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Diatonic scale

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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.

Contents

Theory of diatonic scales

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 itrself 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.

The earliest diatonic scales

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.

See also

External links

References

Scales in Equally tempered music [http://encycl.opentopia.com/ edit ]
By interval : diatonic | chromatic | whole tone

By number of pitch classes : ditonic | tritonic | tetratonic | pentatonic | hexatonic | heptatonic | octatonic

Diatonic Scales and Keys 



  
 Sharps 
 Flats


major
minor
major
minor


0
 C (major), A (minor)


1
G
E
F
D


2
D
B
B♭
G


3
A
F♯
E♭
C


4
E
C♯
A♭
F


5
B
G♯
D♭
B♭


6
F♯
D♯
G♭
E♭


7
C♯
A♯
C♭
A♭




lower case letters in the circle of fifths are minor


the table indicates the number of sharps or flats in each scale







































 




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