Editing Diatonic set theory

{{Short description|Application of musical set theory to the diatonic scale}}
'''Diatonic set theory''' is a subdivision or application of [[set theory (music)|musical set theory]] which applies the techniques and [[musical analysis|analysis]] of [[discrete mathematics]] to properties of the [[diatonic collection]] such as [[maximal evenness]], [[Myhill's property]], [[well formed generated collection|well formedness]], the [[deep scale property]], [[cardinality equals variety]], 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]]), who published in the journal ''[[Mathematical Systems Theory]]'', and [[Erv Wilson]], working entirely outside of the academic world.

==See also==
*[[Bisector (music)|Bisector]]
*[[Diatonic and chromatic]]
*[[Generic and specific intervals]]

==Further reading==
*Balzano, Gerald, "The Pitch Set as a Level of Description for Studying Musical Pitch Perception", ''Music, Mind and Brain, the Neurophysiology of Music'', Manfred Clynes, ed., Plenum Press, 1982.
*Carey, Norman and Clampitt, David (1996), "Self-Similar Pitch Structures, Their Duals, and Rhythmic Analogues", ''[[Perspectives of New Music]]'' 34, no. 2: 62–87.
*[[Kraig Grady|Grady, Kraig]], (2007), [http://anaphoria.com/wilsonintroMOS.html "An Introduction to the Moments of Symmetry"], Wilson Archives, anaphoria.com
*Johnson, Timothy (2003), ''Foundations of Diatonic Theory: A Mathematically Based Approach to Music Fundamentals'', Key College Publishing. {{ISBN|1-930190-80-8}}.

===Precursors===
*Rahn, Jay (1977), "Some Recurrent Features of Scales", ''[[In Theory Only]]'' '''2''', nos. 11–12: 43–52.
*[[David Rothenberg|Rothenberg, David]], (1977), "A Model for Pattern Perception with Musical Applications", ''[[Mathematical Systems Theory]]'', part I: '''11''', 199–234 {{doi|10.1007/BF01768477}}; part II: 353–372 {{doi|10.1007/BF01768486}}; part III: (1978) '''12''', 73–101 {{doi|10.1007/BF01776567}}.
*[[Erv Wilson|Wilson, Erv]] (1975), [http://anaphoria.com/mos.PDF "Handwritten letter to John Chalmers pertaining to 'Moments of Symmetry'/'Tanabe Cycle'], 26 April 1975, 27 pages, anaphoria.com

{{Set theory (music)}}

{{stub-music theory}}

[[Category:Diatonic set theory| ]]
[[Category:Music theory]]
[[Category:Musicology]]