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Musicology commonly classifies note scales as either hemitonic or anhemitonic. Hemitonic scales contain one or more semitones and anhemitonic scales do not contain semitones. For example, in Japanese music the anhemitonic ''yo'' scale is contrasted with the hemitonic ''in'' scale.〔Anon. (2001) "Ditonus", ''The New Grove Dictionary of Music and Musicians'', second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan Publishers; Bence Szabolcsi (1943), "Five-Tone Scales and Civilization", ''Acta Musicologica'' 15, Fasc. 1/4 (January–December): pp. 24–34, citation on p. 25.〕 The simplest scale in most common use over the planet, the atritonic anhemitonic ("Major") pentatonic scale, is anhemitonic, so also the whole tone scale. A special subclass of the hemitonic scales is the cohemitonic scales.〔Christ, William (1966). ''Materials and Structure of Music'', v.1, p. 39. Englewood Cliffs: Prentice–Hall. LOC 66-14354.〕 Cohemitonic scales contain two or more semitones (making them hemitonic), in particular such that two or more of the semitones fall consecutively in scale order. For example, the Hungarian minor scale in C includes F-sharp, G, and A-flat in that order, with semitones between. Ancohemitonic scales, by contrast, possess either no semitones (and thus are anhemitonic), or possess semitones (being hemitonic) but ordered such that none are consecutive.〔Tymoczko, Dmitri (1997). "The Consecutive-Semitone Constraint on Scalar Structure: A Link between Impressionism and Jazz", ''Intégral'', v.11, (1997), p. 135-179.〕 In some uses, as vary by author, only the more specific second definition is understood. Examples are numerous, as ancohemitonia is favored over cohemitonia in the world's musics: diatonic scale, melodic major/melodic minor, Hungarian major, harmonic major scale, harmonic minor scale, and the so-called octatonic scale. Hemitonia is also quantified by the number of semitones present. Unhemitonic scales have one and only one semitone; dihemitonic scales have 2 semitones; trihemitonic scales have 3 semitones, etc. In the same way that an anhemitonic scale is less dissonant than a hemitonic scale, an unhemitonic scale is less dissonant than a dihemitonic scale. The qualification of cohemitonia versus ancohemitonia combines with the cardinality of semitones, giving terms like: dicohemitonic, triancohemitonic, and so forth. The importance of this lies in the fact that an ancohemitonic scale is less dissonant than a cohemitonic scale, the count of their semitones being equal. In general, the number of semitones is more important to the perception of dissonance than the adjacency (or lack thereof) of any pair of them. Additional adjacency between semitones (once adjacency is present) does not necessarily increase the dissonance, the count of semitones again being equal.〔Keith, Michael. 1991. ''From Polychords to Polya : Adventures in Musical Combinatorics'', p. 45. Princeton: Vinculum Press. ISBN 978-0963009708.〕 Related to these semitone classifications are ''tritonic'' and ''atritonic'' scales. Tritonic scales contain one or more tritones and atritonic scales do not contain tritones. A special monotonic relationship obtains between semitones and tritones as scales are built by projection, q.v. below. The harmonic relationship of all these categories lies in their bases of semitones and tritones being the severest of dissonances—avoiding these is often desirable. The most-used scales across the planet are anhemitonic. Of the remaining hemitonic scales, the ones most used are ancohemitonic. This fundamental importance is confirmed by study of these categories, in which the names of the commonest scales appear frequently. == Quantification of hemitonia and its relationship to ancohemitonia == Most of the world's music is anhemitonic, perhaps 90%.〔Keith, Michael. 1991. ''From Polychords to Polya : Adventures in Musical Combinatorics'', p. 43. Princeton: Vinculum Press. ISBN 978-0963009708.〕 Of that other hemitonic portion, perhaps 90% is unhemitonic, predominating in chords of only 1 semitone, all of which are ancohemitonic by definition.