To install click the Add extension button. That's it.

The source code for the WIKI 2 extension is being checked by specialists of the Mozilla Foundation, Google, and Apple. You could also do it yourself at any point in time.

Kelly Slayton
Congratulations on this excellent venture… what a great idea!
Alexander Grigorievskiy
I use WIKI 2 every day and almost forgot how the original Wikipedia looks like.
Live Statistics
English Articles
Improved in 24 Hours
Added in 24 Hours
Show all languages
What we do. Every page goes through several hundred of perfecting techniques; in live mode. Quite the same Wikipedia. Just better.

William Sethares

From Wikipedia, the free encyclopedia

William A. Sethares
Born (1955-04-19) April 19, 1955 (age 66)
Alma materCornell University
Known forConsonance
Scientific career
FieldsSignal processing and music theory
InstitutionsUniversity of Wisconsin–Madison

William A. Sethares (born April 19, 1955) is an American music theorist and professor of electrical engineering at the University of Wisconsin. In music, he has contributed to the theory of Dynamic Tonality and provided a formalization of consonance.

Consonance and dissonance

Among the earliest musical traditions, musical consonance was thought to arise in a quasi-mystical manner from ratios of small whole numbers. (For instance, Pythagoras made observations relating to this, and the ancient Chinese Guqin contains a dotted scale representing the harmonic series.) The source of these ratios, in the pattern of vibrations known as the harmonic series, was exposed by Joseph Sauveur the early 18th century and even more clearly by Helmholtz in the 1860s.

In 1965, Plomp and Levelt[1] showed that this relationship could be generalized beyond the harmonic series, although they did not elaborate in detail.

In the 1990s, Sethares began exploring Plomp and Levelt's generalization, both mathematically and musically. His 1993 paper On the relationship between timbre and scale[2] formalized the relationships between a tuning's notes and a timbre's partials that control sensory consonance. A more accessible version also appeared in Experimental Musical Instruments as "Relating Tuning and Timbre"[3] These papers were followed by two CDs, Xenotonality and Exomusicology (some songs from which can be freely downloaded here), which explored the application of these ideas to musical composition.

In his 1998 book Tuning, Timbre, Spectrum, Scale,[4] Sethares developed these ideas further, using them to expose the intimate relationship between the tunings and timbres of Indonesian and Thai indigenous music, and to explore other novel combinations of related tunings and timbres. Where microtonal music was previously either dissonant (due to being played with harmonic timbres to which it was not "related"), or restricted to the narrow range of harmonically related tunings (to retain sensory consonance), Sethares's mathematical and musical work showed how musicians might explore microtonality without sacrificing sensory consonance.

As one reviewer of the second edition[5] of this book wrote, "Physics had built a prison round music, and Sethares set it free."[6] Another reviewer wrote that it "is not only the most important book about tuning written to date, but it is the most important book about music theory written in human history."[7]

Musica Facta

Sethares' conception of consonance is one of the foundation-stones of a new research program called Musica Facta.[8]

See also


  1. ^ R. Plomp and W. J. M. Levelt (October 1965). "Tonal Consonance and Critical Bandwidth". Journal of the Acoustical Society of America. 38 (4): 548–560. doi:10.1121/1.1909741. hdl:2066/15403. PMID 5831012.
  2. ^ Sethares, William (September 1993). "Local consonance and the relationship between timbre and scale". Journal of the Acoustical Society of America. 94 (3): 1218–1228. doi:10.1121/1.408175.
  3. ^ Sethares, William (September 1992). "Relating Tuning and Timbre". Experimental Musical Instruments. IX (2).
  4. ^ Sethares, William (January 1998). Tuning, Timbre, Spectrum, Scale (1st ed.). New York: Springer. ISBN 978-3-540-76173-0.
  5. ^ Sethares, William (November 2004). Tuning, Timbre, Spectrum, Scale (2nd ed.). New York: Springer. ISBN 978-1-85233-797-1.
  6. ^ Luca Turin (September 2004). "The sound of impossible objects". NZZ Folio.
  7. ^ Scott, X. J. " / tuning / book reviews". Retrieved 2009-09-20.
  8. ^ Musica Facta:

Further reading

External resources

This page was last edited on 6 August 2021, at 13:15
Basis of this page is in Wikipedia. Text is available under the CC BY-SA 3.0 Unported License. Non-text media are available under their specified licenses. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc. WIKI 2 is an independent company and has no affiliation with Wikimedia Foundation.