Diatonic set theory is a subdivision or application of
musical set theory 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 (3 ...
of
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 continu ...
to properties of the
diatonic collection such as
maximal evenness,
Myhill's property,
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
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 ...
), 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 ' ...
'', 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 in a remote area of northwest Chihuahua, Mexico, where he lived until the age of fifteen. His mother taught ...
, working entirely outside of the academic world.
See also
*
Bisector
*
Diatonic and chromatic
Diatonic and chromatic are terms in music theory that are most often used to characterize scales, and are also applied to musical instruments, intervals, chords, notes, musical styles, and kinds of harmony. They are very often used as a p ...
*
Generic and specific intervals
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 ...
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
''Perspectives of New Music'' (PNM) is a peer-reviewed academic journal specializing in music theory and analysis. It was established in 1962 by Arthur Berger and Benjamin Boretz (who were its initial editors-in-chief).
''Perspectives'' was fir ...
'' 34, no. 2: 62–87.
*
Grady, Kraig, (2007)
"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. .
Precursors
*Rahn, Jay (1977), "Some Recurrent Features of Scales", ''
In Theory Only
''In Theory Only'' () was a peer-reviewed academic journal specializing in music theory
Music theory is the study of the practices and possibilities of music. ''The Oxford Companion to Music'' describes three interrelated uses of the term "mu ...
'' 2, nos. 11–12: 43–52.
*
Rothenberg, David, (1977), "A Model for Pattern Perception with Musical Applications", ''
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 ' ...
'', part I: 11, 199–234 ; part II: 353–372 ; part III: (1978) 12, 73–101 .
*
Wilson, Erv (1975)
"Handwritten letter to John Chalmers pertaining to 'Moments of Symmetry'/'Tanabe Cycle' 26 April 1975, 27 pages, anaphoria.com
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Musicology