Among the earliest musical traditions, musical consonance was thought to arise in a quasi-mystical manner from ratios of small whole numbers. 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 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 These papers were followed by two CDs, and , which explored the application of these ideas to musical composition. In his 1998 book , Sethares developed these ideas further, using them to expose the intimate relationship between the tunings and timbres of and indigenous music, and to explore other novel combinations of related tunings and timbres. Where microtonal music was previously either dissonant, or restricted to the narrow range of harmonically related tunings, 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."
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. This consistency of fingering across tunings, which they called tuning invariance, enables a performer, using an isomorphic keyboard and compatible 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. 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 developed a freely available software-based synthesizer, the , 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 . 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.
''Musica Facta''
Sethares' conception of consonance is one of the foundation-stones of a new research program called Musica Facta.
