but distinct pulses. This is in contrast with the light single pulse per measure generally projected in the second section. The articulation of these pulses in mm. 27-30 in the right hand has the effect of speeding up the surface activity in the music while the sustained tonic chord slows the harmonic motion. The final measures ( characterized by Example 3.3) recapitulate features from the first section, alternating between a 2+4 group and a hemiola figure. Schoenberg employs the final line of text itself as a commentary on the kinetic effect of the various groupings he explores in the 3 song. 'Fiihlt, fuhlt er es nicht?!" (Doesn't he feel it?!) is set clearly in g over a hemiola in the piano part that is analogous to mm. 10-11. In the song Nicht Dock!, Schoenberg uses a hemiola figure comparable to that found in Madchenfruhling. At several points in the g music, the notated g meter temporarily shifts through compositional 3 3 means to 4. As in the previous song, 4 typically functions as a cadential figure and part of a piano interlude. More interesting, though, is the treatment of the refrain "das ist was fur alte Leute," which first appears in mm. 7-8 of the song (Example 4.1). g The music up to this point is predominantly in g. In m. 7 the metric 2 notation of the vocal part and the piano left-hand changes to 4 while the g piano right-hand reverts to g. At first consideration, the combined effect of 12 the two notated meters may be implying a temporary shift to jg, but the dotted eighth-sixteenth note figure in the voice and piano left-hand (m. 7) 2 confirms the 4 time signature of the outer voices. This refrain is repeated exactly in mm. 36-37. In each case the shift in meter seems abrupt, a 3 sensation that is heightened by the preceding g measure, a truncated form of m. 1. In a similar figure at m. 60 (Example 4.2), Schoenberg opts for 2 notating the implied 4 meter in the voice as a 2-against-3 rhythm. In this measure the combined rhythms of the voice and the piano's upper line do 12 project a ^g meter through the use of a characteristic long-short pattern, as 12 is shown on the lower staff of the example where the implicit -jg meter is made explicit. The continuous eighths in the voice project the four pulses of the meter (here lacking the dotted eighth-sixteenth note figure of m. 7), and piano right-hand provides both a figuration that supports the meter and a counter-melody, that in itself has the sense of a pulse that is shifted to the right two sixteenth-notes, but when combined with the rest of the music, articulates the long-short pattern. The piano left-hand has the potential for 12 hemiola, but it is suppressed by the jg meter projected by the upper parts. Measures 65-66 contain the last statement of the refrain with the text modified to "das ist was fur junge Leute" (see Example 4.3). This setting combines the characteristics from mm. 7-8 and m. 60. Schoenberg 2 dispenses with changing the written meter but writes the ^  passage in the voice using a duple indication, as in m. 60. Unlike m. 7, the bass line now g remains in g, so that the outer voices project a 2-against-3 polyrhythm. The middle staff seems somewhat ambiguous in m. 65. On first consideration, one is apt to associate it with the meter of piano left-hand, thus hearing it in g g. But one can also associate it with the vocal line as well i f attention is drawn to the text. If this happens, the attacks of the vocal line group the 12, middle staff into jg. Schoenberg plays with this metric ambiguity of the piano right-hand in m. 66. The tones of the counter-melody mimic the vocal g line but also project the g meter of the piano left-hand by means of its quarter-note eighth-note rhythm. I l l The analyses of the last two songs show that the use of meter as a compositional device which is manipulated and developed is demonstrable even from Schoenberg's earliest works. We have also seen with both Schoenberg and Brahms that shifts to a temporary secondary meter are often foreshadowed by areas in the music that slightly contradict the primary meter. These areas are small zones of metric ambiguity and instability, where the primary meter's integrity is momentarily undermined through means that weaken or avoid its pulse, stress pattern, or both. As we shall see in Das Buch der hangenden Garten, metric ambiguity can also occur in music that has not as yet established a primary meter, and it can affect quite extensive passages. As can be gathered from the title of this thesis, manipulation of meter in music will be differentiated into two types: fluctuating meter and suspended meter, terms which are borrowed from Schoenberg's own writing on extended tonality.9 Later in this thesis, the concepts of fluctuating meter and suspended meter will be developed through analysis as interdependent ideas. In fact, we shall see that it is sometimes difficult to separate them. But for the purpose of clarification, fluctuating meter will be defined in this section independently. Our attention will then turn to Das Buch der hangenden Gtirten. Simply stated, fluctuating meter will involve the sequential shifting of meters from one to another. The obvious case where the written meter changes in the score hardly requires comment. However, we already have seen two other types of fluctuating meter. For example, in the Brahms 6 3 String Quartet (Example 1.1), the notated g meter fluctuates to 4 in m. 9. In this case, the two meters share a common measure length, and also a common note value in their respective pulse's first subdivision: the eighth-3 6 note. It is grouping the eighth-notes into pairs (4) or triplets (g) that differentiates the two meters. A slightly different case involves meters that do not share the same measure lengths, as in Nicht Doch! (Example. 4.1). In this song the regrouping of the sixteenth-notes from 4+2, to 4+4+4 (see 3 mm. 9-11), creates a kind of hyper-measure, a 4 meter extending across two written measures, as in the familiar Baroque hemiola. 9 Arnold Schoenberg, "Concerning Fluctuating and Suspended Tonality," Theory of Harmony, 384-385. As one meter fluctuates to another, metric instability can arise, but in a limited sense, usually occurring during an adjustment period in which the old meter is abandoned, and the new meter is established. The degree of instability depends on whether the shift in meter is prepared or expected, and also on the stability and commensurability of the meters involved. Fluctuating meter occurs throughout Das Buck der hangenden Garten, in formulations varying from the fairly simple to the quite complex. The following are three excerpts from the cycle in which fluctuating meter occurs. These excerpts are presented in this section as convenient and pertinent examples of fluctuating meter, and will be discussed for their general attributes (rather than for their individual subtleties). 4 Example 5 is drawn from the cycle's final song, which opens in 4. The rhythm of the piano introduction alternates between a dotted-eighth-sixteenth note figure and a triplet-eighth figure, suggesting a colloquy 4 12 between two similar meters, 4 and g . When the vocal part begins in m. 13, the meter fluctuates to g, then to g. As shown in the example, the meter changes are both indicated in the score. The dotted barline of m. 14 perhaps suggests that Schoenberg was thinking of m. 13 and 14 as a combined 4 measure, one which truncates the song's 4 meter by an eighth-note. Immediately following m. 14 the music returns to the original meter. Even 12 so, the triplet rhythm of m. 15 suggests or recalls the g feel of m. 5. Beginning in m. 15, triplets become increasingly prominent in the Q music, so much so that Schoenberg indicates a change to g in the piano 12 right-hand halfway through m. 23, and then finally to g in both hands of the piano in m. 24. Though shifts between simple and compound meters are not necessarily remarkable in themselves, in this song we can note that the fluctuation to the compound meter beginning in m. 24 is a metric development of the piano introduction's triplet figures.10 Example 6 is an excerpt from the fourth song. This song also makes frequent meter changes, but unlike the other songs in the cycle, there are no notated time signatures whatsoever. Obvious from the excerpt, however, is the fact that barlines delineate metric units, and that the meter of a particular measure is easily determined. The music previous to the excerpt clearly defines a quarter-note pulse for the song. Measures 9-10 2 3 project ^ and 4 , respectively, where m. 10 augments the gesture of m. 9 by a quarter-note. In both measures, the rhythms used are typical for the 2 5 meters, clearly defining them. Similarly, mm. 11-12 project 4 and g, where m. 12 presents a variation of m. 11, repeating its bass line, but with the Ab augmented to a dotted quarter-note, and the second eighth in the piano 5 right hand augmented to a quarter-note. Perhaps the g meter is at first less clear than the others. Because of the dotted quarter-note downbeat, the A3 in the bass might be heard as a syncopation at first. But this sensation is only momentary. The gesture (A3-F#3) can only function here as a strong-weak pattern, as it was previously defined in m. 11. In m. 12 this gesture 5 demarcates the asymmetrical 3+2 grouping of the g meter. The following 5 two measures (not shown in the example) continue and reinforce the g of m. 12. Thus, in this excerpt, the durations of the measures and their music define their respective meters fairly clearly, even though the music 1 0 In these measures, editorial triplet figures, [3], are added to the example, as Schoenberg chose to omit them in the piano part, using the notated time-signatures and brackets to delineate the meter's pulse and the rhythms. quickly fluctuates through three different meters in only