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Diatonic scale
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In music theory, a diatonic scale (from the Greek d?at??????, meaning "[progressing] through tones", also known as the heptatonia prima and set form 7-35) is a seven note musical scale comprising five whole steps and two half steps, in which the half steps are maximally separated. Thus between each of the two half steps lie either two or three whole steps, with the pattern repeating at the octave.
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In music theory, a diatonic scale (from the Greek d?at??????, meaning "[progressing] through tones", also known as the heptatonia prima and set form 7-35) is a seven note musical scale comprising five whole steps and two half steps, in which the half steps are maximally separated. Thus between each of the two half steps lie either two or three whole steps, 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 were all of the 'church' modes. What are now called major and minor were, during the medieval and Renaissance periods, only two of seven modes formed by a diatonic scale beginning on each of the seven notes of the octave; thus, the half-steps were positioned at different distances from the starting tone in each of these seven scales. By the start of the Baroque period, the notion of musical key was established梑ased on a central triad rather than a central tone. Major and minor scales came to dominate until at least the start of the 20th century, partly because their intervallic patterns are suited to the reinforcement of a central triad. Some church modes survived into the early 18th century, as well as appearing occasionally in classical and 20th century music, and later in modal jazz.
Using the 12 notes of the chromatic scale, 12 major and 12 minor scales can be formed. 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. The black (or "short") keys were an innovation that allows the adjacent positioning of most of the diatonic whole-steps (all in the case of C major), with significant physical and conceptual advantages.
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𣇻𣇼𣇻; these numbers stand for whole tones (2 semitones) and half tones (one semitone). This scale pattern is often also described in terms of steps or tones as 'whole-whole-half-whole-whole-whole-half', whole and half referring to whole tones (or whole steps) and half tones (or half steps) respectively. 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朢e朚i朏a朣ol朙a朣i朌o".
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朣i朌o朢e朚i朏a朣ol朙a." Alternately, the natural minor can be seen as a composite of two different tetrachords of the pattern 2𢴐𣇻𣇼. In solfege "Do朢e朚i朏a朣ol朙a朣i朌o."
Western harmony from the Renaissance 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 specific properties that 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 is strictly proper, i.e., 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, ascending minor, harmonic minor, harmonic major, and locrian major scales; of these, all but the last are well-known and constitute 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 may have been the first to consider the notion, 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.
| C | D | E | F | G | A | B | C |
|---|
| 1 | 9/8 | 5/4 | 4/3 | 3/2 | 5/3 | 15/8 | 2 |
The earliest diatonic scales
The earliest claimed occurrence of diatonic tuning is in the 45,000 year-old so-called "Neanderthal flute" found at Divje Babe. Although there is no consensus that this is a musical instrument, there has been one claim that it played a diatonic scale.
There is other 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.
9,000 year old flutes found in Jiahu, China indicate the evolution, over a period of 1,200 years, of flutes having 4, 5 and 6 holes to having 7 and 8 holes, the latter exhibiting striking similarity to diatonic hole spacings and sounds .
See also
External links
- on Eric Weisstein's Treasure trove of Music
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Further reading
- 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.
- Clough, John (1979). "Aspects of Diatonic Sets", Journal of Music Theory 23: 45-61.
- Franklin, John C. (2002). "Diatonic Music in Greece: a Reassessment of its Antiquity", Mnemosyne 56.1, 669-702
- 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 1-930190-80-8.
- 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
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