〔 Of the remaining 10%, perhaps 90% are dihemitonic, predominating in chords of no more than 2 semitones. The same applies to chords of 3 semitones.〔Keith, Michael. 1991. ''From Polychords to Polya : Adventures in Musical Combinatorics'', p. 48-49. Princeton: Vinculum Press. ISBN 978-0963009708.〕 In both later cases, however, there is a distinct preference for ancohemitonia, as the lack of adjacency of any two semitones goes a long way towards softening the increasing dissonance. The following table plots sonority size (downwards on the left) against semitone count (to the right) plus the quality of ancohemitonia (denoted with letter A) versus cohemitonia (denoted with letter C). In general, ancohemitonic combinations are fewer for a given chord or scale size, but used much more frequently so that their names are well known. Column "0" represents the most commonly used chords.,〔 avoiding intervals of M7 and chromatic 9ths and such combinations of 4th, chromatic 5ths, and 6th to produce semitones. Column 1 represents chords that barely use the harmonic degrees that column "0" avoids. Column 2, however, represents sounds far more intractable.〔 Column 0, row 5 are the full but pleasant chords: 9th, 6/9, and 9alt5 with no 7.〔Wilmott, Brett. (1994) ''Mel Bays Complete Book of Harmony Theory and Voicing'', p.210. Pacific, Missouri: Mel Bay. ISBN 978-1562229948.〕 Column "0", row "6", is the unique whole tone scale.〔Hanson, Howard. (1960) ''Harmonic Materials of Modern Music'', p.367. New York: Appleton-Century-Crofts. LOC 58-8138.〕 Column "2A", row "7", a local minimum, refers to the diatonic scale and melodic major/melodic minor scales.〔Hanson, Howard. (1960) ''Harmonic Materials of Modern Music'', p.362-363. New York: Appleton-Century-Crofts. LOC 58-8138.〕 Ancohemitonia, inter alii, probably makes these scales popular. Column "2C", row "7", another local minimum, refers to the Neapolitan major scale, which is cohemitonic and somewhat less common but still popular enough to bear a name.〔Hanson, Howard. (1960) ''Harmonic Materials of Modern Music'', p.363. New York: Appleton-Century-Crofts. LOC 58-8138.〕 Column "3A", row "7", another local minimum, represents the Hungarian major scale, and its involution, and the harmonic major scale and involution harmonic minor scale of the same.〔Hanson, Howard. (1960) ''Harmonic Materials of Modern Music'', p.364. New York: Appleton-Century-Crofts. LOC 58-8138.〕 Column "3A", row "6", are the hexatonic analogs to these four familiar scales,〔Hanson, Howard. (1960) ''Harmonic Materials of Modern Music'', p.369. New York: Appleton-Century-Crofts. LOC 58-8138.〕 one of which being the Augmented scale,〔Hanson, Howard. (1960) ''Harmonic Materials of Modern Music'', p.368. New York: Appleton-Century-Crofts. LOC 58-8138.〕 and another the analog of the Octatonic scale - which itself appears, alone and solitary, at Column ">=4A". row "8".〔Hanson, Howard. (1960) ''Harmonic Materials of Modern Music'', p.360. New York: Appleton-Century-Crofts. LOC 58-8138.〕 Column "2A", row "4", another minimum, represents a few frankly dissonant, yet strangely ''resonant'' harmonic combinations: mM9 with no 5, 119, dom139, and M711.〔 As music tends towards increasing dissonance through history, perhaps someday Column 2 will be as acceptable as even Column 1 might be, and Column 3 will finally have a place in the harmony of the world. Note, too, that in the highest cardinality row for each column before the terminal zeros begin, the sonority counts are small, except for row "7" and the "3" columns of all sorts. This explosion of hemitonic possibility associated with note cardinality 7 (and above) possibly marks the lower bound for the entity called "scale" (in contrast to "chord"). As shown in the table, anhemitonia is a property of the domain of note sets cardinality 2 through 6, while ancohemitonia is a property of the domain of note sets cardinality 4 through 8 (3 through 8 for improper ancohemitonia including unhemitonia as well). This places anhemitonia generally in the range of "chords" and ancohemitonia generally in the range of "scales". 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Anhemitonic scale」の詳細全文を読む スポンサード リンク
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