four measures.11 Schoenberg thus preserves here the traditional sense of the barline as a marker of metric units. Our last example of fluctuating meter in this chapter is from song 13 (Example 7.1). In this song the meter fluctuates between 4 and 4, changes that are indicated by time signatures in the score. Though the music's pulse remains for the most part at a constant quarter-note, the many triplet figures indicated throughout the song weaken or loosen the sense of a simple division of the pulse normally implicit in the notated meters. We can see this in m. 10, where only the third beat corresponds to the duple division of the meter. Many of the measures in the song also have the sense 9 12 3 4 of g and g , rather than the notated 4 or 4, as in m. 11, where the continuous 12 4 triplets lends the music more to g , than the notated 4. Example 7.2 summarizes the music's fluctuation through four meters in effect in mm. 12 10-13. To account for the implied g meter in m. 11 created by the continuous triplets, Example 7.2 shows the quarter-note pulse of m. 10 equaling a dotted quarter-note in m. 11. More interesting, however, is the metric fluctuations in m. 13, the final measure of the song. Measure 13 of Example 7.1, can be thought of as two measures, as shown by a dotted 3 barline in Example 7.2, in which the first two beats project a 4 meter through a hemiola figure created out of the triplets. Here, a kind of metric modulation results in which the pulse is accelerated to two-thirds of the notated one. The original pulse-duration returns for the final two notated g beats of the music, suggesting g. 1 1 This, however, is not true of the song's opening measures, as will be discussed in Chapter 2. It is in this song that the analogy between fluctuating meter and fluctuating tonality is the strongest. Concerning fluctuating tonality, Schoenberg wrote: "If the key is to fluctuate, it will have to be established somewhere. But not too firmly; it should be loose enough to yield." 1 2 The above excerpt shows how this statement can equally be applied to fluctuating meter. The triplet figures in the music loosen the sense of the simple subdivision of the pulse, preparing and allowing for the accelerated pulse at the hemiola, and the fluctuating meters of m. 13. 1 2 Arnold Schoenberg, "Concerning Fluctuating and Suspended Tonality," Theory of Harmony, 385. Vlns* Y rtaF r r r r r : ¥ e -f € etc. Dim J ni) J Example 1.1: Brahms, String Quartet No. 3 in Bb Major (Opus 67). mm. 1-4. to 8 h 1" > > > J J J ^ 1 # t •a *" r*" —T T ? ~f~ ~f~ ~f~ f etc. . z ^ i — —J 7 l » = f = > > > j i , J J J H 1—s •a < T 1 etc. 7 I - " 4 Example 1.2: Brahms, String Quartet No. 3 (Opus 67), mm. 8-9. . 63 ft * j ' zhM?—:? 1*—f Lf— si— —« *s— */ —s 4 4 '4' r? >— 2 Nr u > - J — ^— • v 7 — i J -2 U-rr=t== V-X 0— 1 > m m —J-> —^ fl J J-V-—4 S * — 1 \ J m r Example 1.3: Brahms String Quartet No. 3 (Opus 67), mm. 63-65. Example 1.4: Brahms, String Quartet No. 3 (Opus 67), mm. 96-97 and mm, 101-103. Example 2.1: Brahms, Abenddammerung (Opus 49 No. 5), mm. 1-2. Example 2.2: Brahms, Abenddammerung (Opus 49 No. 5), mm. 21-22. 26 Example 3.1: Schoenberg, Madchenfruhling, mm. 1-15. Ruhiger f#*=f r ~i ) I vdai- son- nen -r Pf .—; r r r j ; 1 re - gen; H f" f T P 1 al - le «j • i -# PP UJ J i J i M r-^ . ' F - ^ _ 1 • F - P r. Example 3.2: Schoenberg, Madchenfriihling, mm. 27-30. Jit 1 ~ ~ f P JF <M \lk r_r i Fuhlt, M P1 fiihlt er es r i nicht?! pp—i*— <¥k / -0-1 ~*~ ' ~ / f* ~ -J-L\ Example 3.3: Schoenberg, Madchenfruhling, mm. 40-43. E x a m p l e 4 . 1 : S c h o e n b e r g , Nicht Dock!, m m . 6-8 . — h — h — 1 1 g> ' I V Siehst } — J — < -—# * d u , M a - de l f f f i f f 12 J) -S-L '—d 0- -0-0 J>J) J5 b J>J) -J Example 4.2: Schoenberg, Nicht Doch!, m. 60. co E x a m p l e 4 .3 : S c h o e n b e r g , Nicht Doch!, m m . 6 5 - 6 6 . from the piano introduction, right-hand 4 P r 3 -4 1: 4 <h4—1 V ) vocal )art if ^ * Sr M 4 - I — w ir be - vo h 1 - k er - ten die i - be nd - dii - stern Lau - b( ) ;n piano part [3] 13 j [ 3 1 Example 5: Schoenberg, Opus 15 No. 15. Example 6: Schoenberg, Opus 15 No. 4, mm. 9-12. Example 7.1: Schoenberg, Opus 15 No. 13, mm. 10-13. 10 J.J. J>.J> 1 J J J I !82 1 J. J.J. | J. J. JJ. || J J J i g J.J. Example 7.2 8? CHAPTER 2 SUSPENDED METER IN SCHOENBERG'S DAS BUCH DER HANGENDEN GARTEN As fluctuating meter was considered in some respects analogous to Schoenberg's term fluctuating tonality, suspended meter will be similarly considered analogous to suspended tonality. In his commentary on suspended tonality, Schoenberg writes: "[its] purely harmonic aspect will involve almost exclusive use of explicitly vagrant chords," chords called such "because of their multiple meaning."1 Frequently in Das Buch der hangenden Garten, musical gestures simultaneously offer several possible metric interpretations, thus suspending any one single meter. For example, a single gesture may be interpreted as a downbeat, an anacrusis, or an internal beat. Each different interpretation offers different possibilities for metric interpretation, just as a vagrant chord's multiple tonal functions offer reference to different possible key centres. Metric ambiguity will be a salient feature of suspended meter, much more so than with fluctuating meter. Fluctuating meter exploits ambiguity in a limited sense. Music that moves between meters must at 1 Arnold Schoenberg, Theory of Harmony, 384, and Structural Functions of Harmony, 44. times be metrically loose enough, or ambiguous, to yield to change, but the question of whether a passage is to be heard in one meter or another is generally certain at some point. Over the next two chapters it will be shown that some passages in Das Buck der hangenden Garten integrate metric ambiguity to such an extent that the question of what meter a passage is in can only be answered indefinitely. Such music will be said to have a suspended meter, and the concepts pertinent to suspended meter will emerge in the following discussion. In this chapter, five excerpts from the cycle will represent how Schoenberg uses suspended meter in the opus; When possible, suspended meter will be discussed in conjunction with issues related to harmony and the setting of the poetry. I The first excerpt is from the opening of the eleventh song, presented in Example 8 (page 54). The first phrase of music effectively ignores the notated common-time signature and the barlines. This phrase consists of two streams of music clearly differentiated by the piano's two staffs. The left hand of the piano sounds a descending figure 3 in three groups of four sixteenth-notes, perhaps implying ^ meter that begins an eighth-note before the first barline. .The first attack of the right hand is notated in a typically anacrustic position, a beat before the barline. But because there is no previous .music, and because of the syncopation across the barline, this opening attack sounds more as a downbeat than a pick-up. The four-note motive of the right hand then moves through a Bb minor/major triad in a steady dotted-quarter-note 12 pulse, suggesting a single measure of g (as shown below the excerpt). The stress pattern implicit in g is supported by the gesture's contour, the F3 providing a high point in the contour, that bisects the gesture into two strong-weak patterns, each composed of a minor third. (This meter is effectively an augmentation of the notated common-time signature.) As the two metric streams of the two hands interact, they lessen the possibility of either meter being effectively projected, each weakening the sense of the other. Metric ambiguity arises and suspended meter results. Beginning in the second phrase, the left hand and the right hand are aligned, perhaps creating the sense of a downbeat, but one that 3 12 conforms with neither the 4 of the left hand preceding, nor the g of the right hand. Even though the meter of the first phrase is suspended, this alignment in phrase 2 changes the metric sense of the music. But in phrase 2 the meter is also indeterminate as metric ambiguity is increased even further. The suspended meter of these measures, however, is not created out of the interaction of two metric streams, as in the previous phrase, but because there exists within the music the potential for multiple conflicting metric interpretations. Though these possibilities will not be explored here, it can be said that they arise because various elements in the phrase can be interpreted as having more than one metric function. For example, if the dotted quarter-note pulse of the right hand's opening is heard as continuing through this music, the quarter-note rest of m. 2 could be heard as marking a new downbeat, and the first attack of the second phrase would function as syncopation. This attack could also function, however, as the downbeat of a new measure, paralleling the function of first phrase's opening attack. Similarly, almost every attack in the second phrase can be heard as either syncopated or as falling on the beat, in large part because the left hand {F,B} in mm. 2-3 lasts 7 eighth-notes, a duration that conforms 12 3 with neither the right hand's opening g , nor the left hand's 4, nor the notated common time signature. This results in music that has a fairly high degree of metric ambiguity, or suspended meter. II Example 9.1 presents the opening measures of the second song, comprising two lines of poetry. As a result of George's choice of words, the shimmering quality of the poetry's language imparts a suspended ambience to the poem throughout. He describes the gardens as including groves that alternate ("abwechseln") with fields of flowers, halls with multi-coloured ("buntbemalten") tiles, iridescent ("schillern") fish, trilling ("trillern") birds, and golden rushes that rustle ("sauseln"). The tonal ambiguity of the opening sonorities