Irrational Transcendence Woodwind Quartet - Digital Sheet Music

SKU: A0.912918

Scored for sax quartet (soprano, alto, tenor, baritone). Appropriate to any concert or recital setting. In mathematics, there exists a unique set of figures known as "transcendental numbers." A transcendental number is a real or complex number that is not algebraic-that is, it is not a root of a non-zero polynomial equation with rational coefficients. These are rare because it is extremely difficult to prove that a number meets all the mentioned criteria. All transcendental numbers are irrational, since all rational numbers are algebraic. I find esoteric mathematical phenomena quite fascinating. One finds here that very tangible aspects of daily life are often described in ways that are quite complex and even confounding. There is an almost mystical magnetism to digging deeply into the universe around us. In this set of miniatures (four in all), I endeavor to find interesting ways to apply some of these transcendental numbers in music for saxophones. Miniature One: π "Pi" is the best known of the transcendent numbers. In this piece, I take the whole number of pi (3) and apply it formally (three sections, each divided into three sub-units, every third of which is distinct from the rest via articulation and dynamic level; three pulses of rest between each sub-unit; rhythmic expression determined through three different rhythmic bases). I took the first 45 decimal places of pi, divided them into units of 5 each, and applied the numerals to an aleatorically-determined basic rhythmic unit (16th note, eighth note, quarter note). The first section is in unison/octaves. The second explores pandiatonic harmony and the final makes use of the whole chromatic scale. Miniature Two: e The natural logarithm (abbreviated "e") is of eminent importance in mathematics, alongside 0, 1, π and i. All five of these numbers play important and recurring roles across mathematics, and are the five constants appearing in one formulation of Euler’s identity. Like the constant π, e is irrational: it is not a ratio of integers. Also like π, e is transcendental: it is not a root of any non-zero polynomial with rational coefficients. I used the first 20 decimal places of e, divided into segments of five, then assigned each segment to a part. These numbers were used to determine the rhythmic values, with soprano and alto using an eighth note as a basis, and tenor and baritone using the quarter note. The leading whole number of e (2) I used to govern the overall formal structure (there are 2 cycles of each rhythmic pairing then ends with two cycles tutti). Miniature Three: Cahen’s Constant Cahen’s constant is an infinite series of unit fractions, with alternating signs. This constant is named after Eugène Cahen, who first formulated and investigated its series in 1891. It is notable as being one of a small number of naturally occurring transcendental numbers for which we know the complete continued fraction expansion. I took the first 12 decimal places and translated them into rhythmic durations, using the sixteenth note as the basic unit. I then took the sum of each pair of integers within the decimal places and assigned the output to chromatic pitches. The final episode features this rhythm in augmentation and using the previously-derived pitches as elements of seventh chords. Learn more about me at bnelsonmusic.wordpress.com.