This paper is a comparative exploration into the concepts of repetition and

Transcription

1 A Musical Mind in an Information Theory World: Refining Concepts of Repetition and Progression Through Comparative Musical Analysis Leslie Tilley University of British Columbia This paper is a comparative exploration into the concepts of repetition and progression in music, through the lens of information theory. Until recently, many scholars have viewed repetition or cyclicity, and progression or change, as mutually exclusive organizing principles. On the one hand, we had the West, which prided itself on change and linearity on progress both in its cultural development and its common practice tonality. Ideas of individual geniuses, scientific progress, capitalism this was our own rhetoric for Western culture; and it bled over into our musical rhetoric: harmonic progression, a sonata s development section, climax and resolution. Our music was all about change and progress. On the other side, we had a music culture like Bali. Clifford Geertz showed us, in his beautifully lyrical prose, a Bali whose every aspect was cyclic from its belief in reincarnation and its calendar and naming systems down to its repetitive, colotomic music. Balinese gamelan, with its repeating melodies, and recurring gong strokes that marked both an ending and a beginning, was purely cyclical, and, like Geertz s Balinese society, lack[ed] climax because it [took] place in a motionless present, a vectorless now. Of course there is some truth to this. Balinese music does have many essential elements that are cyclic, and Western Classical music does exhibit goal-oriented harmonic motion; but these were still oversimplified ways of looking at the

2 music, which also had potentially dangerous consequences from the perspective of cultural analysis. Happily, in recent years, a dialogue has opened that places these two extremes on a continuum, with each music culture seen as taking freely from elements along that continuum. Andrew McGraw, for instance, has explored ideas of progression in Balinese gamelan music, by examining temporal transformations that obfuscate the simple cycle, particularly the extreme tempo variations inherent in the music that basic Western notation simply flattens. 1 McGraw claims that the clear-cut cyclicity we see in Balinese music may simply be due to our own categorical perceptions, to the condensation and accumulation of similarities and differences between objects and events 2 as we have learned to see them in our culture. We have been taught to see harmonic progression as a form of change, or linearity; we have not been taught to analyse tempo changes over the course of a piece in the same light. In this paper, I compare repetition and progression in Western common practice music, Balinese gamelan, and the Southern Ewe dance-drumming of Ghana, using information theory as the unifying frame for comparison. Information theory is a branch of communications theory used to precisely measure and compare different kinds of messages, in terms of the number of digital bits required to convey them. The quantity of information in a message is measured in terms of its predictability. Some messages are highly predictable. For instance, a string of words that is just one-two-three-one-twothree-one-tow-three-one-two-three, because it is completely redundant without variation, is entirely predictable and so can be said to contain almost no information. It would take 1 Andrew Clay McGraw, Different Temporalities: The Time of Balinese Gamelan, Yearbook for Traditional Music 40, 2008: Hoopen as quoted in McGraw,

3 very few bits to convey this message; one would simply need to communicate one-twothree-repeat-ad-nauseum. By contrast, some statements are highly unpredictable, what information theory calls original. Citrus, lackadaisical, Egypt, hopscotch, jostling, counterproductive, frumpy, onomatopoeia, the, yet, is virtually an impossible message to predict. Given the word frumpy, we would almost never guess onomatopoeia to be the following word. So we say that original statements have a high quantity of information, and that a message s information is inversely proportional to its probability. Information theory has found that most verbal messages are in a middle-ground between certain and impossible. I would like to put forward the idea that each musical system also tends toward a balance between repetition and change a balance between noinformation and infinite-information. Repetition be it a rhythmic motif, a harmonic progression, a recurring melody, a recurring tonal center, or even a regular meter with its recurring pattern of strong and weak beats is required in music for humans to perceive structure. It may be repetition of qualities existing only within that piece like a recurring rhythmic motif, or of qualities existing across many pieces in the same genre like the highly probable occurrence of a tonic chord following a dominant chord at the end of a phrase in Western common practice music. Whether the repetition is local and piece-specific, or the general repetitive characteristics of a genre, it will combat what Leonard Meyer calls cultural noise the distance between the habit responses possessed by the audience member, and those required to understand the musical style. As John Rahn says: 3 3 Leonard B. Meyer, Music, the Arts, and Ideas: Patterns and Predictions in Twentieth-Century Culture, 2 nd Edition (Chicago: The University of Chicago Press, 1994 (orig. pub d 1967)): 16 3