supports this shimmering, or suspended atmosphere. The harmony moves from a D-root (mm. 1-2) to an Eb-root (m.3), outlined by both the piano left hand and the vocal-line, implying, at least for the first two measures, a D tonality. The chord built on the low D-root includes, however, an unresolved dissonant member, the C#. This pitch creates an augmented triad (F,A,C#), which is set off by register above the low D octave. As Schoenberg notes in his Theory of Harmony, augmented triads are functionally indefinite in a tonal context.2 Here the Arnold Schoenberg, Theory of Harmony, 241. augmented triad slightly obscures the sense of a D-tonality, but offers no definite sense of a different one. The dissonance of the chord is strong enough to somewhat obscure its function as a tonic chord, yet the chord's lack of context in mm. 1-2 does not suggest an alternative interpretation. This tonal ambiguity is actually intensified over m. 3 when the harmonic root changes to Eb, while the right-hand retains the F-augmented triad, repeating it at quarter-note intervals: even though the filled in vocal-third (G4,Eb4) in m. 3 supports the Eb bass, the harmony of mm. 1-2 is sustained over the new root, further loosening a sense of a D-tonality. Consequently, in these opening measures, a tonal centre is effectively suspended. This effect is heightened, perhaps, by the overall whole-tone sonority in m. 3, {Eb,F,G,A,C#}. Complementing this tonal ambiguity is the suspended meter of these measures. The vocal-line attempts to project a stable metric pattern, but, as will be shown, it is one that not only contradicts the written meter, but is also obscured by the piano part. To show how Schoenberg accomplishes this, the poetic meter and its setting in the vocal line will be considered first. The poem's meter is trochaic tetrameter, four metric feet projecting a strong-weak stress pattern. Observing Schoenberg's use of a simple one-to-one relationship between the poem's metric foot and the music's pulse, this implies a musical setting using either a duple or a quadruple simple meter with the first syllable of text falling on a strong beat of the measure. For example, if Schoenberg were to use one eighth-note for every syllable of 4 text, the trochaic meter of the poem would yield two ^ measures (see Example 9.2). The given musical meter is in fact common time, but "Hain," the poem's first stressed syllable, is extended to a dotted-quarter-note in duration, and also set on a metrically weak beat in measure one. The agogic accent on "Hain" seems to shift the vocal line's barline "to the right" by a quarter-note, represented on the lower staff of Example 9.3, weakening the integrity of the stress pattern indicated by the musical meter. As we shall see, Schoenberg uses this technique in combination with others to obscure or weaken not only the given meter, but also this initial suggestion of a displaced common-time meter. Due to the relative lack of activity in the piano part, it is primarily the vocal part that projects the meter in the passage. The poem's first two lines are set in two phrases of five beats each, delineated by the breath mark. Comparing Example 9.2 with 9.4, we can see how 4 Schoenberg extends the implicit 4 meter of the poem's trochaic meter to 5 two 4 by extending the durations on "Hain" and "Blu-" to a dotted-5 quarter-note. Consequently, these two phrases both project a 4 meter, not the four beats per measure of the written time signature. Observe, however, that the written barlines of Example 9.1 across mm. 2 and 3 do in a sense remain functional in the projected meter. As written barlines, they are not signaled by any event in the music, but as intra-measure barlines, as shown by dotted barlines in Example 9.4, they 5 group the 4 measures into 3+2 and 2+3 quarters respectively, to create a four-part symmetrical pattern that is supported by the text. "Hain," "Paradiesen," "wechselt" and "Blutenwiesen," the primary signifiers in the text, also signal the suggested barlines and intra-measure barlines of the example. 5 The piano part undermines the 4 vocal meter of Example 9.4. In itself, the opening piano chord sounds (and is written) like a downbeat, establishing the placement of the first pulse in the music. The second attack in the music begins the vocal line and establishes a quarter-note pulse as the duration between the two attacks. But as Examples 9.3 and 9,4 show, from the perspective of the vocal line, the attack on "Hain" can also function as a downbeat. The conflict between these two potential downbeats creates metric ambiguity, as a listener tries to establish the primacy for one downbeat over the other. Perhaps the possession of a score would favor the written piano downbeat, but nevertheless, metric ambiguity is created. The piano's second attack, written as a syncopation across mm. 2-3, also interferes with the interpreted meter of the vocal line. (Compare Example 9.1 with Example 9.4). The agogic stress on "Bluten" is felt, but the preceding Eb octaves weaken it. Only when the voice and the piano coincide on the syllable "-wiesen" is a convincing and coordinated metric stress produced. These two events again call into question the placement of the barline. Both the Eb octaves and the chord that coincides with "wiesen" could also potentially mark barlines. Thus the 5 establishment of the 4 meter implicit in the vocal line is undermined by the piano part, suspending any possibility of a clear sense of meter. Throughout the song, similar observations can be made. The written time-signature is never clearly defined by the music. It is suspended through phrasings and syncopations that contradict or disregard it. Furthermore, the meters implied by the music regularly fluctuate and are also undermined or suspended through similar means, so that the metric fluidity of the song works in concert with the music's tonal ambiguity and the poem's ambience. In the opening measures of this song, suspended meter results from the interaction of the piano and the vocal line, each with different but only weakly projected metric characteristics. I l l The third poem in the cycle introduces three events to the narrative: the main character's thoughts upon entering the gardens; his first meeting with the garden's priestess; and his offer of service to her. The first two lines of the poem, "Als Neuling trat ich ein in dein Gehege;/ Kein Staunen war vorher in meinen Mienen," can be loosely translated as: "As a novice I stepped into your reserve/ No expectations were in my thoughts." Example 10.1 presents Schoenberg's setting of the these lines in mm. 1-4 of the third song. The first two measures create a very interesting musical effect, but one which is difficult to define in simple terms. The harmony is full of tonal implications, yet seems non-directional and repetitive, lending a sense of stasis to the music. At the same time, the dotted rhythms and ostinati give the music a sense of forward impetus or momentum. In addition, although the vocal line and the piano right hand clearly project a quarter-note pulse, the music's meter is at best vague until the third measure, a result of the metric independence of the three staffs in mm. 1-2, which converge into a common meter in mm. 3-4. The writing is such in the first two measures that the piano and the vocal part each suggest a different tonality, one weakening the other. The piano part points to a C tonal centre. In particular, the ostinato in the left hand <D,G,C> almost suggests a II-V-I progression (see Example 10.2). The accompanying pitch material, particularly the Eb and Bb, imply a minor mode. This tonality, however, is weakened by the construction of the chords. Neither the dominant nor the tonic chords of C minor are clearly articulated by their pitch content. The chord built above the G suggests a V 1 ^ chord, but it lacks a B natural, the leading-note of a C tonality. The status of the tonic C minor triad is called into question with added non-chord-tones, {C,Eb,G} plus {Bb,F}. Schoenberg arranges this chord in stacked fourths with an added fifth above the root: {C,F,Bb,Eb} plus {G}. Although it is possible to hear the lowest pitch in a fourth chord as a root, its stability is less than that of a root-position major or minor triad. Here this chord serves as much to loosen a C tonality than to establish it. Tonality is further obscured by the vocal line which leans towards Eb major in mm. 1-2. Its diatonic pitch content outlines an Eb major chord as it circles around Eb and G. The A A Eb tonality is further supported by a 2„\ melodic cadence, preceded twice A A A by a rj-^ motion, and beginning on g. The vocal line and the piano part, it would seem, work against each other, suspending tonality. In the vocal rhythm, Schoenberg uses several notational devices: two accents on weak beats, dotted barlines, and a parenthesized barline. Along with the poetic meter and the musical rhythms, these help establish the vocal line's meter. Example 10.3 extracts the vocal line and provides a metric scansion on the lower staff that interprets the functions of these devices. The stress pattern projected by the first three syllables of the text is weak-strong-weak, which Schoenberg complements with the rhythm sixteenth-dotted-eighth-sixteenth. This creates an anacrusis on "Als," makes "Neuling" sound as a downbeat, and places the first effectual downbeat of the vocal part a quarter-note to the right of that in the score. Though the written and the effective meter of the music are the same, they are out of phase with each other by a 4 quarter-note. The first interpretive 4 measure is grouped into 2+2 quarters by the dotted barline and the first accent. The meter then 3 fluctuates to 4, its downbeat delineated by the second dotted barline, the accent, and the dotted quarter-note, the longest