[Flash 9 is required to listen to audio.]
William Sethares: “Ten Fingers”
From the album Xentonality (1998)
William Sethares is a professor of Electrical and Computer Engineering at the University of Wisconsin-Madison. His musical research centers on the possibilities and problems offered by microtonality or xenharmony, that is, partitions of the pitch continuum other than the conventional 12-tone equal temperament that has dominated Western music for over a century.
In particular, Sethares has investigated the relationship between timbre and tuning system. He argues (and demonstrates with audio examples) that our conventional sense of consonance and dissonance of musical intervals is based on our hearing them played by instruments with harmonic spectra, that is, instruments whose overtones are related to the fundamental as whole number multiples (2f, 3f, 4f, etc.). 12-tone equal temperament (or 12-tet, to use the lingo) is a system of tuning that approximates the intervals inherent in sounds with harmonic spectra, such as those created by most string instruments and open pipes. But the harmonic spectrum is not as universal as we are typically taught: sound sources such as bells and metal bars, while possessing determinate pitch, have overtones in nonharmonic proportion to the fundamental (for example, 1.6f, 2.9f, etc.).
Sethares shows that one can construct custom scales based on the timbral properties of any given sound, such that the dissonance (measured in terms of beating between frequencies in close proximity) is minimized or controlled. One can also reverse the process, starting with a tuning system (for example, one of Sethares’ favorites, 10-tet), and determining the overtone structure needed for instruments to play within this tuning with the minimum of dissonance. Thus unusual tunings that might sound grating with harmonic timbres are made strangely consonant—but still distinct and different from 12-tet with harmonic timbres.
This example, whose full title is “If God Had Intended Us to Play in Ten Tones Per Octave, Then He Would Have Given Us Ten Fingers,” is composed for an artificial guitar-like timbre specially constructed to play in 10-tone equal temperament. It is from his 1998 album Xentonality, and also found on the CD included with his book Tuning, Timbre, Spectrum, Scale. His 2002 release, Exomusicology, uses his ideas on the relationship between timbre and tuning to explore “the music and culture of fictitious creatures and nonexistent alien species.”
One of Sethares’ imaginary musical instruments: the “Trident,” a marimba that plays in 7-tone equal temperament
Played 70 time(s).
February 15, 2011, 1:07pm
