Pythagorean apotome
| Inverse | major seventh (for minor second); diminished octave (for augmented unison); augmented octave (for diminished unison) |
|---|---|
| Name | |
| Other names | minor second or diatonic semitone; augmented unison and diminished unison or chromatic semitone |
| Abbreviation | m2; A1 |
| Size | |
| Semitones | 1 |
| Interval class | 1 |
| Just interval | 16:15, 17:16, 27:25, or 25:24 |
| Cents | |
| Equal temperament | 100 |
| 24 equal temperament | 100 |
| Just intonation | 112, 105, 133, or 71 |
A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, 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. For example, C is adjacent to C♯; the interval between them is a semitone.
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.
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