duration so far. The 4 third measure returns to 4, now in coordination with the notated meter. The truncated second measure thus shifts the effective barline to the left a quarter-note, aligning the written and projected meters for the first time. The piano part, although aligned with the written meter, projects two different durations of pulse (refer back to Example 10.1). Although the piano right hand and the voice are very similar in m. 1, the piano 4 right hand supports the written 4 meter with its dotted eighth-plus-sixteenth rhythm and quarter-note pulse, its downbeat supplied by the left-hand's initial D2. The left hand augments this rhythm to a dotted-2 quarter-plus-eighth, projecting a half-note pulse, resulting in a 2 meter, perhaps only marginally different than the right-hand's quadruple meter, yet clearly present. The metric misalignment between the piano part and the vocal part for the first two measures generates a degree of metric tension in the music, obscuring the metric integrity of both parts, and consequently suspending a clearly definable overall meter. Adding to this tension is the sense that two different pulse durations are projected by the piano, a half-note pulse in the piano left hand and a quarter-note pulse in the piano right hand. This metric tension is heightened at the beginning of the second line of text, when the meter of the vocal line fluctuates momentarily to 4, then dissipates when the vocal part aligns with the piano at the downbeat of m. 3. The highly repetitive writing in these measures provokes the effect of music that is tumbling over itself. As the meter stabilizes in m. 3, it might be said that the "Neuling's" initial steps ("treten") into the gardens become more self-assured. I V Example 11.1 reproduces the first two measures of the fourth song, setting the poem's first line. The bass line and the accompanying harmony, though highly chromatic, imply a deceptive cadence (or progression) in a B tonality (see Example 11.2). But the sense of tonality in these measures is weakened almost to the point of being completely suspended through four means: the deceptive cadence itself, the highly chromatic decorative-notes in the melody line, the free exchange of pitch material between the major and minor modes, and the lowered leading note.3 Throughout the song, the harmonic language suspends a clear sense of tonality, though the structure of the music and its gestures obviously make tonal references or have tonal origins. Complementing the music's suspended tonality is its suspended meter. In this song, the score offers no time signature at all, probably because the durations of the measures, and consequently the music's meter, change with some frequency, exemplifying fluctuating meter. For example, the first measure, which is five quarter-notes long, is followed by three measures that alternate between two and three 3 The progression, for example, becomes audibly clearer if an A# is substituted for the A natural in the middle voice of the V 1 3 chord. quarter-notes in length. The music then settles down into measures of two quarters in length for several bars. Later in the song, the measure lengths shift to five eighths and then finally to four quarters in the closing measures. To this frequent fluctuation of measure lengths (and by implication, meter), is added further metric ambiguity, this suspension of meter between the vocal and piano parts, as will now be demonstrated. Even from the very first measure, the meter is effectively suspended, just as is the tonality. This effect is created by three conflicting metric ideas: one projected by the vocal line, one indicated by the score itself (through measure lengths and barlines), and one projected by the piano. Consider the vocal line itself. The notation of the first two 5 measures (Example 11.1) suggests 4 grouped as 3+2 quarters, followed 2 by 4. The initial rest indicates that the first attack should fall on a weak part of a quarter-note beat and the second attack on the beat. This is supported by the poetic meter, for the first two syllables project a weak-strong pattern. This creates an anacrustic sense to the first written eighth-note, calling into question the placement of the first barline, and possibly shifting it to the right a quarter-note, as shown in Example 11.3. The example re-notates the music with the first attack as a pick-up, and 2 the remaining music easily falling into 4. This meter might be 5 considered as a kind of counterpoint to the 4 meter of the score, weakening or even suspending it. This metric counterpoint may be one 5 reason why Schoenberg did not explicitly write 4 at the beginning of m. The piano part further suspends the ^ meter by projecting its own set of meters. In particular, the piano's first three attacks create a 3 strong-weak-weak stress pattern, implying a measure of a g. Similarly, the second and third piano chords force metric re-interpretations of the music and the poetry. Example 11.4 re-bars the piano music in a manner that accounts for its projected meters. The fluctuating meters of Example 11.4 make good sense so far as the piano is concerned. But Example 11.4 also applies the same scansion to the vocal line, to show how the opening meter in the piano undermines the anacrustic feel of the vocal line's first attack and ignores the initial eighth-note rest. It also counters the meter of poem's first foot, incorrectly extending it to three syllables, "Da mei-ne," and changing its accent pattern to a dactylic foot, a strong-weak-weak pattern. Correcting this faulty scansion of the vocal line, but still retaining the implicit fluctuating meter of the piano part, Example 11.5 combines the vocal scansion of Example 11.3 with the piano scansion of Example 11.4. This example demonstrates how the vocal meter and the fluctuating piano meters combine to effectively suspend meter in the opening, in a way that seems, to borrow a word from the poem, "reglos." (And oddly enough, it is that word that makes the first point of agreement between the voice and the piano.) The example conveniently demonstrates how suspended meter typically arises from an unresolved contrapuntal tension between interacting metric strands, and also illustrates how fluctuating meter (in the piano part) helps contribute to this tension. 50 V The final excerpt (Example 12.1) is from the opening of the tenth song. The indicated meter is alia breve, and the first attack is written as a syncopation. It is difficult to hear this attack as a syncopation, however, because there is no previous music. Thus, the opening chord sounds as if it were on the beat. Whether it should be heard as the music's first downbeat or as a pick-up measure is not clearly defined by the music. In addition, it is unclear from the first two attacks whether the pulse of the music is in quarter-notes, half-notes (as indicated in the score), or dotted-half-notes. This ambiguity of meter and pulse is a salient feature of not only the opening measure, but also mm. 2-4. As a listener weighs possible metric interpretations latent within m. 1 against the ensuing music, several competing metric interpretations arise in the passage, resulting in a suspended meter. Shortly, Examples 12.2 and 12.3 explore two of these possible interpretations latent within mm. 1-4 of the song. It should be noted that Examples 12.2 and 12.3 are offered as possibilities latent within the music, rather than proposed as "solutions." It is the ambiguity of the passage that evokes multiple contradictory interpretations and gives rise to a suspended meter. In addition, although m. 4 is analogous to m. 2, and the right hand's G#4-A4 in m. 3 is analogous to the same gesture in m. 1, the following interpretations arise from attempts to hear the passage without the fore-knowledge of these parallelisms, exploring different ways in which a first-time listener might react to m. 1, and test those reactions against the music as it occurs. If the first chord is interpreted as a downbeat, and its long-short rhythm interpreted as projecting a quarter-note pulse, the first measure 3 is heard in 4, as shown in Example 12.2. The downward leap from the A 4 to the D 4 then effectively marks a new downbeat. At this point in the music, two metric functions have been established: a rising line is anacrustic, and a descending leap creates metric stress. In m. 2 of Example 12.2, the left hand begins to move in an ascending gesture in quarter-notes. The quarter-notes at first seem to confirm the triple meter and quarter-note pulse interpreted in m. 1. But when the gesture continues to rise past the third quarter-note (B-C# octaves), the sense of the triple meter in m. 1 is weakened. This weakening of the meter occurs because at the fourth quarter-note, a descending gesture paralleling that across mm. 1-2 is anticipated to confirm the interpreted 3 4 meter of m. 1, and to continue this meter through m. 2. Instead, the line moves higher at the fourth quarter-note, frustrating the 3 confirmation of the 4 meter and the attempt to hear its continuation. 