Motional Devices in William Bolcom's Non-Tonal Piano Works

by Luke Dahn

Very little thorough analysis of William Bolcom’s non-tonal music exists at present. Several factors may explain such analytical paucity. First, Bolcom is known primarily for his neo-tonal works (such as his many rags and cabaret songs), as well as for his whimsical and often tongue-in-cheek approach to composition. Non-serious neo-tonal music does not lend itself to seriously rigorous analytical methods of non-tonal music. Further, Bolcom has produced very few non-tonal piano works.(1) Therefore Bolcom is ignored and gets swept under the proverbial rug. There simply does not exist enough music to develop a "Bolcom approach."

However, perhaps the most genuine reason is an oft-cited one: our standard pitch-dominated analytical methodologies yield little useful information with such music. To show that this is the case with Bolcom’s non-tonal music is one of the purposes of this essay. An application of standard pitch class set theory, for example, will give us some information, but will prove to be bankrupt in showing us either how Bolcom operates in regard to pitch, or how the music coheres and develops its own logic. Those analysts who wish to fit music neatly into systematized categories, charts, or matricies showing its tightly-knit nature will be frustrated with Bolcom. This is not meant to imply that Bolcom is not concerned with pitch class sets and symmetry in general. It will be shown that he is indeed interested in these things at times. But symmetry and systematic employment of pitch material does not appear to be his primary concern, and thus, will not explain the general logic of his music. The following quotation from the composer will suffice in showing his largely intuitive approach to composition, eschewing rigorous pre-compositional systems:

Tonality, and what composers want and need from it, has inevitably changed. I see it as a tension between contraries; at its extremes this is reinforced by the simultaneous presence of amazing stylistic evolution on the one hand and an equally amazing conservatism on the other. This tension, more or less constant, produces a potential richness of musical energy that for my part I find enormously fecund and exciting. With the growth of skill in the management of this tension, it becomes possible to arrive at a musical speech that is at once coherent and comprehensible and in constant expansion. I have found this more fruitful that the employment of any musical language that depends for its coherence on an a priori eschewing of elements, a rigid adherence to an equally a priori system of generating tones, or a wholesale rejection of what our century has discovered on the horizons of musical style by turning totally to the past.(2)

This paper will show that by thinking in motional terms we may be in much better position to grasp the general logic and coherence of Bolcom’s non-tonal music. Musical motion or movement has greater importance here than do pitch class set groupings. Thus, pc-sets are relegated to an inferior role, while contour, melodic direction, voice-leading, and dynamics come to the forefront. It will be shown that pitch content itself is subservient to and is dictated by motion or movement. Furthermore, concepts such as tension resolution can be equated with motional resolution. The concept of entropy provides a useful metaphor for us here. In order to show how motion dictates pitch content for Bolcom, two of his Pulitzer Prize-winning Twelve New Etudes will be examined: Etudes 1 and 8 subtitled "Fast, furious" and "Rag infernal" respectively. (The etudes will henceforth be referred to by their subtitles.) Along the way, several of Bolcom’s signature compositional techniques that emphasize his concern for musical movement (or, in certain cases, musical immovability) will be illustrated.

The initial stages of employing pitch class set analysis to "Fast, furious" will readily show the limitations of such a method. Chart 1 below indicates the entire make-up of Bolcom’s melodic writing in the piece. (The pitch material in the piece’s "pitch constellations" is omitted here, but will be discussed later.) All interlocking trichords were identified and their occurrences totaled. The fact that every single trichord is represented, and that many trichords have numerous occurrences shows that Bolcom has no systematic approach of pc set application. Identifying tetrachords, rather than trichords, in like manner would yield no more consistency.

Chart 1: trichordal make-up of "Fast, furious"

TrichordsOccurrences%
[012]115% trichords with [01] = 68%
[013]3716%
[014]4821%
[015]2612%
[016]3013%
[024]94%
[025]178%
[026]136%
[027]10%
[036]2210%
[037]94%
[048]21%
225100%

(Italicized trichords are invariant sets.)

Information resulting from such analytical methods is by no means entirely futile. Several things can be gleaned from Chart 1. First of all, Bolcom prefers trichords that contain the [01] dyad in general, and prefers the [014] and [013] trichords in particular. Secondly, at least for this piece, Bolcom tends to avoid, though not completely, trichords that are invariant or symmetrical. However, because of the intuitive and unsystematic nature of Bolcom’s approach regarding pitch selection, it is difficult to assess the importance of this kind of information. And once we embark on an investigation of the motional features of this music, we will see the relative unimportance of pitch-class-set analysis.

