Diatonic scale
In
music theory, a
diatonic scale (from the Greek
διατονικος, meaning "[progressing] through tones", also known as the
heptatonia prima) is a seven-note musical
scale comprising five whole-tone and two half-tone steps, in which the half tones are maximally separated. Thus between two half-tone steps there are either two or three whole tones, with the pattern repeating at the
octave. The term
diatonic originally referred to the
diatonic genus, one of the three
genera of the ancient Greeks.
These scales are the foundation of the European
musical tradition. The modern major and minor scales are diatonic, as are all of the so-called 'church'
modes. What we now call major and minor were, during the
medieval and
Renaissance periods, only two of many different
modes formed by taking the diatonic scale to begin on different degrees. During the period of
Baroque music the notion of musical
key emerged and the major and minor scales came to dominate throughout the 18th and 19th century. Some church modes survived into the early 18th century, as well as appearing occasionally in
Classical and
20th century music.
Within the twelve notes of the
chromatic scale, there are twelve distinct diatonic scales. The white keys on a piano map out the seven
notes of one such diatonic scale, repeated in each
octave. The modern musical keyboard, with its black notes grouped in twos and threes, is essentially diatonic; this arrangement not only helps musicians to find their bearings on the keyboard, but simplifies the system of key signatures compared with what would be necessary for a continuous alternation of black and white notes.
Technically speaking, diatonic scales are obtained from a
chain of six successive
fifths in some version of
meantone temperament, and resulting in two
tetrachords separated by
intervals of a
whole tone. If our version of meantone is the twelve tone
equal temperament the pattern of intervals in
semitones will be 2-2-1-2-2-2-1; these numbers stand for whole tones (2 semitones) and half tones (1 semitone). The
major scale starts on the first note and proceeds by steps to the first octave. In
solfege, the syllables for each scale degree are "Do-Re-Mi-Fa-So-La-Ti-Do".
The
natural minor scale can be thought of in two ways, the first is as the
relative minor of the major scale, beginning on the sixth degree of the scale and proceeding step by step through the same tetrachords to the first octave of the sixth degree. In solfege "La-Ti-Do-Re-Mi-Fa-So-La." Alternately, the natural minor can be seen as a composite of two different tetrachords of the pattern 2-1-2-2-1-2-2. In solfege "Do-Re-Mé-Fa-So-Lé-Té-Do."
Western
harmony from the
Renaissance up until the
late 19th century is based on the diatonic scale and the unique
hierarchical relationships, or
diatonic functionality, created by this system of organizing seven notes. Most longer pieces of
common practice music
change key, which leads to a hierarchical relationship of diatonic scales in one key with those in another.
The diatonic scale has some specific properties which mark it out among seven-note scales.
David Rothenberg conceived of a property of scales he called
propriety, and around the same time
Gerald Balzano independently came up with the same definition in the more limited context of equal temperaments, calling it
coherence. Rothenberg distinguished
proper from a slightly stronger characteristic he called
strictly proper. In this vocabulary, there are five proper seven-note scales in
12 equal temperament. None of these are strictly proper, which means none are coherent in the sense of Balzano, but in any system of
meantone tuning with the fifth flatter than 700
cents, they are strictly proper. The scales are the diatonic scale, the
ascending minor scale, the
harmonic minor scale, the
harmonic major scale, and the
locrian major scale; of these, all but the last are well-known and in fact consitute the backbone of diatonic practice when taken together.
Among these four well-known variants of the diatonic scale, the diatonic scale itself has additional properties of what has been called
simplicity, because it is produced by iterations of a single generator, the meantone fifth. The scale, in the vocabulary of
Erv Wilson, who seems to have been the first to consider the notion, is what is sometimes called a
MOS scale.
The diatonic collection contains each interval class a unique number of times (Browne 1981 cited in Stein 2005, p.49, 49n12).
Diatonic set theory describes the following properties, aside from propriety:
maximal evenness,
Myhill's property,
well formedness, the
deep scale property,
cardinality equals variety, and
structure implies multiplicity.
It has been argued that the diatonic scale is so natural that it appeared early in human history. A claim that the so-called "
Neanderthal flute" found at
Divje Babe exhibits diatonic tuning is highly dubious, since there is no consensus it is even a musical instrument, and in any event it would only have had four notes; but there is much better evidence that the
Sumerians and
Babylonians used some version of the diatonic scale. This derives from surviving inscriptions which contain a tuning system and musical composition. Despite the conjectural nature of reconstructions of the piece known as the
Hurrian hymn from the surviving score, the evidence that it used the diatonic scale is much more soundly based. This is because instructions for tuning the scale involve tuning a chain of six fifths so that the corresponding circle of seven
major and
minor thirds are all consonant-sounding, and this is a recipe for tuning a diatonic scale. See
Music of Mesopotamia.
*
Pitch*
Piano key frequencies*
Diatonic Scale on Eric Weisstein's Treasure trove of Music
*
Natural Bases of Scales and
The 7-Note Solution -- Why are so many 5 & 7-note scales found among ancient writings and artifacts?)
*
Tonalsoft Encyclopedia of Microtonal Music-theory* [
1]
* [
2]Flute debate
*Balzano, Gerald J. (1980). "The Group Theoretic Description of 12-fold and Microtonal Pitch Systems",
Computer Music Journal 4 66-84.
*Balzano, Gerald J. (1982). "The Pitch Set as a Level of Description for Studying Musical Pitch Perception",
Music, Mind, and Brain, Manfred Clynes, ed., Plenum press.
*Browne, Richmond (1981). "Tonal Implications of the Diatonic Set",
In Theory Only 5, nos. 1 and 2: 3-21
*Clough, John (1979). "Aspects of Diatonic Sets",
Journal of Music Theory 23: 45-61.
*Fink, Robert (2005).
On the Origin of Music. Greenwich. ISBN 0912424141.
*Franklin, John C. (2002). "Diatonic Music in Greece: a Reassessment of its Antiquity",
Mnemosyne 56.1, 669-702 [
3]
*Gould, Mark (2000). "Balzano and Zweifel: Another Look at Generalised Diatonic Scales", "Perspectives of New Music"
38/2, 88-105
*Johnson, Timothy (2003).
Foundations of Diatonic Theory: A Mathematically Based Approach to Music Fundamentals. Key College Publishing. ISBN 1930190808.
*Kilmer, A.D. (1971) "The Discovery of an Ancient Mesopotamian Theory of Music'".
Proceedings of the American Philosophical Society 115, 131-149.
*David Rothenberg (1978). "A Model for Pattern Perception with Musical Applications Part I: Pitch Structures as order-preserving maps",
Mathematical Systems Theory 11 199-234 [
4]
*Stein, Deborah (2005).
Engaging Music: Essays in Music Analysis. New York: Oxford University Press. ISBN 0195170105.