3 The sense of 4 as a potential meter for this passage is further weakened by the middle voice-pair in the right hand in m. 2 that begins to project a half-note pulse, undermining the interpreted quarter-note pulse of m. 1. The upper voice of the right hand joins the ascending line of the left hand, and the music continues to build anacrustic energy. The triple meter and quarter-note pulse of m. 1 is abandoned, and meter is suspended until the anticipated descending A 4 - D 4 gesture of mm. 1-2 in the example is repeated across the example's mm. 2-3 to provide a new interpretation. Only then can a meter be applied to Measure 2 in 4 retrospect, here interpreted as ^ Measure 3 of Example 12.2 confirms a half-note pulse; and the parallelisms between mm. 1 and 3. and mm. 2 and 4 of the score (Example 12.1) become apparent. In the final measure of Example 12.2, the notated alla-breve meter begins to emerge. As a listener works through the potential meters and pulses of Example 12.2, a simultaneous alternative interpretation also arises, shown in Example 12.3. In this example's opening measure, the long-short rhythm is interpreted as potentially projecting a dotted-half-note pulse. As in Example 12.2, the registral leap from A4 to the D4 also marks the first barline. But in the present example, the listener is anticipating a confirmation of a compound meter. As shown in m. 2 of the example, the music can potentially confirm one. The six quarter-notes are readily grouped into two beats of three quarter-notes each in Q the ^ meter; though the syncopation in the middle voice-pair perhaps weakens this meter. The D-octaves in the left hand of m. 3 and the chord built above it provide a potential metric stress, suggesting a new barline. The repetition of the <A4,D4> gesture in this interpretation's third measure now functions to truncate the pulse to a half-note and the 3 remaining music of the example results in a 2 hemiola measure, supported by the three half-note chords of the inner voices, and perhaps even partially prepared by the syncopation in the inner voices of the example's second measure. Examples 12.2 and 12.3 present only two interpretations and others are no doubt possible; since they show that suspended meter arises in this passage primarily because there are at least two possible interpretations of pulse presented in the opening gesture, neither of which is really confirmed or denied by the senses of pulse in mm. 2-3 of Example 12.1. It is not that any one scansion takes precedence over another, but that the metric ambiguity of the music presents the potential for multiple scansions—including those explored here, and also others. As the .music points to various interpretations of pulse and meter, which it subsequently denies as another possibility becomes apparent, meter is suspended. In this chapter we have explored how suspended meter can arise out of two different techniques. In Examples 8-11 we saw suspended meter created out of two competing metric strands. And in the latter part of Example 8 and in all of Example 12, we have explored how suspended meter can also arise from competing scansions even when the music is viewed as a homophonic texture. In the following chapter, we will examine in detail a passage in which suspended meter arises through competing scansions that exhibit qualities of both techniques. Example 8: Schoenberg, Opus 15 No. 11, mm. 1-4. 55 Ruhige Bewegung ( J ca 76) j r - ; ^ i|J'p j> l ji j> j? ,j> J ^  l J i '^ «H <u.' _i;—A) -i) A) _n _y * Hain in die - sen Par- a - die -sen wech-selt ab mit Blti - ten -wie - sen. Example 9.1: Schoenberg, Opus 15 No. 2, mm. 1-3. Hain in die - sen Par- a - die -sen wech-selt ab mit Blu - ten -wie - sen, Example 9.2 Example 9.3 1 ^ vl',J?J) jJj>J j ' j . ^ J'1^ Hain in die - sen Par- a - die -sen wech-selt ab mit BIU - ten -wie - sen. Example 9.4 MiiBig ( J ca 80) Als Neu-ling j j ' f y . T l trat ich e in in dein Ge- he | „. f l • ge; kein —4(- * 4 Staunen wa 1 f T r \ or- ler in me |$ i-nen ft Mie - nun -7 « g. • • a Ir- s— -..... —k TTT — « — J — • -4 X- J — — • r •— 0-Example 10.1: Schoenberg, Opus 15 No. 3, mm. 1-4. s 1 ) 1 m i * p i \>± -0- stacked 4ths s ^ ™"' — 49 -9- "zJ C-.II V I (?) Example 10.2 Als Neu-Iing trat ich ein in dein Gc- he - ge; kein Staunen war vor-her in mei-nen Mie - nung, Example 10.3 S3 Gehend (Jca68) Da mei- ne Lip-pen reg-los sind und bren —nen. l ^ ^  ^  J ^  I f r r f m Example 11.1: Schoenberg, Opus 15 No. 4, mm. 1-2. appog. ^  }br -p r r 'r B: IV VII 7 /V V7 (III6) VI 13 Example 11.2 Da mei- ne Lip- pen reg-los sind und bren - nen, Example 11.3 v Yy ii? ^Y in Hvy I^ I^J | Da mei- ne Lip- pen reg- los sind und bren —nen, 3 <H V hJ H r Example 11.4 Da mei- ne Lip- pen reg- los sind und bren —nen. T Hp 8 H ^  J ^ *=»*= Example 11.5 CHAPTER 3 A N EXAMINATION OF FLUCTUATING AND SUSPENDED METER LN THE PIANO INTRODUCTION TO THE FIRST SONG Figure 1: Necker Cube The piano introduction to the first song, mm. 1-8 of Das Buch der hangenden Garten (Example 13, page 77), offers an appropriate place for a more detailed exploration of fluctuating and suspended meters.1 A salient and perplexing feature of this opening is the initial eighth-note rest in the first bar of music. This rest is interesting in several respects: it affects both 1 It should be noted that the vocal part actually begins on beat 2 of m. 8, so that there is a slight overlap between the piano introduction and the beginning of the song. As analysis will reveal, the final E4 of m. 8 clearly belongs to the motivic and metric makeup of the piano introduction; however, its temporal isolation from the previous material has formal implications that will be addressed later in the discussion. the aural and visual presentation of the ensuing music, and at the same time induces several different metric interpretations of the music. In particular, this rest allows two seemingly contradictory ways of hearing the pulse in the introduction, ways which are contingent upon whether the rest is or is not actually perceived. This chapter offers a detailed exploration of these implications. Whether or not the rest is perceived depends on many factors, including both performance decisions and the listener's knowledge of the score. The eighth rest can be heard, for example, as a silent downbeat that initiates the music and syncopates opening pitches; or it can be suppressed so that the music is heard as beginning on the first F#2 as though it were on the beat. As we shall see, the kinetic character of the opening measures changes dramatically depending on the perspective taken with regard to this rest. Example 14 compares these two perspectives. Perspective 1 is essentially a reproduction of the piano introduction's first three phrases. Here the eighth-note rest opens the music, and is felt as projecting a silent downbeat. This syncopates the first sounding pitch, F#2, and as the music moves in quarter-note values, the next four pitches are also syncopated. But the sixth and seventh attacks, the G#3 and G3 of m. 2, coincide with the notated pulse and close the first phrase. Perspective 1, that is, projects a phrase that moves from metric "dissonance" (the misalignment of rhythm and pulse), to metric "consonance" (the alignment of rhythm and pulse), and that can only cadence when the latter has been achieved.2 2 The terms metric "dissonance" and "consonance" are borrowed from Harald Krebs, "Some Extensions of the Concepts of Metrical Consonance and Dissonance," Journal of Music Theory 31.1 (Spring 1987): 99-120, but applied here with slightly different meanings. As shown in the example, this first phrase is easily parsed into two motives designated a andb. The large registral leap from F#2 to G#3 in m. 2 delineates these two motives and is striking in several ways. Until the F#2 sounds for the second time (m. 2), one has heard only quarter-note durations (regardless of whether they are heard as syncopated or not). The repetition of F#2 creates an effect of pitch closure, but a truncation of the quarter-note pulse to an eighth unsettles this effect, and is emphasized by the leap up to G#3, by the half-note duration (and agogic accent) received by that pitch, and by the relative syncopation of motive a and b against one another. As also indicated in Perspective 1, variants of these two motives form the remaining phrases of the piano introduction. The structure of the second phrase parallels that of the first: (1) a silent down-beat initiates the motion of the second phrase at a'; (2) this variant of motive a again contradicts the pulse through syncopation; and (3) b\ a variant of motive b, follows and supports the pulse of the music. The third phrase consists only of an extended a motive-variant, labeled a", and is also initiated by an eighth-note rest followed by syncopated quarter-notes. The final phrase of the introduction in the left hand of mm. 6-8 consists only of the beginning of motive a. But now, by virtue of the augmentation, it corresponds to the written pulse. This last statement of the motive might therefore be viewed as a resolution of conflicting pulses and metric dissonances, an idea that will be pursued a little later. Perspective 2 of Example 14 presents an opposing view of the introductory measures. The initial eighth rest is omitted, suggesting that the music does not actually begin until the first sounding pitch, the F#2.3 By the second attack the pulse and tempo of the music are established. Here, the rhythmic and metric relations examined in Perspective 1 are reversed. Motive a and its variants now support the pulse while motive b along with its variant syncopate against the pulse. Perspective 2 thus projects a phrase that moves from metric consonance to metric dissonance, with a much more "open" effect at the end of each phrase than in Perspective 1. The function of the eighth rests have consequently changed; they now feel as if they close the phrases, rather than initiate them. The two perspectives of the example are summarized in the following table, highlighting their reversed orientations: Motive a Motive b Eighth rests Perspective 1 syncopated not syncopated initiate phrases Table 1 Perspective 2 not syncopated syncopated close phrases The two perspectives of Example 14 are abstract projections of two different orientations of pulse in the music. Regardless of which 3 Perspective 2 (and the subsequent syncopations) expresses doubts about how a performer is meant to project the opening eighth-note rest that Schoenberg has written in the first place. perspective is taken, motive a and motive b will syncopate against