Direction of line. An initial hearing of "Fast, furious" will reveal that Bolcom is very much interested in gesture and directional lines. All phrases move towards a local telos. They rarely encompass a narrow stationary range, but rather move to the bottom of the piano or shoot up to its extreme high register. The lowest A is struck four times, three of which end a phrase. The highest C is struck five times, all five times occurring near the piece’s climax. There are eleven phrases in the short piece (again not counting the "constellation" figures which are superimposed on the phrases). Of the eleven phrases, eight of them either begin or end with that phrase’s highest or lowest note. It is also no accident that even the forearm clusters in the piece are never to be blocked, but rolled. Even these mini sound masses are given direction.

EXAMPLE 1: "Fast, furious" a) p.2, sys.1; b) p.3, sys.1

Voice leading. The very phrase "voice leading" possesses motional connotations. For Bolcom, adherence to voice leading principles, nontraditional though they may be, very often dictates pitch content. Examine the chords in the opening of the eighth etude, "Rag infernal:"

EXAMPLE 2: First four measures of "Rag infernal"

In these first four measures of "Rag infernal," Bolcom retains at least one common tone between successive chords, with the exception of the final chord, which marks a registral shift. The notes that are not retained as common tones always move by half step (again with the exception of the final chord). This type of controlled movement pervades the left hand writing throughout the rag.

Voice-leading also plays an important role within single line passages, which often contain contrapuntal lines embedded within them. The penultimate phrase of "Fast, furious" (Ex.3) possesses such embedded lines. (The whole tone quality of the passage also reflects Bolcom’s affinity for the scale.)

EXAMPLE 3: Penultimate phrase in "Fast, furious"

For Bolcom, tonal implications, which often result from allowing voices to lead where they may, are a welcomed byproduct and are not to be eschewed. While never establishing any tonal center, Bolcom’s music often gives glimpses of tonality. Here is where Bolcom’s atonality, or "nontonality" as Bolcom would probably prefer to call it,(3) breaks from the goals of many other atonal composers such as Schoenberg, who tried to avoid tonal implications at all costs. We have with Bolcom a kind of inversion of Schoenberg’s "emancipation of dissonance." Here, it is consonance that is emancipated. Several phrases from "Fast, furious," such as the two in example 4, have strong tonal implications. The first hints at Gb major or possibly Db major. The second suggests a bluesy A major, (though the extreme register’s muddiness impedes its audibility).

EXAMPLE 4: Two phrases from "Fast, furious," p.1, sys.2

Contour motives. Another feature of Bolcom’s music that evidences his general lack of particularity in the realm of pitch class material are his contour motives. Unlike melodic motives, as conceived of in the usual sense, contour motives do not concern specific intervallic structure, only directional structure. The opening two pages of the "Rag infernal" present such a contour motive. The motive is DUDDU,(4) and it occurs three times in the opening section, and even though the third time is partial and interrupted, the motive connection is quite audible.

EXAMPLE 5: Contour motives from the beginning of "Rag infernal"

Of course, salient features of the passages other than simple directional ones contribute to its recognizability. For example, the third element in each phrase is higher than the beginning element. Stated in another way, inherent to this particular contour motive is the fact that the first U interval is greater than the first D interval. I have a hunch that a thorough application of recent studies in contour to Bolcom’s music would prove to be enlightening.(5)

If we are employing ideas of motion and movement to help explain the overall logic of Bolcom’s non-tonal music, it naturally follows that the concepts of stability and tension resolution can also be thought of in motional terms. Lack or decrease of motion can give a sense of resolution in certain cases, can firmly anchor a passage in other cases, and can even stifle and stagnate in still others. Several compositional techniques employing motional decline will now be examined.

Pitch constellations. One of Bolcom’s favorite techniques of stabilizing the music is through the use of what I shall call "pitch constellations," or arrays off pitches that are fixed in their registral placements. Passages containing these constellations exclude all pitches not found within the constellation. Such constellations usually stability the music, resolving or reducing the pitch activity for a given period of time. Both etudes discussed here include them. "Fast, furious" contains seven constellations in all. Three of them contain six pitches, three others contain seven pitches, and the remaining one contains four pitches. Interestingly, no two constellations make up identical pitch class sets, which further indicates that Bolcom does not interest himself with systematic application of pc-sets. However, the [014] trichord, whose significance in the piece was indicated by Chart 1 above, figure predominantly in all seven constellations.

