Limit (music)
The term limit was introduced by Harry Partch,[1] who used it to give an upper bound on the complexity of harmony; hence the name.
Harry Partch, Ivor Darreg, and Ralph David Hill are among the many microtonalists to suggest that music has been slowly evolving to employ higher and higher harmonics in its constructs (see emancipation of the dissonance).
[citation needed] In medieval music, only chords made of octaves and perfect fifths (involving relationships among the first three harmonics) were considered consonant.
In the West, triadic harmony arose (contenance angloise) around the time of the Renaissance, and triads quickly became the fundamental building blocks of Western music.
The major and minor thirds of these triads invoke relationships among the first five harmonics.
Around the turn of the 20th century, tetrads debuted as fundamental building blocks in African-American music.
[citation needed] In conventional music theory pedagogy, these seventh chords are usually explained as chains of major and minor thirds.
Partch's theoretical prediction of the sensory dissonance of intervals (his "One-Footed Bride") are very similar to those of theorists including Hermann von Helmholtz, William Sethares, and Paul Erlich.
[6] According to music software producer Tonalsoft: "An udentity is an identity of an utonality".
[8]In the late 1970s, a new genre of music began to take shape on the West coast of the United States, known as the American gamelan school.
The central figure of this movement was the American composer Lou Harrison[citation needed].
Unlike Partch, who often took scales directly from the harmonic series, the composers of the American Gamelan movement tended to draw scales from the just intonation lattice, in a manner like that used to construct Fokker periodicity blocks.
Prime-limit tuning and intervals are often referred to using the term for the numeral system based on the limit.
In musical temperament, the simple ratios of just intonation are mapped to nearby irrational approximations.
