William Sethares
Encyclopedia
William A. Sethares is an American music theorist and professor of Electrical engineering
and who is known primarily for his contributions to music theory, including dynamic tonality
and a formalization of the source of 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 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 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" 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, Sethares developed these ideas further, using them to expose the intimate relationship between the tunings and timbres of Indonesian and Thai indigienous 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."
By early 2006, the Isomorphic Conspiracy had discovered that such keyboards also had the same fingering in every tuning, too—or, at least, every tuning of what the Conspiracy came to call the syntonic temperament
. This consistency of fingering across tunings, which they called tuning invariance, enables a performer, using an isomorphic keyboard
and compatible synthesizer
(or software synthesizer
), to play a given tonal piece in any of a wide range of tunings. The Conspiracy turned its attention to identifying the means by which different isomorphic keyboards could be compared, and identified the Wicki/Hayden keyboard
as being optimal for the syntonic temperament's wide tuning range.
In addition to being able to play in any fixed tuning with consistent fingering, the tuning invariance of isomorphic keyboards enables performers to change a piece's tuning on the fly, along the syntonic temperament's smooth tuning continuum, while retaining consonance (or, optionally, while introducing dissonance to any tonal structure). It soon became clear that this dynamic tonality
offered an entirely novel means of controlling tension and release
.
To put these ideas into practice, Sethares (with collaborators and students) developed a freely available software-based synthesizer, the TransFormSynth, which enables a performer to bend tunings polyphonically during performance. In April 2008, Sethares used the TransFormSynth to compose and record the first musical piece that used dynamic tonality, which he called "C to Shining C" (although the piece, as recorded, is not actually in any musical key
). A single chord is played throughout the piece, yet it gains a feeling of tension and release
through its tuning progression from 19-tone equal temperament tuning to 5-tone equal temperament tuning and back, complemented by a slower timbre progression from a fully harmonic timbre to a fully tuning-aligned timbre.
In 2009, Sethares led the Isomorphic Conspiracy's extension of Dynamic tonality to include a wider variety of tunings, including
All of these different tunings can be controlled with identical fingering and full consonance using a dynamic-tonality-capable synthesizer such as the TransFormSynth and an isomorphic keyboard. (The TransFormSynth maps the Wicki/Hayden note-layout to the standard QWERTY keyboard, so that no special keyboard is necessary.)
Electrical engineering
Electrical engineering is a field of engineering that generally deals with the study and application of electricity, electronics and electromagnetism. The field first became an identifiable occupation in the late nineteenth century after commercialization of the electric telegraph and electrical...
and who is known primarily for his contributions to music theory, including dynamic tonality
Dynamic tonality
Dynamic tonality is tonal music which uses real-time changes in tuning and timbre to perform new musical effects such as polyphonic tuning bends, new chord progressions, and temperament modulations, with the option of consonance. The performance of dynamic tonality requires an isomorphic keyboard...
and a formalization of the source of consonance
Consonance and dissonance
In music, a consonance is a harmony, chord, or interval considered stable, as opposed to a dissonance , which is considered to be unstable...
.
Consonance and dissonance
Among the earliest musical traditions, musical consonanceConsonance and dissonance
In music, a consonance is a harmony, chord, or interval considered stable, as opposed to a dissonance , which is considered to be unstable...
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
Guqin
The guqin is the modern name for a plucked seven-string Chinese musical instrument of the zither family...
contains a dotted scale representing the harmonic series.) The source of these ratios, in the pattern of vibrations known as the harmonic series
Harmonic series (music)
Pitched musical instruments are often based on an approximate harmonic oscillator such as a string or a column of air, which oscillates at numerous frequencies simultaneously. At these resonant frequencies, waves travel in both directions along the string or air column, reinforcing and canceling...
, was exposed by Joseph Sauveur
Joseph Sauveur
Joseph Sauveur 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 the son of a provincial notary...
the early 18th century and even more clearly by Helmholtz 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 paper on the relationship between timbre and scale formalized the relationships between a tuning's notes and a timbre
Timbre
In music, timbre is the quality of a musical note or sound or tone that distinguishes different types of sound production, such as voices and musical instruments, such as string instruments, wind instruments, and percussion instruments. The physical characteristics of sound that determine the...
's partials that control sensory consonance
Consonance and dissonance
In music, a consonance is a harmony, chord, or interval considered stable, as opposed to a dissonance , which is considered to be unstable...
. A more accessible version also appeared in Experimental Musical Instruments as "Relating Tuning and Timbre" 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
Musical composition
Musical composition can refer to an original piece of music, the structure of a musical piece, or the process of creating a new piece of music. People who practice composition are called composers.- Musical compositions :...
.
In his 1998 book Tuning, Timbre, Spectrum, Scale, Sethares developed these ideas further, using them to expose the intimate relationship between the tunings and timbres of Indonesian and Thai indigienous 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."
Dynamic tonality
In 2003, Sethares began an informal collaboration with Andrew Milne and Jim Plamondon, whimsically called the Isomorphic Conspiracy. Its aim was to explore the musical relationships exposed by isomorphic keyboards, which are an unusual design of two-dimensional keyboards that have the intriguing characteristic of having transpositional invariance—that is, "the same fingering in every key."By early 2006, the Isomorphic Conspiracy had discovered that such keyboards also had the same fingering in every tuning, too—or, at least, every tuning of what the Conspiracy came to call the syntonic temperament
Syntonic temperament
The syntonic temperament is a system of musical tuning in which the frequency ratio of each musical interval is a product of powers of an octave and a tempered perfect fifth, with the width of the tempered major third being equal to four tempered perfect fifths minus two octaves and the width of...