EXAMPLE 6: Seven pitch constellations of "Fast, furious"

These constellations provide a much needed stabilization in the center section of the piece. Pitch activity is reduced and restricted, and the audible effect is one of stabilization. Prior to the appearance of these constellations, no single pitch appears in close proximity with another of its appearances.

A large twelve-pitch constellation emerges towards the end of "Rag infernal." (Two notes, C# and F#, have more than one appearance in the constellation, so the twelve-pitch constellations does not make up a twelve-tone aggregate.) This grand constellation reaches a span of four octaves plus a tritone, and lasts for nineteen measures. Thus, its grandness is both vertical and horizontal.

EXAMPLE 7: Grand constellation in "Rag infernal," mms. 90-108

Unlike those in "Fast, furious," the welcomed sense of resolution that this constellation initially brings quickly turns into stagnation due to its length. The piece gets "stuck" in the constellation quagmire, and its musical activity becomes smothered and stifled. The ragtime stride rhythm attempts to resurface but cannot really do so until the constellation has fully expended itself. The reappearance of the ragtime rhythm afterwards is very welcomed, and, ironically, provides a kind of resolution, a restoration of normal order. So here is a case in which the decrease of pitch activity and harmonic rhythm via the use of pitch constellations, in a way, ultimately defeats its own purpose.

Immovable Pitches. Related to these fixed constellations are other types of immovable pitches. Sometimes they are chords, while other times they are single pitches. Three passages in "Rag infernal" are anchored by single pitches in this manner. The first passage contains and obstinate Eb4 whose initial appearance is marked in measure 52 by a sforzandississimo (sfffz), and whose duration, through repetition, lasts for fourteen measures. Interestingly, the appearance of the Eb occurs at precisely the time that the ragtime rhythm in the left hand is interrupted and disappears. The Eb thus takes over the anchoring agent for the piece. The second shorter passage (mms. 76-79) contains an Ab4 that is obstinately restruck at a regular dotted half-note pulse, and the third passage (mms. 86-89) contains the Ab4 along with the returning Eb4, both of which are again persistently restruck in a syncopated regular dotted half note pulse.

Tension resolution. In the previously discussed cases, lack of movement resulted from pitch immovability and provided anchored stability. But lack of movement can also provide a resolution of tension or of a high activity level. Entropy here provides a useful metaphor. A state of motional resolution is often reached when musical entropy has taken its course, and a passage is finally exhausted of its energy. Entropic effect is evident in both small and large-scale structure. As mentioned before in discussing line direction, it was noted that very few of the eleven phrases in "Fast, furious" are without directional shape. Also important is the fact that, with one exception, none of the eleven phrases end without a diminuendo marking. (The one exceptional phrase, which ends with a dramatic crescendo to an accented fortissimo, occurs at the piece’s climax.) These phrase endings may not be accompanied by stationary or immovable pitch content, but they do represent a cessation of motion due to its dynamic shape (and also due to the rather obvious fact that they are followed by silence).(6)

Motional resolution also occurs in large-scale structures. An excellent example arises in the closing section of "Rag infernal." The previously active chordal melodies that occur in the early stages of the piece finally resolve themselves to a pair of fixed alternating chords. Movement ceases. All energy is expended, and the sense of resolving finality is a readily audible one, much akin to the resolving effect of a slowing harmonic rhythm in common practice tonality.

EXAMPLE 8: "Rag infernal:" chordal activity resolves at the piece’s end.

Pitch Generators and Pitch Fulcrums. The final technique to be discussed may be the most interesting because it includes facets of all the techniques already addressed. But it is also perhaps the most musically interesting, and the application of this final technique yields very appealing audible effects. Two prime examples occur in "Rag infernal." In both cases, Bolcom formulates some pitch-generating process that spins out his musical material. Both cases take the form of a sequence, and both contain what I call "pitch fulcrums," or pitches that do not move and that provide a kind of point of reference by which everything else moves.

