Diatonic set theory is a subdivision or application of

musical set theory Musical set theory provides concepts for categorizing musical objects and describing their relationships. Howard Hanson first elaborated many of the concepts for analyzing tonality, tonal music. Other theorists, such as Allen Forte, further devel ...

which applies the techniques and

analysis Analysis (: analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (38 ...

discrete mathematics Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous f ...

to properties of the

diatonic collection In music theory a diatonic scale is a heptatonic (seven-note) scale that includes five whole steps (whole tones) and two half steps (semitones) in each octave, in which the two half steps are separated from each other by either two or three wh ...

such as

maximal evenness In scale (music) theory, a maximally even set (scale) is one in which every generic interval has either one or two consecutive integers specific intervals-in other words a scale whose notes (pcs) are "spread out as much as possible." This prop ...

Myhill's property In diatonic set theory a generic interval is the number of scale steps between notes of a collection or scale. The largest generic interval is one less than the number of scale members. (Johnson 2003, p. 26) A specific interval is the clo ...

, well formedness, the

deep scale property In music, a common tone is a pitch class that is a member of, or common to (shared by) two or more scales or sets. Common tone theorem A common tone is a pitch class that is a member of, or common to, a musical scale and a transposition of ...

cardinality equals variety The musical operation of scalar transposition shifts every note in a melody by the same number of scale steps. The musical operation of chromatic transposition shifts every note in a melody by the same distance in pitch class space. In genera ...

, and

structure implies multiplicity In diatonic set theory structure implies multiplicity is a quality of a collection or scale (music), scale. For collections or scales which have this property, the interval series formed by the shortest distance around a diatonic circle of fifths be ...

. The name is something of a misnomer as the concepts involved usually apply much more generally, to any periodically repeating scale. Music theorists working in diatonic set theory include Eytan Agmon, Gerald J. Balzano, Norman Carey, David Clampitt, John Clough, Jay Rahn, and mathematician Jack Douthett. A number of key concepts were first formulated by David Rothenberg (the

Rothenberg propriety In diatonic set theory, Rothenberg propriety is an important concept, lack of contradiction and ambiguity, in the general theory of musical scales which was introduced by David Rothenberg (music theorist), David Rothenberg in a seminal series of ...

), who published in the journal ''

Mathematical Systems Theory ''Theory of Computing Systems'' is a peer-reviewed scientific journal published by Springer Verlag. Published since 1967 as ''Mathematical Systems Theory'' and since volume 30 in 1997 under its current title, it is devoted to publishing orig ...

'', and

Erv Wilson Ervin Wilson (June 11, 1928 – December 8, 2016) was a Mexican/ American (dual citizen) music theorist. Early life Ervin Wilson was born iColonia Pacheco a small village in the remote mountains of northwest Chihuahua, Mexico, where he lived u ...

, working entirely outside of the academic world.

See also

Further reading

Precursors