4 Mary recognizes a similarity of slope of pattern, recognizes that this most recent pattern fits together with other past patterns to make a larger pattern related itself to the most recent, now subpattern, by some (as it were) affine transformation. [ ] Sense is dependent on repetition, without which nothing can be recognized. 4 Thus, when a piece of music becomes too improbable, contains too much information, we are no longer able to understand it. Without repetition, we perceive only chaos. However, we equally shy away from pure repetition, what Rahn calls slavery. For repetition to be lively, to be engaging, it needs a goal a telos. It needs to be able to surprise, to have an uncertain future. Without the possibility of change, we have only boredom, death, slavery. I propose that each musical system under consideration seeks a similar kind of middle ground, a similar balance of elements along our now-continuum whose two extremes are chaos on the one hand, and slavery on the other. Repetition exists in them on many scales, from small 2-beat gestures, to formal structures, to repetition spanning multiple performances. And without confining ourselves to specific pieces, there are certainly parallels to be found at all levels of repetition and progression. Beginning with the smallest scale, each genre in its own way uses immediate repetition of melodic or rhythmic patterns. In an Ewe dance-drumming piece like Gahu, this could be the basic pattern of any of the supporting drums, like the kaganu, which is a two-note pattern that religiously repeats (Fig 1). Slightly more complex is the kidi part, which contains two halves similar but not identical that repeat in an A-A 1 pattern (Fig. 2). Some freedom of variation within each part, and particularly the changing polyrhythmic relationship between these parts and the improvising lead drummer, keep this repetition from becoming slavery. 4 John Rahn, Repetition, Contemporary Music Review 7(2), 1993: 53. 4

5 We can see a similar balance in the elaborating figurations of Balinese gamelan music. In this typical figuration, called norot (Fig. 3), the rhythmic pattern and basic contour is the same for every underlying melody note, but the direction that the melody will take is unpredictable. On a larger scale, once the underlying melody has cycled a few times and is becoming predictable to the point of slavery, the piece will shift to a new underlying melody, or the musicians will perform a new kind of rhythmic accent, or the tempo or associated dance movements will change, or one of the lead instruments will improvise. Something will happen to keep the piece from becoming static. In Western common practice music also, composers will often explore a single short motif, as in these sequences from Bach s C major invention, mm. 3-4 (Fig. 4). Like the Balinese figuration, they explore the same rhythm and melodic contour on different scale degrees. Furthermore, many Western common practice pieces, like fugues, are almost entirely built on just a few motifs, and several scholars have explored how repetition of a single motif can be masked through various forms of motivic exploration. 5 On a slightly larger scale, one could form a parallel between the single recurring bass-line and changing surface motion of a Western passacaglia, with the recurring underlying melody and changing figuration of a Balinese gamelan piece, with the recurring supporting drum patterns and improvised lead drum part of a southern Ewe dancedrumming piece. In each of these cases, the constituent parts may be repetitive, but the overall effect is one of progression. 5 Such as David Beach, Motive and Structure in the 'Andante' Movement of Mozart's Piano Sonata K.545, Music Analysis 3(3), 1984:

6 On a larger scale, we can look at repetitive formal structures, such as alternation, cross-culturally. In Western common practice music, we see alternation in the verse and chorus form, or the rondo form. In Ewe dance-drumming, songs often exhibit this sort of alternation between call and response, or between sung and drummed sections of a piece. In Balinese gamelan, the use of alternating timbres is a common structural feature. Many of the more modern gamelan gong kebyar compositions will feature different instrument sections in alternation. A partial parallel may be drawn between this and Western concerto forms. Finally, looking beyond the scope of a single performance, we can also see a balance between repetition and progression cross-culturally. Western classical music, with its cult of the composer, is the least liberal in the progression of a single piece over multiple performances preferring instead Rahn s répétition, repetition with the goal of perfecting an already fixed structure. 6 However, some interpretation is essential in any given performance of a Western classical piece, and the reason we prize certain conductors and performers even more than composers. In Bali, the identity of a piece is slightly more fluid, with different gamelan groups having their own unique characteristic figuration styles, drum patterns, and tempo fluctuations for a given piece. Variation is even broader in a dancer-controlled piece, or in a context-sensitive piece where the needs of a ceremony dictate the form of the piece. Ewe dance-drumming is similarly free in terms of its overall form controlled by the master drummer, and varied considerably in terms of length, dance moves used, and songs sung, for each performance. An Ewe piece, like Gahu, will always use the same basic elements, but vary them so much 6 Rahn, 50. 6

