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Tom Johnson: Block Design for Piano

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Published on Jan 29, 2012

Performed by R. Andrew Lee - http://randrewlee.com
Tom Johnson - http://www.editions75.com/

From the score:
I call this piece Block Design for Piano because that is the term used by mathematicians in combination theory for a particular configuration of combinations. The configuration here is technically a 4-(12,6,10) block design, which in my musical terms means that there are 12 notes, distributed into 6-note arpeggios, in such a way that every combination of four particular notes comes together exactly 10 times in 10 different arpeggios. In fact, it is also true that every combination of 3 notes comes together 30 times in 30 different arpeggios, every pair of notes occurs 75 times in 75 different arpeggios, and each of the 12 notes occurs 165 times, in exactly half of the 330 arpeggios. In a way, the piece is a realization of Schoenberg's ideal, with exactly equal emphasis of each of the 12 notes. The music follows the numbers note for note, except that they occur two at a time when the difference between them is a major third.

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