The Ascent of Man (Part I)

Concertino for Orchestra, Pianos and Violins. The number 1.1415 is the starting point of this concertino. The expanded integer sequence of this decimal invites the listener into the realm of Euler's Totient Function for coprimes. In mathematics, two integers a and b are said to be coprime if they have no common positive divisor other than 1 or, equivalently, if their greatest common divisor is 1. For example, 14 and 15 are coprime, but 14 and 21 are not, because they are both divisible by 7. A sequence of coprimes formed the basis of a series of notes (with each integer representing a musical note : 1 for A, 2 for A#, 3 for B, 4 for C, etc).

A number of sequences were created, using either eighth notes, quarter notes, or half notes, or combinations of of these. The sequences were jumbled together, though not quite at random. The jumbled sequences produced the opening piano "arpeggios" (The sounding of the tones of a chord in rapid succession -- or in this case, what we have is not exactly a chord, but a mode, in the sense in which Olivier Messiaen uses the word).

From the jumbled sequence come several themes, the first played by solo violin early on after the first piano crescendo. A re-adapted anti-random version of these later becomes the dominant theme of the work, repeated in different keys, and stretched with filters towards the midpoint.

A fugue, based on the simple solo Totient Function Progression is played twice in the piece, first by simple pizzicato, and later, by filtered, tone glided, and random fluctuations, to within fifty cents of the standard notes as defined by equal temperament [In equal temperament tunings, an interval — usually the octave — is divided into a series of equal steps (equal frequency ratios between successive notes). For classical music, the most common tuning system is twelve-tone equal temperament].




The concertino retains its identity or integrity by the use of constant rhythms and the repetition of themes, however different those themes may sound in different tonal contexts. The orchestration is intimate in the first half of the piece, relying mostly on the pianos and solo violins. Later the wider resources of the orchestra are employed, giving the work a greater sense of drama and variety.

Toward the end, during the second playing of the fugue, the music leaps out of its expected context and into a kind of perpetuum mobilum -- the rhythmic depiction of an irresistible force of nature or machine. Bach, Mozart, Prokofiev, Bartok and Barber have often made use of this device. The resolution comes with two restatements of the primary theme, first by several filtered string instruments, and then by the brass ensemble.

Category:

Music

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[blacksun3788]

Nice!