. This consistency of fingering across tunings, which they called tuning invariance, enables a performer, using an isomorphic keyboard
Isomorphic keyboard
An isomorphic keyboard is a musical input device consisting of a two-dimensional array of note-controlling elements on which any given sequence and/or combination of musical intervals has the “same shape” on the keyboard wherever it occurs – within a key, across keys, across octaves, and across...
and compatible synthesizer
Synthesizer
A synthesizer is an electronic instrument capable of producing sounds by generating electrical signals of different frequencies. These electrical signals are played through a loudspeaker or set of headphones...
(or software synthesizer
Software synthesizer
A software synthesizer, also known as a softsynth is a computer program or plug-in for digital audio generation. Computer software which can create sounds or music is not new, but advances in processing speed are allowing softsynths to accomplish the same tasks that previously required dedicated...
), to play a given tonal piece in any of a wide range of tunings. The Conspiracy turned its attention to identifying the means by which different isomorphic keyboards could be compared, and identified the Wicki/Hayden keyboard
Wicki-Hayden note layout
In music, the Wicki-Hayden note layout is a key layout for musical instruments that offers some advantages over the traditional keyboard layout.-History:...
as being optimal for the syntonic temperament's wide tuning range.
In addition to being able to play in any fixed tuning with consistent fingering, the tuning invariance of isomorphic keyboards enables performers to change a piece's tuning on the fly, along the syntonic temperament's smooth tuning continuum, while retaining consonance (or, optionally, while introducing dissonance to any tonal structure). It soon became clear that this dynamic tonality
Dynamic tonality
Dynamic tonality is tonal music which uses real-time changes in tuning and timbre to perform new musical effects such as polyphonic tuning bends, new chord progressions, and temperament modulations, with the option of consonance. The performance of dynamic tonality requires an isomorphic keyboard...
offered an entirely novel means of controlling tension and release
Tension and release
Tension and Release is an often used term for analyzing music, to describe how music keeps the interest of a listener. In Western tonal music, ranging from European classical music to modern pop, tension is often thought to derive from the dominant chord...
.
To put these ideas into practice, Sethares (with collaborators and students) developed a freely available software-based synthesizer, the TransFormSynth, which enables a performer to bend tunings polyphonically during performance. In April 2008, Sethares used the TransFormSynth to compose and record the first musical piece that used dynamic tonality, which he called "C to Shining C" (although the piece, as recorded, is not actually in any musical key
Key (music)
In music theory, the term key is used in many different and sometimes contradictory ways. A common use is to speak of music as being "in" a specific key, such as in the key of C major or in the key of F-sharp. Sometimes the terms "major" or "minor" are appended, as in the key of A minor or in the...
). A single chord is played throughout the piece, yet it gains a feeling of tension and release
Tension and release
Tension and Release is an often used term for analyzing music, to describe how music keeps the interest of a listener. In Western tonal music, ranging from European classical music to modern pop, tension is often thought to derive from the dominant chord...
through its tuning progression from 19-tone equal temperament tuning to 5-tone equal temperament tuning and back, complemented by a slower timbre progression from a fully harmonic timbre to a fully tuning-aligned timbre.
In 2009, Sethares led the Isomorphic Conspiracy's extension of Dynamic tonality to include a wider variety of tunings, including
- Equal tuningsEqual temperamentAn equal temperament is a musical temperament, or a system of tuning, in which every pair of adjacent notes has an identical frequency ratio. As pitch is perceived roughly as the logarithm of frequency, this means that the perceived "distance" from every note to its nearest neighbor is the same for...
, such as 12-tone equal temperament (abbreviated "12-tet"), 19-tet19 equal temperamentIn music, 19 equal temperament, called 19-TET, 19-EDO, or 19-ET, is the tempered scale derived by dividing the octave into 19 equal steps . Each step represents a frequency ratio of 21/19, or 63.16 cents...
, and 31-tet31 equal temperamentIn music, 31 equal temperament, 31-ET, which can also be abbreviated 31-TET, 31-EDO , , is the tempered scale derived by dividing the octave into 31 equal-sized steps...
; - Non-equal tunings such as 1/4-comma meantoneMeantone temperamentMeantone temperament is a musical temperament, which is a system of musical tuning. In general, a meantone is constructed the same way as Pythagorean tuning, as a stack of perfect fifths, but in meantone, each fifth is narrow compared to the ratio 27/12:1 in 12 equal temperament, the opposite of...
and Pythagorean tuningPythagorean tuningPythagorean tuning is a system of musical tuning in which the frequency relationships of all intervals are based on the ratio 3:2. This interval is chosen because it is one of the most consonant...
; - Irregular tunings such as circulating or "well" temperamentsWell temperamentWell temperament is a type of tempered tuning described in 20th-century music theory. The term is modelled on the German word wohltemperiert which appears in the title of J.S. Bach's famous composition, The Well-Tempered Clavier...
; and - Closely related rank-2Rank of an abelian groupIn mathematics, the rank, Prüfer rank, or torsion-free rank of an abelian group A is the cardinality of a maximal linearly independent subset. The rank of A determines the size of the largest free abelian group contained in A. If A is torsion-free then it embeds into a vector space over the...
Just IntonationJust intonationIn music, just intonation is any musical tuning in which the frequencies of notes are related by ratios of small whole numbers. Any interval tuned in this way is called a just interval. The two notes in any just interval are members of the same harmonic series...
tunings,
All of these different tunings can be controlled with identical fingering and full consonance using a dynamic-tonality-capable synthesizer such as the TransFormSynth and an isomorphic keyboard. (The TransFormSynth maps the Wicki/Hayden note-layout to the standard QWERTY keyboard, so that no special keyboard is necessary.)