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Pythagorean apotome : ウィキペディア英語版
Semitone

A semitone, also called a half step or a half tone,〔''Semitone'', ''half step'', ''half tone'', ''halftone'', and ''half-tone'' are all variously used in sources.()()()()()()

Aaron Copland, Leonard Bernstein, and others use "half tone".()
()()()

One source says that ''step'' is "chiefly US",() and that ''half-tone'' is "chiefly N. Amer."()
〕 is the smallest musical interval commonly used in Western tonal music,〔Miller, Michael. (''The Complete Idiot's Guide to Music Theory, 2nd ed'' ). (IN ): Alpha, 2005. ISBN 1-59257-437-8. p. 19.〕 and it is considered the most dissonant when sounded harmonically.
It is defined as the interval between two adjacent notes in a 12-tone scale (e.g. from C to C). This implies that its size is exactly or approximately equal to 100 cents, a twelfth of an octave.
In a 12-note approximately equally divided scale, any interval can be defined in terms of an appropriate number of semitones (e.g. a whole tone or major second is 2 semitones wide, a major third 4 semitones, and a perfect fifth 7 semitones.
In music theory, a distinction is made between a diatonic semitone, or minor second (an interval encompassing two staff positions, e.g. from C to D) and a chromatic semitone or augmented unison (an interval between two notes at the same staff position, e.g. from C to C). These are enharmonically equivalent when twelve-tone equal temperament is used, but are not the same thing in meantone temperament, where the diatonic semitone is distinguished from and larger than the chromatic semitone (augmented unison.) See Interval (music)#Number for more details about this terminology.
In twelve-tone equal temperament all semitones are equal in size (100 cents). In other tuning systems, "semitone" refers to a family of intervals that may vary both in size and name. In Pythagorean tuning, seven semitones out of twelve are diatonic, with ratio 256:243 or 90.2 cents (Pythagorean limma), and the other five are chromatic, with ratio 2187:2048 or 113.7 cents (Pythagorean apotome); they differ by the Pythagorean comma of ratio 531441:524288 or 23.5 cents. In quarter-comma meantone, seven of them are diatonic, and 117.1 cents wide, while the other five are chromatic, and 76.0 cents wide; they differ by the lesser diesis of ratio 128:125 or 41.1 cents. 12-tone scales tuned in just intonation typically define three or four kinds of semitones. For instance, Asymmetric five-limit tuning yields chromatic semitones with ratios 25:24 (70.7 cents) and 135:128 (92.2 cents), and diatonic semitones with ratios 16:15 (111.7 cents) and 27:25 (133.2 cents). For further details, see below.
The condition of having semitones is called hemitonia; that of having no semitones is anhemitonia. A musical scale or chord containing semitones is called hemitonic; one without semitones is anhemitonic.
==Minor second==

The ''minor second'' occurs in the major scale, between the third and fourth degree, (''mi'' (E) and ''fa'' (F) in C major), and between the seventh and eighth degree (''ti'' (B) and ''do'' (C) in C major). It is also called the ''diatonic semitone'' because it occurs between steps in the diatonic scale. The minor second is abbreviated m2 (or −2). Its inversion is the ''major seventh'' (''M7'', or ''+7'').
. Here, middle C is followed by D, which is a tone 100 cents sharper than C, and then by both tones together.
Melodically, this interval is very frequently used, and is of particular importance in cadences. In the perfect and deceptive cadences it appears as a resolution of the leading-tone to the tonic. In the plagal cadence, it appears as the falling of the subdominant to the mediant. It also occurs in many forms of the imperfect cadence, wherever the tonic falls to the leading-tone.
Harmonically, the interval usually occurs as some form of dissonance or a nonchord tone that is not part of the functional harmony. It may also appear in inversions of a major seventh chord, and in many added tone chords.
In unusual situations, the minor second can add a great deal of character to the music. For instance, Frédéric Chopin's Étude Op. 25, No. 5 opens with a melody accompanied by a line that plays fleeting minor seconds. These are used to humorous and whimsical effect, which contrasts with its more lyrical middle section. This eccentric dissonance has earned the piece its nickname: the "wrong note" étude. This kind of usage of the minor second appears in many other works of the Romantic period, such as Modest Mussorgsky's ''Ballet of the Unhatched Chicks''. More recently, the music to the movie ''Jaws'' exemplifies the minor second.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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