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 tonal music. Other theorists, such as Allen Forte, further developed the ...

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 any heptatonic 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 whole steps, ...

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 proper ...

Myhill's property In diatonic set theory a generic interval is the number of scale Step (music), steps between note (music), notes of a Set (music), collection or scale (music), scale. The largest generic interval (music), interval is one less than the number of sc ...

, 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. 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 in a seminal series of papers in 1978. The concept was in ...

), who published in the journal ''

Mathematical Systems Theory Dynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called ''c ...

'', and

Erv Wilson Ervin Wilson (June 11, 1928 – December 8, 2016) was a Mexico, Mexican/United States, American (dual citizen) music theory, music theorist. Early life Ervin Wilson was born in a remote area of northwest Chihuahua (state), Chihuahua, Mexico, wher ...

, working entirely outside of the academic world.

See also

Further reading

Precursors