Sudoku Variations (2006)

Composed by Tamar Diesendruck in Los Angeles, California, December 2006

Notes by the composer, January 7, 2007

 3 8 9 6 5 2 7 4 1
 2 1 4 7 3 9 6 8 5
 5 6 7 8 4 1 9 2 3
 8 6 3 2 9 4 5 1 7
 9 4 2 5 7 1 3 6 8
 1 7 5 6 3 8 4 9 2
 4 2 6 9 3 8 1 7 5
 8 5 7 1 2 6 4 9 3
 3 1 9 7 5 4 2 8 6

As the listener probably knows, the game of Sudoku involves filling in numbers in a 9 X 9 grid such that each line, as well as each inner square of 3 X 3 contains one of each numeral from 1 to 9. Numbers therefore can't repeat in any direction. So what does this have to do with music? In the case of this piece, the numerals are used to determine meter; each variation uses the numerals from one line of the grid; therefore, each variation is 9 measures long, and each measure has a different time signature from 1 pulse to 9 pulses per measure, and none of the patterns repeat.

Originally, I started fooling around with the concept of using Sudoku numbers as meter simply because as I was contemplating a completed puzzle, I noticed that I was inwardly feeling the pulses for each number. What a dandy idea, I thought, to map a Sudoku puzzle to a composition's rhythmic groupings. As it turns out, at least the way I started to conceive of making a piece, it was quite challenging. I liked the idea of creating music for each number (meter) that would always be associated with that number, and the idea that these musical fragments could work with one another in any order. This would be fine if I didn't care at all about musical continuity or closure, but, ... I do; I think my fascination with this idea was in the paradox and challenge of creating the sense of continuity and (occasional) closure while projecting each numeral with its own particular musical identity each time it appears (so the same material has to be convincing in any part of a phrase or section). There was also the matter of creating more than one musical line, and incorporating into the piece some of the elegance of the Sudoku grid design, in which every numeral fulfills multiple functions.

The final design of my piece introduces a musical fragment for each numeral in the first 9 bars which together form a playful tune in the left hand, accompanied in the right hand by one note at the start of each bar. This opening variation plus the next 8 variations follow the numbers of the grid horizontally from left to right, reading the rows in order from top to bottom; the second 9 variations use a combination of the horizontal rows and the vertical columns, (read from top to bottom, in order from left to right). So each hand expresses a different series of meters, and each of these variations is a simultaneous projection of two lines of the grid, one horizontal, one vertical. The 19th and last variation closes off the set by reusing the first horizontal row, this time in reverse order, to end on the opening square's 3 pulses.

The primary challenges in fulfilling this abstract and eccentric idea were to create a larger sense of shape, and to find ways to make the continuity of each series of meters seem musically interesting (if not necessary). My game was to project the numbers of the grid by expressing each one with the fragments of music I created for these numbers from the first horizontal line of the grid; I decided to stick with the notes conceived in the first variation, but use tempo, texture, register, and dynamics freely to create a musical narrative. "Sticking with the notes" should be interpreted loosely, however, as it involved many transformations, some traditional (inversion, transposition), some not. Through such mutations, these "musical bits" take on different identities, yet the process seems to insure that there are shared qualities across the variations.

One advantage of this project was knowing that Elaine would play the premiere. In addition to her technical virtuosity and musical spirit, I knew she would be able to project the strange balance of elements in the piece. Using my idea results in a work, that like the original Sudoku grid, has an overall design, but in which each element is stubbornly itself. In addition, the piece has a volatile, mercurial quality, from a kind of nonchalance and mock drama to a few surprising passages of unexpected emotion. So, what started out as an idea that really shouldn't work, resulted in a project that was fun, and satisfying to work out. I hope it is as fun and satisfying for Elaine and the audience.

Sol LeWitt jpg above from se.easyart.com.