Measures 69 through 75 provide the first example. Here Bolcom sets up a pitch constellation that proceeds to collapse or implode onto itself (again entropy being a useful metaphor), creating an inverted wedge. The constellation is comprised of eleven pitches, six in the right hand and five in the left, each of which move inward at a regular interval toward the constellation’s center. Below are the seven successive permutations that the collapsing constellation undergoes in the process. (Dotted barlines do not correspond to barlines in the score, but only serve the purpose of distinguishing chord changes in the collapsing wedge.)

EXAMPLE 9: Collapsing constellation in "Rag infernal," mm. 70-75

The left hand column below the grand staff indicates the intervallic movement of each constellation pitch. (For example, the –[03] at the top of the column indicates that the top note descends at the interval of a minor third.) Several things are noteworthy here. Notice that three pitches remain constant: C in the right hand, and B and G# in the left hand (once again indicating Bolcom’s affinity for the [014] trichord). These provide "pitch fulcrums" on which the constellation collapses, another kind of anchoring device. Notice also that Bolcom has arranged the right hand constellations so that the pitches in each chord are symmetrically distributed vertically. This means that each chord comprises an invariant pc-set, though no single invariant set is duplicated in the right hand. Voice-leading here is once again of primary importance, since voice-leading dictates the symmetrical nature of the chord structures. The left hand, in contrast with the right hand, only strives towards symmetry, reaching it ultimately at its final chord. The succession affirms once again Bolcom’s approval of tonally implicated pitch collections. The right hand’s fourth sonority obviously suggests C major and/or a minor. The left hand’s third sonority gives us g# minor, and ends with a bluesy E major. This constellation collapse gives a striking aural, entropic effect.

The second example of the utilization of pitch generators and pitch fulcrums occurs later in the same piece. Here, chordal trichords undergo the same kind of sequential process.

EXAMPLE 10: "Rag infernal," mms. 112-115

The sequence of highest note or voice in the chord consists of a move up a perfect fifth then down an augmented fourth. The lowest voice ascends a major third followed by a descent of a minor third. And the middle voice gives us alternating G#s and As, once again providing a fixed but swiveling pitch fulcrum. With the fulcrum in place, the resulting trichords are different with each successive sequence, showing once more that Bolcom is more interested in voice-leading principles than pc-set application.

This study has suggested that for Bolcom motion is of primary importance. In many ways motion dictates pitch content. Tension and resolution can be conceived of as motional tension and motional resolution. Many of Bolcom’s favorite compositional devices are also motional (and sometimes non-motional) in nature. Furthermore, since Bolcom overtly disdains rigorous precomposiitonal pitch-generating systems, we should not expect that analytical methods, which are so effective in deconstructing such systems, will be very useful. Therefore analytical approaches emphasizing motion should be embraced for this music, and studies such as Michael Freidmann’s on contour(7) and John Roeder’s on metric pulse stream(8) should prove to be fruitful.


1. To my knowledge, only three of Bolcom’s solo piano works would fit this category: the Twelve Etudes (1954-64), the Twelve New Etudes (1977-86), and the Nine Bagatelles (1996). (back to paragraph)
2. From the afterword in the score of Twelve New Etudes, publ. E.B. Marks, 1986. (back to paragraph)
3. In an afterword to the score, Bolcom speaks of a "fusion of tonality into non-centered sound (often miscalled ’atonal’)." Other etudes in the set have much stronger tonal implications than the two being analyzed here. "1. Fast, furious" may be the least tonal of all twelve etudes. (back to paragraph)
4. As might be intuited, D = down and U = up. (back to paragraph)
5. Michael Friedmann’s article "A Methodology for the Discussion of Contour: its Application to Schoenberg’s Music," with its description of "contour agency series," "contour classes," and "contour interval successions," would be an excellent place to begin such a study. JMT 29/2 (Fall, 1985) 223-248. The works of Robert Morris and Elizabeth West Marvin would also be helpful. (back to paragraph)
6. It is interesting that we refer to volume level and volume indications by the motional terms "dynamics." See Zbikowski, Conceptualizing Music (2002); Saslaw in JMT 40 (1996); Brower in JMT 44 (2000); and Marion Guck’s writings. (back to paragraph)
7. Friedmann, Michael L. "A Methodology for the Discussion of Contour: Its Application to Schoenberg’s Music," Journal of Music Theory 29/2 (Fall 1985), 223-248. (back to paragraph)
8. Roeder, John. "Interacting Pulse Streams in Schoenberg’s Atonal Polyphony," Music Theory Spectrum 16 (1994), 231-249. (back to paragraph)