William A. Sethares (born April 19, 1955) is an American music theorist and professor of

electrical engineering Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the l ...

at the University of Wisconsin. In music, he has contributed to the theory of

Dynamic Tonality Dynamic tonality is a paradigm for tuning and timbre which generalizes the special relationship between just intonation and the harmonic series to apply to a wider set of pseudo-just tunings and related pseudo-harmonic timbres.Duffin, R.W., 20 ...

and provided a formalization of

consonance In music, consonance and dissonance are categorizations of simultaneous or successive sounds. Within the Western tradition, some listeners associate consonance with sweetness, pleasantness, and acceptability, and dissonance with harshness, unple ...

Consonance and dissonance

Among the earliest musical traditions, musical

was thought to arise in a quasi-mystical manner from ratios of small whole numbers. (For instance,

Pythagoras Pythagoras of Samos ( grc, Πυθαγόρας ὁ Σάμιος, Pythagóras ho Sámios, Pythagoras the Samos, Samian, or simply ; in Ionian Greek; ) was an ancient Ionians, Ionian Ancient Greek philosophy, Greek philosopher and the eponymou ...

made observations relating to this, and the ancient Chinese

Guqin The ''guqin'' (; ) is a plucked seven-string Chinese musical instrument. It has been played since ancient times, and has traditionally been favoured by scholars and literati as an instrument of great subtlety and refinement, as highlighted b ...

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 Joseph Sauveur (24 March 1653 – 9 July 1716) was a French mathematician and physicist. He was a professor of mathematics and in 1696 became a member of the French Academy of Sciences. Life Joseph Sauveur was born in La Flèche, the son of a ...

the early 18th century and even more clearly by

Helmholtz Hermann Ludwig Ferdinand von Helmholtz (31 August 1821 – 8 September 1894) was a German physicist and physician who made significant contributions in several scientific fields, particularly hydrodynamic stability. The Helmholtz Association, ...

in the 1860s. In 1965, Plomp and Levelt 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 pape
''On the relationship between timbre and scale''
formalized the relationships between a

tuning Tuning can refer to: Common uses * Tuning, the process of tuning a tuned amplifier or other electronic component * Musical tuning, musical systems of tuning, and the act of tuning an instrument or voice ** Guitar tunings ** Piano tuning, adjusti ...

's notes and a

timbre In music, timbre ( ), also known as tone color or tone quality (from psychoacoustics), is the perceived sound quality of a musical note, sound or musical tone, tone. Timbre distinguishes different types of sound production, such as choir voice ...

's partials that control sensory

. A more accessible version also appeared in ''

Experimental Musical Instruments ''Experimental Musical Instruments'' was a periodical edited and published by Bart Hopkin, an instrument builder and writer about 20th century experimental music design and custom made instrument construction. Though no longer in print, back iss ...

'' a
"Relating Tuning and Timbre"
These papers were followed by two CDs
Xenotonality
an
Exomusicology
(some songs from which can b

, which explored the application of these ideas to

musical composition Musical composition can refer to an original piece or work of music, either vocal or instrumental, the structure of a musical piece or to the process of creating or writing a new piece of music. People who create new compositions are called ...

. In his 1998 boo
''Tuning, Timbre, Spectrum, Scale''
Sethares developed these ideas further, using them to expose the intimate relationship between the tunings and timbres o
Indonesian
an
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 of this book wrote, "Physics had built a prison round music, and Sethares set it free." 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."

''Musica Facta''

Sethares' conception of consonance is one of the foundation-stones of a new research program called ''Musica Facta''.''Musica Facta'': http://musicafacta.org

References

External resources

Webpage of Professor William Sethares at the University of Wisconsin
{{DEFAULTSORT:Sethares, William A. 1955 births People from Massachusetts American music theorists University of Wisconsin–Madison faculty Living people Electrical engineering academics Cornell University alumni Control theorists

Consonance and dissonance

''Musica Facta''

See also

References

Further reading

External resources