one another, and the music will sound as if the pulse oscillates between the two perspectives, perhaps in a kind of metric counterpoint. This oscillation offers a metric analogy to the Necker Cube shown above as Figure 1 (page 61). Like this three dimensional line drawing which appears to have more than one orientation, the metric orientation of the excerpt seems also to oscillate between the two perspectives of Example 14.4 We can also note that in the score, because of the ties over the barlines, the downbeats of mm. 2,4, and 5 are not signaled notationally. Both of these features highlight how the music is metrically more complicated than the written time signature suggests. Metric ambiguity is created through these features and it is intensified through the music's asymmetrical phrase lengths, all of which contribute to a suspended meter. But unlike most of the examples in Chapter 2, the meter here is not suspended because two simultaneous and distinct metric strands interact contrapuntally. Instead, a single line is now involved, and meter is suspended because two possible metric interpretations of the same strand interact with (and against) one another. (That being said, certain polyphonic aspects of this "single" strand will be explored later.) A salient feature of this piano introduction is thus that there are several possible metric interpretations, a result of its metric ambiguity and suspended meter. The following analyses explore four of these possibilities. Each of the following readings draws attention to different motivic materials and pitch collections in the music. Different scansions not only 4 The Necker cube, a visual illusion, is what Gestalt psychologists call an example of "ambiguity and object reversal." The corner marked a, for example, can be perceived as being in the foreground, or in the background, changing as a viewer's orientation changes. project different kinetic experiences, but also project different pitch relationships latent within the piano introduction. Example 15.1 is the first of such readings. The initial eighth-note rest is omitted, interpreting the opening (F#2) as a downbeat, following Perspective 2 of Example 14. The music is segmented into four large pitch-class sets shown above the staff. The subset (014), first expressed by the opening pes <F#,D,F>, is embedded in each of these sets, once in z, and three times in w, x, and y, suggesting a high degree of motivic unity in the passage. In addition to pitch-class sets, the interval-class succession for each phrase is given below the staff. They show how ic<4> marks the beginning of phrases 1, 2 and 4. They also show how phrases 2-4 are commentaries on the opening phrase. Phrase 2 truncates the structure of phrase 1, repeating its first three pitches and sounding two repetitions of the opening ic<4,3>. Phrase 3 expands on the material of phrase l's lower register with an interval-class succession that is a re-ordered subset of the opening phrase. (The first four elements of phrase 3, <2,4,1,3>, are a re-ordering of those in phrase 1, <4,3,1,2>.) These two sections are also related through an inversion of contour, as shown in Example 15.2; they are not, however, members of the same set class. The final phrase signals a close to the piano introduction with a repetition of the opening phrase's first pitches, the fourth being displaced up by two octaves. 2 In Example 15.1, the music is interpreted as being primarily in ^ 3 with one fluctuation to g (m. 11 of the example). The quarter-note rhythm of the first four attacks, along with their arrangement into two pairs of descending dyads, establishes the duple strong-weak stress pattern of the interpreted meter. Measure 5 repeats the descending dyad idea, but mm. 8-2 10 vary it, grouping into 4 units with ascending dyads. Measure 11 is 3 truncated to g not because of any inherent rhythmic pattern, but in response to its surrounding material: the agogic accent in the following measure, the half-note F#2, is hard not to hear as downbeat. This pitch has previously marked barlines in mm. 1 and 5 of the example, and a descending leap, often a large one, has also signaled barlines (mm. 5, 8, 9 and 10). The length of the E3 in mm. 10-11 perhaps also weakens the sense of pulse that was operative in mm. 1-9, making it easier for the ear to hear the F#2 as a downbeat. Nevertheless, we shall see that this F# and the subsequent material may also in be considered syncopated, even in the context of Example 15.1. Example 15.3 presents three metric levels operating in Example 15.1. Level 1 presents the music's rhythm, Level 2 represents the music's pulse 2 by a stream of quarter-notes, and the half-notes of Level 3 represent the 4 meter. Levels 2 and 3 are interpretive levels that are a result of the rhythms in the music which are subsequently used by a listener as a metric template. In particular, mm. 1-2 of the example establishes a quarter-note 2 pulse and 4 meter, as does m. 5 and mm. 8-10. Measures 3-4 and mm. 6-7 are syncopated against Level 2 by virtue of a shorter duration; the quarter-note rhythm changes to an eighth-note on beat one of mm. 3 and 6. After these syncopations, Levels 2 and 3 are reinforced again in m. 5 and mm. 8-10. By contrast with the syncopations in mm. 3-4 and mm. 6-7, mm. 10-11 syncopates by lengthening the quarter-note rhythm to a quarter-note plus a dotted quarter-note. Measures 12-15 then presents the half-note rhythm of the earlier metric Level 3, but displaced by a dotted-quarter-note. This displacement results in what might be called a structural syncopation, where the material of mm. 12-16 is, in effect, syncopated against mm. 1-11, a development of the syncopations in mm. 3 and 6. Example 16.1 presents a second metric interpretation of the music. In this example, the large registral leaps are interpreted as delineating barlines. (The fourth phrase is omitted, as it would not change from Example 15.1.) The result suggests that the music may be heard as fluctuating between several irregular meters, a markedly different kinetic experience than that suggested by Example 15.1. In the present example, the music establishes the basic pulse as a quarter-note, but in measures 1-4 of the example the last pulse in each measure is consistently augmented to a dotted-quarter-note to produce the beat-values that are indicated below the staff. We will comment on the beat-values for mm. 5 and 6 shortly. First, the status of the final eighth-notes in mm. 1 and 3 requires some comment. In the present example they are interpreted as falling on the weak part of a dotted-quarter beat (by contrast with their interpretation in Example 15.1). It is how the subsequent material is perceived that allows for the present interpretation of these eighth-notes. They are immediately followed by a change in register, and a half-note rhythm (see mm. 2 and 4 of the example). In both cases it is possible to hear these attacks of half-notes as receiving stronger stresses (because of their agogic accents) than the eighth-notes in question, and as marking new downbeats in fluctuating meters. When the half-notes of mm. 2 and 4 are heard in this manner, the final eighths of mm. 1 and 3 can in retrospect be grouped with the final beats of their respective measures as suggested in Example 16.1. Grouping the last two attacks in the example's first measure, E2-9 F#2, into a single dotted quarter-note pulse results in a g meter with a rather unusual grouping into a quadruple meter (2+2+2+3), rather than the more traditional interpretation as a triple meter (3+3+3). Table 2 summarizes the groupings of the example's meters and their type in the order that they appear: Measure Type Grouping m. 1 quadruple 2+2+2+3 (eighth-notes) m. 2 triple 2+2+3 (eighth-notes) m. 3 duple 2+3 (eighth-notes) m. 4 triple 2+2+3 (eighth-notes) m. 5 duple 3+2 (quarter-notes) m. 6 duple 2+3 (eighth-notes?) Table 2 The table shows that even though the music fluctuates through several irregular meters, they are altered forms of traditional types of meters (duple, triple and quadruple), and except for m. 5, they have an extended last beat. The grouping in m. 6 of Example 16.1 is perhaps difficult to hear, since it consists of a single held note, but based on the previous measures, it is reasonable to suggest that is would be felt as 2+3. We have not yet commented on m. 5 of Example 16.1. Its beginning and ending are delineated by two registral leaps, from A#3 to Eb2, and from 5 Db2 to E3. Its five quarter-notes determine the ^ meter. It does not display the extended final beat of the other measures, since here the quarter-note rhythm is unchanging. At a higher level of organization, however, the registral leap Db2-C3 does group the measure into 3+2 quarter-notes. This grouping is in some respects the opposite of that displayed by the other measures in the example; the first group of m. 5 has the extended duration, rather than the last group. In addition to its fluctuating meter, Example 16.1 suggests the possibility that the music can be thought of as two different registeral streams, the barlines of the example conveniently parsing the music is such a manner. The opening motive now consists of the first five attacks, <F#2,D2,F2,E2,F#2>, the return to the F#2 providing a sense of closure to this gesture. Its ic<4,3,l,2> is commented on by each of the example's following measures, most obviously by m. 3, which truncates m. 1. In the higher register, m. 2 of the example reiterates ic<l> of m. 1, transposed to <G#3,G3>; the <C#4,A#3> in the high register of m. 4 draws attention to ic<3>; and in mm. 5 and 6 the two leaps to the middle register, pitches C3 and E3, project an ic<4> between them. These three intervals heard in the higher registers are thus an expanded unfolding of m. l's opening three interval-classes in retrograde: <4,3,1> becomes <1,3,4>. Example 16.2 presents a segmentation of the lower and middle registers that is suggested by the barlines of Example 16.1. The present example includes the material of the piano introduction's fourth phrase (mm. 6-8 of the score), in order to show a pahndromic unfolding of pcsets. The first and last motives belong to the set-class (0134), while the middle three segments present the set classes of two of its three trichordal subsets, (014) and (024). This latter whole-tone trichord, which begins the third phrase of the passage, is itself intervallically symmetrical, and its temporal position functions as an axis of symmetry amongst the five pcsets of the example. The function of the third phrase as such an axis point once again draws our attention to the relationship between it and the opening of the passage. In addition to the inversion of contour described in the discussion of Example 15.2, and the symmetrical function described here, several other relationships can be noted between these two gestures. Referring back to Example 16.1, the initial Eb of m. 5 might also be viewed as displacing the ic<4> incipit of the basic motive (as defined in mm. 1 and 3) by a quarter-note. The interval classes of m. 5 are also clearly a re-ordering of those in m.l . Moreover, Example 16.3 shows one way to transform m. 1 into m. 5 through their dyads. To the left of the dotted barline the example puts the two tetrachords of m. 1 and m.5 in their normal order. Both tetrachords contain one whole-tone and one semitone, and the example highlights these dyads, showing two transposition operations that transform one to the other. To the right of the dotted barline, the pitches appearing as in the score. These relationships between mm. 1 and 5 point to a high degree of motivic integration in the piano introduction. Example 16.1 has shown fluctuating meters are latent within the piano introduction. In both Examples 15.1 and 16.1 the initial eighth-note rest from the score was omitted, elaborating Perspective 2 of Example 14. Example 17, however, takes into account the initial eighth-rest of the score, as in Perspective 1 of Example 14, and assumes that this rest is successfully projected, syncopating the ensuing five attacks. In Example 17, the first five attacks in the lower register are 5 interpreted in 4, even though the syncopations may make it difficult to project. As before, the leap to the G#3 creates a metric stress that marks a new barline, so then the half-note-quarter-note rhythm of G#3-G3 projects 4. The material of m. 3 in the example is syncopated just as m. 1 was, yet 3 there is nothing inherent in its rhythm to contradicts the 4 meter established in m. 2; thus it is interpreted as continuing this meter. The 3 half-note-quarter-note gesture of m. 4 continues to reinforce 4. Measure 5 is 11 5 interpreted as in g, and m. 6 of the example in g. The metric structure of these two measure's meters can be thought of as paralleling that of m. 1 11 5 and m. 2 respectively. That is, m. 5's g meter is analogous to m. l's 4 5 augmented by an eighth-note. Similarly, m. 6's g meter is analogous to m. 3 2's 4 meter truncated by an eighth-note. This augmentation and truncation of m. 1 and m. 2's meters in m. 4 and m. 5 allows for variation in metric feel between phrases 1 and 3 of the music (mm. 1-2 and mm. 5-6 of the example, respectively), yet at the same time creates a sense of balance between them, since the described augmentation and truncation cancel each other out so that the total length of phrase 3 remains the same as phrase 1. The lower staff of Example 17 measures the lengths of each phrase in half-notes, showing this parallelism between the total lengths of phrase 1 and phrase 3. In the lower staff, phrase 4 (mm. 7-8 of the example) is sectioned into two parts, 5-half-notes plus 1-half-note for the final E 4 . Phrase 4 is interpreted in this manner to take into account the isolation of the final E 4 from the rest of the music by the F2 dotted half-note and by register. It should also be noted that the vocal line begins a quarter-note before the E 4 , so that there is a small overlap between the piano introduction and the first line of text. The status of the E 4 is thus somewhat ambiguous. It seems to produce closure for the piano introduction by completing the repetition of the opening <F#,D,F,E> motive, but it also is part of the vocal accomp animent. The measurement of the piano introduction's phrase lengths in half-notes is not meant to suggest that hypermeters are operative in the music (in the sense of larger groupings of stress patterns at the half-note value), since the many syncopations deny this possibility; instead it suggests that the phrase lengths may be considered somewhat analogous to meter only in the limited sense of overall duration, and that meter and phrase lengths express two different levels of metric organization in the music. With this in mind, the lower staff of Example 17 also shows a fluctuation through several phrase lengths, somewhat analogous to fluctuating meter, but without the hierarchical subdivisions characteristic of meter. Finally, it shows a balance between phrases 1 and 3, which together total 8 half-notes, and phrases 2 and 4, which also together total 8 half-notes, in a relatively similar manner to the balance described between mm. 1-2 and mm. 4-5: phrase 2 truncates phrase l's 4-half-note length by one half-note, which is then compensated by phrase 4's 5-half-note duration of its first three attacks. (This balance suggests itself as a possible rationale for isolating the final E4 from the rest of the introduction.) Earlier in the discussion, Example 16.1 raised the possibility that the piano introduction can be viewed as two different registeral streams of music. Our final look at these measures develops this view somewhat further. The music will be presented here as two independent registral streams that each project relatively stable meters; but as they interact with one other, metric ambiguity arises, suspending a clear sense of any one meter. In order to present this view, Example 18.1 develops a hypothetical metric and motivic template out of the material from the lower register only, presenting this material as a continuous succession of pitches. Once this template is developed, the material from the upper register will be re-introduced and the interaction of the two registered streams will be discussed. Example 18.1 extracts the material of the lower register of the score with the initial eighth-rest of the score omitted, following Perspective 2 of Example 14. This stream of material is easily segmented into four related motives, identified on the example as X , X ' , X " and X. This segmentation in part suggests the barlines of the example. The first five attacks start to establish a pattern of descending dyads that project a strong-weak pattern in quarter-notes. But the fifth and sixth attacks both sound F#2, and this repetition creates a relatively stronger attack on the latter F#2, which is thus interpreted as marking a new barline, establishing the first meter in 5 retrospect as 4. The F#2 of the example's m.2 also initiates a variation of motive X . X ' varies X in such a way as to include two (014) and two (013) subsets, elaborating the (014) and (013) subsets of X itself. Within the emerging motivic discourse based on X, the third measure of the example is delineated by the beginning of X ". X " extends X to 5 notes; it not only contains two (014) and two (013) subsets like X ' , but also contains (OA) and (024) subsets like X . Even more so, X " contains transpositions of both X (0124) and X ' (0134) as subsets, so it consequently develops both of the preceding tetrachords. The registral leaps Eb2-E3 and E3-F#2 are 4 interpreted as delineating barlines, resulting in the 4 meter established in 5 m. 2 being truncated to g in m. 4. Balance and closure are created by the return to X in mm. 5-8 of the example, here interpreted as fluctuating back 75 4 to 4. Thus the lower register of the piano introduction can be viewed as an independent stream of music that presents and develops a single motive while fluctuating through several meters. Example 18.2 now re-introduces the upper registral material. Here it is also viewed as an independent metric stream, one that has the effect of interrupting the metric unfolding of the lower registral stream described above. The G#3-G3 is the first interruption. The leap to the upper registral stream interrupts the pulse of the lower register, suspending its unfolding as the G#3-G3 gesture is sounded. This gesture, in itself, while suspending 3 the pulse and meter of the lower register projects its own pulse and 4 meter, even though its pulse is out of phase with that of the lower stream by an eighth-note. The return to the lower register at X ' similarly interrupts the pulse and meter of the upper registral stream, and resumes that of the lower stream, but begins where it left off, with the rest at the end of the lower register's m. 1. The lower register is again interrupted, now by the 3 C#4-A#3 gesture, which resumes the pulse and 4 meter of the upper stream. Following this gesture the music returns once again to the pulse and meter of the lower registral stream, again resuming with an eighth-rest. The leap from Db2 to C3 confirms an expected change to the higher registral stream, but here its interruptive effect is limited to register only, as its pulse now coincides with that of the lower stream. It is at this point that the two registral streams converge: the C3 and the E3 belong to both the high register and to the low register as a part of X " . And as already observed in Example 16.1, the interval classes of the interrupting upper register are derived from the first three interval classes presented by motive X . Setting this narrative in the context of the actual score, the music may be conceived as two registral streams that interact in a kind of metric counterpoint, creating metric dissonance and suspended meter as the music shifts from one stream to the other. As the two streams converge, the dissonance dissipates and finally resolves in the final, augmented statement of X . The inclusion of the score's initial rest into this model has a limited effect, as it is the misalignment of the two stream's pulses that creates metric ambiguity. Example 18.2 might be viewed as a more elaborate working out of Example 14 that combines both Perspective 1 and Perspective 2. As the registers shift in the music, so does the sense of pulse and meter analogous to the changing perspectives of the Necker Cube. This chapter has explored several different metric interpretations of the piano introduction from the first song of the cycle. It is the metric ambiguity of these measures that allows for these multiple interpretations, notably the indeterminate function of the initial eighth-note rest, the ties across the barlines, the metric implications of the registral leaps, and the irregular phrase lengths. As the various metric interpretations surface through different acts of hstening to the music, the possibility of hearing it in any one meter is suspended. Whereas we discussed earlier how the metric suspension is achieved in the introduction within monophony by competing scansions, we have also indicated how metric suspension could also be understood to arise from the interaction of two different registral streams, whose meters interact in a counterpoint that is interruptive or alternating, rather than simultaneous. Example 13: Schoenberg, Opus 15 No. 1, mm. 1-8. Perspect ive 1 ' I f " mo t ive a pi • —i r 1 not ive b 1 i a' 1 b' 1 1 ^ a" 1 1 r-1—i ^ = . / 1 Z H-P e r s p e c t i v e ! ^ f 1 - i H r i $ - 1 — H =^= 1 P u 1 1 b# |M = ^ =#= a 1 5 !— r I r a r i - If ' ^ J : Example 14 w=6-2(012346) x=5-21(01458) y=5-3(01245) 1Q_ o 1 /• — v ic<4, 3, 1, 2, 2, 1> i c<4, 3, 4, 3> ic< 2, 4, 1, 3, 1> z=4-2(0124) m 15_ ic<4, 3, 1> Example 15.1 phrase 1 phrase 3 ||J j J ; J=^^ <-. +, - > <+, Example 15.2 + > • J J 'J J'J>J. 'J>J r'J J ' J O J r'J J'J J'J JU-'J ' J ' J ' J J J J J J j T j J I J J J J J J J J J J J J J.J J J J J J J J J J ,J J J J J J J J J J J J J J J J Example 15.3 i c < l > ic<3> ic<4> m ic<4, 3, 1> * v i* ^ ic< 4 , 3, 1, 2> ic<2, 4, 1, 3> etc. J J J J. J J J- J J. JJ1 J - J Example 16.1 y >r -> fl* ^ * w * k w f» y I l I l I l 1 . i I 4-2(0124) 3-3(014) 3-6(024) 3-3(014) 4-2(0124) Example 16.2 T l T7 A ^ t-2(0124) 4-11(013! 0 V x\ ' iJ T l Example 16.3 {jJ J J J . |4 J : 4 J J 5 els i j Example 17 88 X (0124) X' (0134) X" (01245) X (0124) =' *E If* § ^ — Example 18.1 82 ic<l> ic<3> ic<4> 6 * - r-is X' X" Example 18.2 CONCLUDING REMARKS We have seen in this thesis that Schoenberg treated meter as a malleable compositional material from the very early stages of his development as a composer. We have also seen through our study of selected passages from Das Buch der h&ngenden Garten how Schoenberg's treatment of meter developed into quite complex formulations, ones that are integrated with the music's harmonic language. The resultant music has been described as either displaying a fluctuating meter or a suspended meter, terms that suggest an analogy with Schoenberg's own terms schwebende and aufgehobene Tonalitat. In essence, fluctuating meter involves the sequential shifting of meters in a single stream of music; it can be explicitly notated in the score, or can arise by implication in the music. Metric ambiguity is a factor in fluctuating meter, but only in a limited sense. Metric ambiguity momentarily arises as one meter changes to another, but the individual meters themselves are rarely ambiguous. With suspended meter, however, metric ambiguity exists to such an extent in the music that the question of what meter a passage is in can only be answered indefinitely. In Chapter 2, the examples of suspended meter involved several interacting metric streams. The suspension of meter typically arose from the contrapuntal opposition or tension between these streams, that prevented the meter of any one stream from dominating. The chapter also illustrated how fluctuating meter can contribute to suspended meter. At the end of Chapter 2, and in the analysis of the song cycle's opening measures (Chapter 3), suspended meter was shown to arise from conflicting metric interpretations latent within the music when it was viewed as a single metric strand. Later in Chapter 3, we saw that the piano introduction could also be viewed as two registral streams, and suspended meter was shown to arise from their interaction. Fluctuating and suspended meter are an integral part of this music, as important to it as its pitch material. Instances can be found in every song of the cycle. Quite often, in the opening measures of a song the notated meter is undermined by an initial rest that displaces the music's first downbeat (as seen in the first four songs and in songs ten and eleven), loosening the notated meter, or sometimes even undermining it. While the ensuing song presents its initial motivic material, the meter fluctuates or is suspended. Fluctuating and suspended meter complement the ambiguous harmonic language of the song cycle (as well as the special qualities of George's poems). The music owes much of its gestural and pitch content to traditional harmonic concepts, yet these gestures often project only vague references to tonality. This music may be a prime example of Schoenberg's terms fluctuating and suspended tonality. An appropriate and useful analogy for fluctuating and suspended meter (and perhaps fluctuating and suspended tonality also) is the Necker cube. The two perspectives latent within its representation create a sense of instability and ambiguity as they fluctuate from one to another. This fluctuation between the two perspectives, and ultimately the suspension of the question as to which perspective dominates, is not only analogous to Schoenberg's vagrant chords, but also analogous to the metric instability and ambiguity created in Das Buch der hangenden Garten as meters fluctuate from one to another, or as multiple metric possibilities arise and change in any given passage. SELECTED BIBLIOGRAPHY Childs, Barney. "Poetic and Musical Rhythm: One More Time." Music Theory, Special Topics. Edited by Richard Browne. New York: Academic Press Inc., 1981: 33-57. Cohn, Richard L. "The Dramatization of Hypermetric Conflicts in the Scherzo of Beethoven's Ninth Symphony." 19th-century Music 15/3 (Spring 1992): 188-206. . Metric and Hypermetric Dissonance in the Menuetto of Mozart's Symphony in G minor, K. 550." Integral 6 (1992): 1-33. Cooper, Grosvenor W. and Leonard B.Meyer. The Rhythmic Structure of Music. Chicago: University of Chicago, 1960. Dumling, Albrecht. Die fremde KLange der hangenden Garten. Mtinchen: Kindler, 1981. Epstein, David. Shaping Time: Music, The Brain, and Performance. New York: Schirmer Books, 1995. Porte, Allen. "The Magical Kaleidoscope: Schoenberg's First Atonal Masterwork, Opus 11, No. 1." Journal of the Arnold Schoenberg Institute 5/2(1981): 127-168. . "Concepts of Linearity in Schoenberg's Atonal Music: A Study of the Opus 15 Song Cycle." Journal of Music Theory 36.2 (Fall 1992): 285-381. Frisch, Walter. The Early Works of Arnold Schoenberg 1893-1908. Berkeley: University of California Press, 1993. Hertz, David Michael. The Tuning of the Word: The Musico-literary Poetics of the Symbolist Movement. Carbondale and Edwardsville: Southern IUinios University Press, 1987. Kramer, Jonathan. The Time of Music: New Meanings, New Temporalities, New Listening Strategies. New York: Schirmer Books, 1988. Kramer, Lawrence. Music and Poetry: The Nineteenth Century and After. Berkeley: University of California Press, 1984. Krebs, Harald. "Some Extensions of the Concepts of Metrical Consonance and Dissonance." Journal of Music Theory (Spring 1987): 99-120. . "Dramatic Functions of Metrical Consonance and Dissonance in Das Rheingold." In Theory Only 10/5 (1988): 5-21. . "Rhythmische Konsonanz und Dissonanz." Musiktheorie 9/1 (1994): 27-37. Lewin, David. "Towards the Analysis of a Schoenberg Song (Opus 15 No. XI)." Perspectives of New Music 12 (1973-1974): 43-86. . "On Harmony and Meter in Brahms's Op. 76, No. 8." 19th-century Music IV (1981): 261-265. . "Vocal Meter in Schoenberg's Atonal Music, with a Note on a Serial Haupstimme." In Theory Only 6/4 (1982): 12-36. . Generalized Musical Intervals and Transformations. New Haven and London: Yale University Press, 1987. Morrison, Charles D. "Syncopation as Motive in Schoenberg's Op. 19, Nos 2, 3, and 4." Music Analysis 11/1 (1992): 75-93. Odgen, Will. "How Tonality Functions in Schoenberg's Opus 11, No. 1." Journal of the Arnold Schoenberg Institute 5/2 (1981): 169-181. Roeder, John. "Pitch and Rhythmic Dramaturgy in Verdi's Luxaeterna." 19th-century Music 14/2 (Fall 1990): 169-185. . "Interacting Pulse Streams in Schoenberg's Atonal Polyphony." Music Theory Spectrum 17(1995): 231-249. Schoeberg, Arnold. Structural Functions of Harmony. Edited by L. Stein. New York: W. W. Norton & Company Inc., 1969. . Style and Idea: Selected Writings of Arnold Schoenberg. Edited by Leonard Stein. Translations by Leo Black. London: Faber & Faber, 1975. . Theory of Harmony. 1911. Translated by Roy E. Carter. Berkeley University of California Press, 1978. . The Musical Idea and the Logic, Technique, and Art of Its Presentation. Edited, translated and with a commentary by Patricia Carpenter and Severine Neff. New York: Columbia University Press, 1995. 91 Yeston, Maury Alan. The Stratification of Musical Rhythm. New Haven: Yale University Press, 1976. 

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