7 between performances that, in many ways, a single piece is more aptly called a style or genre. So, while Southern Ewe dance-drumming and Balinese gamelan music may, at first glance, seem more repetitive than Western classical music, in fact, when explored over the course of several performances, we see far more change, far more progression in the seemingly more cyclic music cultures. We now turn to a comparative analysis of two specific pieces the first movement of Beethoven s Piano Sonata No. 1 in f-minor, and the introductory section of a well-known classical Balinese gamelan gong kebyar piece called Oleg Tumulilingan, or Oleg. Information theory states that any structure built on a system of rules will begin with a high level of information a high level of systemic uncertainty as we establish what the rules are. 7 Then, the longer we work within that system, the more familiar we become with that particular structure s rules, and the more the probability of certain events increases. Thus, as we progress through any given structure, systemic uncertainty, and so the quantity of information, decreases. Musical structures work in the same way. During the first cycle of a gamelan piece, we don t know what direction the underlying melody will take, and so information is high. However, each time it repeats, it becomes more predictable, and so contains less information. The same is true of a Western common practice piece. At the beginning of the piece, we don t know what rhythmic or melodic motifs the composer will choose to explore, or precisely how the piece will work through the stylistic norms of the genre; these patterns emerge as the piece progresses. However, music is a more complicated system, because it is a human-made, not a natural 7 Meyer, 15. 7

8 system. So, the composer, acting as surrogate for the culture itself, introduces what Meyer calls designed uncertainty, to combat the tendency toward the tedium of maximum certainty. Thus, as systemic uncertainty decreases, designed uncertainty is slowly added, to maintain the delicate balance between chaos and slavery. Consider a single phrase from each piece. Looking only at the surface-level motion the rhythmic-melodic motifs in the right hand of the piano, and the fastest elaborating instruments in the gamelan we can see a parallel distribution of systemic and designed uncertainty inherent in each musical system. Beethoven s opening phrase (Fig. 5) follows a familiar common practice construction: a 4-measure antecedent and consequent are followed by a 2-measure intensification through fragmentation and acceleration of motivic repetition, and end with a 2-measure contrasting cadence gesture. A A 1 B. Of course, stylistically, there s nothing unpredictable about Beethoven s construction of the sentence; it is an archetypical common practice sentence. The beauty of this classic structure is that both increased change and increased unpredictability are built into it. As the motifs of the piece become familiar to us, movement and change occur more quickly, keeping repetition from becoming slavery, through fragmentation. Finally, in the cadence gesture, the conventions of style allow the composer the freedom to introduce new melodic material, which is unpredictable in its rhythm and pitch content, as well as its melodic contour. The opening phrase in Oleg (Fig. 6) exhibits similar construction, also typical of the genre 8. The composer starts by establishing the initial motif for several beats, continues with a shorter variant of that motif repeated several times, each time on a 8 There are many other examples of this sort of construction in elaborating parts in Balinese gamelan piece. For another example, see Wayne Vitale, Kotekan: The Technique of Interlocking Parts in Balinese Gamelan Music, Balungan: A Publication of the American Gamelan Institute 4(2), 1990: 12 (Fig. 27.) 8

9 different scale degree, and ends with a contrasting motif. A A 1 B. Comparing the surface motion of the Beethoven and Oleg phrases side by side (Fig. 7), we also see parallels in the distribution of the three motif types. In both, for instance, A lasts longer than B, and B only occurs near the very end, in the last quarter of the phrase. Though each piece is following its own music-cultural conventions, the conventions themselves seem to dictate a similar rate of change and uncertainty a similar distribution of information within each sentence. An analysis of the underlying motion in both phrases the harmonies in the Beethoven and the slow-moving melody in the Oleg will yield similar results. The Beethoven begins with two measures of tonic and two of dominant, followed by the same progression, this time for one measure each, then finally the tonic and first-inversion supertonic each taking up just half a measure, and a one-measure half-cadence on the dominant (Fig. 8). Again we see a typical common practice construction that encourages an increased rate of harmonic change over the course of the phrase. Unpredictability, too, increases near the close of the phrase: the supertonic chord could as easily have been a subdominant or secondary dominant we cannot predict it with certainty and so information increases. In the underlying melody of Oleg, we see a very similar progression resulting in the same two overriding characteristics: increased motion and increased unpredictability (Fig. 9). Like in the Beethoven, the composer of Oleg begins with slow melodic motion, thoroughly establishing the gong tone for the equivalent of 3 half-notes. He then moves away from the gong tone, exploring 2 other pitches before coming back again to the gong 9

