Tiling in My Music

Abstract

Rhythmic canons and other one-dimensional tiling techniques dominated my composing for two or three years, and a number of instrumental pieces, both solo and ensemble, evolved during this time. With numerous examples, I have put together a little survey of different ways in which I have done this, often leaving holes and using other procedures not normally considered correct. It must have been 1999 when Moreno Andreatta gave me a copy of Dan Tudor Vuza’s landmark essay Supplementary Sets and Regular Complementary Unending Canons (Perspectives of New Music, 1991-92), because already in 2000 its influence on me became clear with a Canon in 3, 6 or 9 voices, written for an installation of Martin Riches in Berlin. When the MaMuX meetings at IRCAM began in 2001, I was able to hear regularly the mathematical music theories of Guerino Mazzola, Thomas Noll, Emmanuel Amiot, Franck Jedrzejewski and Harald Fripertinger, as well as Andreatta himself and many occasional visitors, and this information stimulated me more and more. My composing time during the year 2002 was devoted almost exclusively to fitting together little rhythmic tiles, and early in 2003 I brought out the edition Tiilework : 14 Pieces for 14 Solo Instruments. Later that year I wrote Tilework for String Quartet, and Tilework for Piano, though by the end of that year my concentration was already turning more toward combinatorial designs, which is quite a different topic. I recently reread the Vuza essay, and it seems all the more clear to me that this text has been important for all the mathematicians and music theorists cited above, not to mention for Jon Wild and other North American music theorists, and for quite a few composers. I now consider this work the most important music theory treatise of the last 20 years, particularly since it is one of those rare cases where music theory has preceded musical practice. Harmony and counterpoint books, essays on serial techniques, manuals for figured bass, and music analysis texts have generally dealt exclusively with musical procedures already practiced by composers. Only in rare cases like Vuza, Leonhard Euler, and Hugo Riemann have theorists preceded composers, though Henry Cowell’s 1930 book New Musical Resources should also be mentioned. This highly original text never circulated much in Europe, but it was widely read in the U.S. The author never followed up on these theories much in his own music, but John Cage and Conlon Nancarrow both sited this as a seminal influence on their music, and younger American composers such as Kyle Gann, Larry Polanskyn, David First, and John Luther Adams also acknowledge the