While making that determination might seem like a hopelessly subjective endeavor, this question is a relatable one for any musician. When musicians talk about the difference between time signatures, they often speak in terms of embodied pulse. We say that 4/4 “feels” one way, whereas 3/4 “feels” like something completely different. Any dancer knows these differences even more viscerally than any musician — imagine trying to waltz in 4/4. Indeed, it seems that the further away from our brains we get, the easier it is to feel that the difference between 4 and 3 is so much greater than 1 — in truth, they’re an entire universe apart from each other. This understanding is but one example of a qualitative measure of numbers. Within this realm, mathematics (the quantitative measure of numbers) ends and numerology (the qualitative measure of numbers) begins. Of course, numerological considerations can be highly subjective. And while that might make numerology shaky ground for scientific study, its inherent subjectivity makes it a fertile starting point for musical composition.
Each of the three movements of my piece, Numerology, takes some number as its conceptual starting point. These numbers, which I call “cardinal numbers,” are derived from an experimental approach to using playing cards as generative compositional material. This approach is purely speculative and fluid, changing and evolving as the music changes and evolves. Cards, and the numbers derived from those cards, are used as a starting point for the construction of musical parameters. At various points in the three movements, parameters directly influenced by playing cards include rhythm, pitch sets, form, improvisational structures, and electro-acoustic elements. Derived numbers are spun out horizontally into melodies, or stacked vertically into harmonies, creating a matrix of numerology that works to paint a sonic picture of the qualitative aspects of each cardinal number.
The first movement, “Excess,” is a portrait of the cardinal number eleven. Eleven can often symbolize an over-exertion of energy, going one step further than the complete cycle of ten. As such, it either represents a new beginning or a definitive ending.1 “Excess” relies primarily on melodic invention, toying with a four-note motive that expands and contracts throughout the introductory section. The piano’s entrance marks the first statement of the full motive. As the piece develops, the texture becomes denser, almost excessively so. The piece culminates with an improvised saxophone solo in which the percussionist loops a groove that re-appropriates the horizontal rhythms of the introductory motive into a layered vertical structure. The movement ends with an extreme drop in energy, almost as if all the energy spent earlier was a false high, destined to run out.
The next movement, “Counterpoise,” is an exploration of the number six. Being made up of two equal parts of three, six is an exceptionally well-balanced number. It is a balance that can be tipped in either direction, toward either five or seven, both of which are indivisible. As such, six’s balance carries with it a sense of ambivalence.2 “Counterpoise,” then, is on the whole peaceful, but it is a tenuous peace that could be upset at any time. The slow opening is articulated primarily through delicate extended techniques, including vocalizations on the flute, plucking strings on the inside of the piano, and bowing the vibraphone and cymbals. It is enhanced by a bubbling electro-acoustic texture that ebbs and flows with the music. The texture is interrupted by a brief collective improvisation, in which the performers draw on playing cards as source material for their improvisational language. From there, a new texture emerges — much more stable, if still dissonant. Previous gestures that were articulated in unison are varied and re-articulated in canon. Another brief improvisation ensues, and a return to the opening texture ends the movement.
The final movement, “Totality in Motion,” deals with the number ten. Ten is often taken to mean the ending of a cycle — it is a return to oneness after the first nine digits, and also the sum of the first four digits (1+2+3+4). As it symbolizes both completion and a new beginning, it can be seen as a symbol of universal creation — totality in motion.3 “Totality in Motion” begins with a group improvisation, ecstatic and celebratory in character, anchored by a pulsating bass clarinet drone. As that draws to a close, a polyphonic texture emerges, with each instrument playing an equal part. That texture grows into an exploration of simple chordal harmonies, eventually evolving into a fast counterpoint between the piano’s right hand and the bass clarinet, which is doubled by the piano’s left hand. After a piano improvisation, the instruments come together for a climatic ending.
I see Numerology as “chamber music with a jazz attitude.” It is a difficult piece to perform, mostly because it requires performers to be equally adept in interpreting both notated and improvised music. While these approaches are by no means mutually exclusive, they have a vastly different feel —a qualitative difference. Both approaches are valid, and both can coexist. Numerology presents an opportunity to bridge the gap between these two seemingly disparate approaches.
1 Jean Chevalier and Alain Gheerbrant, The Penguin Dictionary of Symbols, trans. John Buchanan-Brown (New York: Penguin Books, 1996), 348-349.
2 Ibid., 884-886.
3 Ibid., 981-982.