10 tone, this time for only one half-note. Then the composer introduces a new tone and repeats an old one to finish the cycle. Again we see both the rate of pitch change and the introduction of new melody notes increase over the course of the phrase. Michael Tenzer has shown that this increased melodic movement and change as a phrase progresses is central to the construction of many Balinese melodies; 9 that, much like the harmony in the Beethoven phrase, an increase in designed melodic uncertainty as systemic melodic uncertainty decreases is inherent in the Balinese compositional process. Since Western music uses such a wide array of chords, but gamelan gong kebyar only has five pitches for its underlying melody, the assumption that the two can be fruitfully compared may not, in fact, be valid. It may be valuable to comparatively analyse more complex harmonic passages not in terms of their chords but in terms of their harmonic function searching for parallels in the distribution of Balinese melody pitches with the distribution of tonic-functioning, pre-dominant-functioning, dominantfunctioning, and sub-dominant-functioning harmonies. Or my analysis may be taken as merely suggestive of the fact that we should search for appropriate cross-domain mappings in cross-cultural analysis. Pulling back the zoom lens somewhat, a comparative analysis of tonal center shifts in the development section of the Beethoven with tempo shifts in Oleg shows some interesting parallels. As you can see on the left side of this chart (Fig. 10), the development section in the Beethoven goes through several different tonal centers from 9 Michael Tenzer, Gamelan Gong Kebyar: The Art of Twentieth-Century Balinese Music (Chicago: The University of Chicago Press, 2000): Ch

11 Ab Major, to bb minor, to c minor, and back to Ab major, before finally returning to the original f-minor. Each tonal center lasts for a different number of measures, with change remaining unpredictable. Yet, the actual harmonic material of the development section is entirely balanced and symmetrical in the context of the genre: with the exception of a few transitional chords moving between tonal centers, Beethoven uses only tonic and dominant chords. Oleg exhibits a similar balance between the low information level of its underlying melodies and the high information level of its tempi, and here I have borrowed from Tenzer s analysis of the piece. 10 The underlying melody in this section of Oleg is very repetitive there are a few different permutations in play, but all exhibit similar melodic motion. What keeps this section from feeling static, are the very dramatic tempo changes throughout, which completely shift the aural focus of the listener. When the underlying melody is played very slowly, its tones are too far apart to be perceived as a unified melodic line, so we focus instead on the elaborating figuration; at a faster pace, the underlying melody becomes the focus. So, two sections that look identical on paper may in fact be perceived very differently. The right-hand side of the chart in Fig. 10 shows the layout of Oleg s tempi. Just as there are four tonal centers in Beethoven s development section, there are four tempi in this section of Oleg slow, fast, peak (the fastest tempo), and the outro, which is very slow. Again, each tempo lasts for a different number of cycles, and the section alternates between them in an unpredictable order. Thus, Oleg s repetitive melodies that move through unpredictable tempo shifts may be said to parallel Beethoven s repetitive chord structures that move 10 Michael Tenzer (Ed.), Analytical Studies in World Music, (Oxford: Oxford University Press, 2006):

12 through unpredictable tonal center shifts. Again on this larger scale, both pieces seek a balance between repetition and progression. A comparative analysis like this raises many questions. Are these analogies still relevant if the culture-bearers do not experience their musics in comparable ways? To discover if they did, we would need to locate cross-culturally competent listeners and extensively test their responses. The problem is that there is an enormous continuum spanning emic to etic positions and no privileged place to be on it. For an audience of Western theorists, or composers, or aestheticians or cognitivists, perhaps the mere fact that parallels can be found validates them. Another concern would be whether or not this kind of reductive search for parallels harmfully masks the uniqueness of each music culture. I have approached my analysis in a spirit of creativity and will leave answering these questions to a future time. Today I only hope to have contributed to the idea that information-theory-based comparative analysis of repetition and progression might offer new insight into the connections between diverse musical systems. 12

13 Musical Examples Fig. 1: Kaganu for Gahu Fig. 2: Kidi for Gahu Fig. 3: Balinese gamelan figuration Fig. 4: Sequences: Bach C Major Invention Fig. 5: Beethoven surface motion 13

14 Fig. 6: Oleg surface motion Fig. 7: Surface Motion Comparative Analysis A A A 1 A 1 B A A 1 _ A 1 _ A 1 _ A 1 B B Fig. 8: Beethoven underlying motion i V i V I--- II 6 --V Fig. 9: Oleg underlying motion u a e u o e Fig. 10: Beethoven tonal center shifts (development) vs. Oleg tempo shifts 4m. A b 3c. fast 1m. trans 3c. peak 8.5ishm. b b 1c. rit 7m. c 6c. slow 2m. trans. b b (2 ndary dom) 1c. accel 5m. A b 3c. peak 24m. f recap (in f) 6c. fast 3c. peak 1c. slow Beethoven: Oleg: 14