Semitone

semitone
Inverse	major seventh (for minor second); diminished octave (for augmented unison); augmented octave (for diminished unison)
Name
Other names	minor second,; diatonic semitone,; augmented unison,; diminished unison,; chromatic semitone
Abbreviation	m2; A1
Size
Semitones	1
Interval class	1
Just interval	16:15, 17:16, 27:25, 135:128, 25:24, 256:243
Cents
12-Tone equal temperament	100
Just intonation	112, 105, 133, 92, 71, 90

A semitone, also called a minor second, half step, or a half tone,^[3] is the smallest musical interval commonly used in Western tonal music,^[4] and it is considered the most dissonant^[5] when sounded harmonically. It is defined as the interval between two adjacent notes in a 12-tone scale (or half of a whole step), visually seen on a keyboard as the distance between two keys that are adjacent to each other. For example, C is adjacent to C♯; the interval between them is a semitone.^[6]

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^[7] between a diatonic semitone, or minor second (an interval encompassing two different 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 if and only if twelve-tone equal temperament is used; for example, they are not the same thing in meantone temperament, where the diatonic semitone is distinguished from and larger than the chromatic semitone (augmented unison), or in Pythagorean tuning, where the diatonic semitone is smaller instead. 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.

^ ^a ^b ^c ^d ^e ^f ^g Duffin, Ross W. (2008). How equal temperament ruined harmony : (and why you should care) (First published as a Norton paperback. ed.). New York: W. W. Norton. p. 163. ISBN 978-0-393-33420-3. Retrieved 28 June 2017.
^ Haluska, Jan (2003). The Mathematical Theory of Tone Systems, p. xxiv. ISBN 0-8247-4714-3. Overtone semitone.
^ Semitone, half step, half tone, halftone, and half-tone are all variously used in sources.[1][2][3][4][5]
Aaron Copland, Leonard Bernstein, and others use "half tone".[6] [7][8][9]
One source says that step is "chiefly US",[10] and that half-tone is "chiefly N. Amer."[11]
^ Miller, Michael. The Complete Idiot's Guide to Music Theory, 2nd ed. [Indianapolis, Indiana]: Alpha, 2005. ISBN 1-59257-437-8. p. 19.
^ Capstick, John Walton (1913). Sound: An Elementary Text-book for Schools and Colleges. Cambridge University Press.
^ "musictheory.net". www.musictheory.net. Retrieved 2024-01-04.
^ Wharram, Barbara (2010). Elementary Rudiments of Music (2nd ed.). Mississauga, Ontario: Frederick Harris Music. p. 17. ISBN 978-1-55440-283-0.

[Duffin-1] ^ ^a ^b ^c ^d ^e ^f ^g Duffin, Ross W. (2008). How equal temperament ruined harmony : (and why you should care) (First published as a Norton paperback. ed.). New York: W. W. Norton. p. 163. ISBN 978-0-393-33420-3. Retrieved 28 June 2017.

[Haluska-2] Haluska, Jan (2003). The Mathematical Theory of Tone Systems, p. xxiv. ISBN 0-8247-4714-3. Overtone semitone.

[3] Semitone, half step, half tone, halftone, and half-tone are all variously used in sources.[1][2][3][4][5]
Aaron Copland, Leonard Bernstein, and others use "half tone".[6] [7][8][9]
One source says that step is "chiefly US",[10] and that half-tone is "chiefly N. Amer."[11]

[4] Miller, Michael. The Complete Idiot's Guide to Music Theory, 2nd ed. [Indianapolis, Indiana]: Alpha, 2005. ISBN 1-59257-437-8. p. 19.

[5] Capstick, John Walton (1913). Sound: An Elementary Text-book for Schools and Colleges. Cambridge University Press.

[6] "musictheory.net". www.musictheory.net. Retrieved 2024-01-04.

[Wharram-7] Wharram, Barbara (2010). Elementary Rudiments of Music (2nd ed.). Mississauga, Ontario: Frederick Harris Music. p. 17. ISBN 978-1-55440-283-0.

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