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Inverse major seventh (for minor second); diminished octave (for augmented unison); augmented octave (for diminished unison)
Other names minor second
or diatonic semitone;
augmented unison and diminished unison
or chromatic semitone
Abbreviation m2; aug1
Semitones 1
Interval class 1
Just interval 16:15; 25:24 (and others)
Equal temperament 100
24 tone equal temperament 100
Just intonation 112; 71 (and others)
Minor second About this sound Play
Augmented unison

A semitone, also called a half step or a half tone,[1] is the smallest musical interval commonly used in Western tonal music,[2] and it is considered the most dissonant[3] 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.

Any other 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[4] between a diatonic semitone, or minor second (an interval encompassing two staff position, 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). The diminished unison also exists, being the inversion of the augmented octave, though some theorists reject the term.[5][6][7] See here 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. 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). The smaller chromatic and diatonic semitones differ from the larger by the syntonic comma (81:80 or 21.5 cents). The smaller and larger chromatic semitones differ from the respective diatonic semitones by the same 128:125 diesis as the above meantone semitones. Finally, while the inner semitones differ by the diaschisma (2048:2025 or 19.6 cents), the outer differ by the greater diesis (648:625 or 62.6 cents). In symmetric five-limit tuning the diatonic semitone with ratio 27:25 does not appear. In 17-limit just intonation, the major diatonic semitone is 15:14 or 119.4 cents, and the minor diatonic semitone is 17:16 or 105.0 cents.[8]

About this sound Listen to a minor second in equal temperament . Here, middle C is followed by D, (melodic semitone), which is a tone 100 cents sharper than C, and then by both tones together (harmonic semitone).


Minor second

The melodic minor second is an integral part of most cadences of the Common practice period.

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).



A harmonic minor second in J.S. Bach's Prelude in C major from the WTC book 1, mm. 7-9. The minor second may be viewed as a suspension of the B resolving into the following A minor seventh chord.
The opening measures of Frédéric Chopin's "wrong note" Étude.


Augmented unison

Augmented unisons often appear as a consequence of secondary dominants, such as those in the soprano voice of this sequence from Felix Mendelssohn's Song Without Words Op. 102 No. 3, mm. 47-49.

The augmented unison does not occur between diatonic scale steps, but instead between a scale step and a chromatic alteration of the same step. It is also called a chromatic semitone. The augmented unison is abbreviated A1, or aug 1. Its inversion is the diminished octave (d8, or dim 8).

Melodically, an augmented unison very frequently occurs when proceeding to a chromatic chord, such as a secondary dominant, a diminished seventh chord, or an augmented sixth chord. Its use is also often the consequence of a melody proceeding in semitones, regardless of harmonic underpinning, e.g. D, D, E, F, F. (Restricting the notation to only minor seconds is impractical, as the same example would have a rapidly increasing number of accidentals, written enharmonically as D, E, F, G, A).

Franz Liszt's second Transcendental Etude, measure 63.

Harmonically, augmented unisons are quite rare in tonal repertoire. In the example to the right, Liszt had written an E against an E in the bass. Here E was preferred to a D to make the tone's function clear as part of an F dominant seventh chord, and the augmented unison is the result of superimposing this harmony upon an E pedal point.


The same spelling can also be referred to as a diminished unison in certain contexts[5][6]




“As late as the 13th century the half step was experienced as a problematic interval not easily understood, as the irrational [sic] remainder between the perfect fourth and the ditone \left(\begin{matrix} \frac{4}{3} \end{matrix} / {{\begin{matrix} (\frac{9}{8}) \end{matrix}}^2} = \begin{matrix} \frac{256}{243} \end{matrix}\right).” In a melodic half step, no “tendency was perceived of the lower tone toward the upper, or of the upper toward the lower. The second tone was not taken to be the ‘goal’ of the first. Instead, the half step was avoided in clausulae because it lacked clarity as an interval.” [9]

A dramatic chromatic scale in the opening measures of Luca Marenzio's Solo e pensoso, ca. 1580. ( Loudspeaker.svg About this sound Play




This excerpt from the first of Arnold Schoenberg's Three Piano Pieces, Op. 11 (m. 40) demonstrates completely unrestrained use of the semitone and related intervals. About this sound Play

Semitones in different tunings


Meantone temperament


The chromatic semitone is usually smaller than the diatonic. In the common quarter-comma meantone, tuned as a cycle of tempered fifths from E to G, the chromatic and diatonic semitones are 76.0 and 117.1 cents wide respectively.

Chromatic semitone 76.0 76.0 76.0 76.0 76.0
Pitch C C D E E F F G G A B B C
Cents 0.0 76.0 193.2 310.3 386.3 503.4 579.5 696.6 772.6 889.7 1006.8 1082.9 1200.0
Diatonic semitone 117.1 117.1 117.1 117.1 117.1 117.1 117.1


Equal temperament

12-tone equal temperament is a form of meantone tuning in which the diatonic and chromatic semitones are exactly the same, because its circle of fifths has no break. Each semitone is equal to one twelfth of an octave. This is a ratio of 21/12 (approximately 1.05946), or 100 cents, and is 11.7 cents narrower than the 16:15 ratio (its most common form in just intonation, discussed below).



For more examples, see Pythagorean and Just systems of tuning below.

Well temperament


Pythagorean tuning


The Pythagorean diatonic semitone has a ratio of 256/243 (About this sound play ), and is often called the Pythagorean limma. It is also sometimes called the Pythagorean minor semitone.

\frac{256}{243} = \frac{2^8}{3^5} \approx 90.2 \text{ cents}

The Pythagorean chromatic semitone has a ratio of 2187/2048 (About this sound play ). It may also be called the Pythagorean apotome or the Pythagorean major semitone. (See Pythagorean interval.)

\frac{2187}{2048} = \frac{3^7}{2^{11}} \approx 113.7\text{ cents}

Just intonation

A minor second in just intonation most often corresponds to a pitch ratio of 16:15 (About this sound play ) or 1.0666... (approximately 111.7 cents), called the just diatonic semitone. This is the most practical just semitone, as it is the difference between a perfect fourth and major third (\tfrac{4}{3} \div \tfrac{5}{4} = \tfrac{16}{15} ). In 5-limit just intonation, there is another semitone of 25:24 (About this sound play ) or 1.04166... (approximately 70.672 cents) available between two major thirds (25:16) and a perfect fifth (3:2), sometimes called a just chromatic semitone, but it is less common. Composer Ben Johnston uses a sharp an accidental to indicate a note is raised 70.6 cents, or a flat to indicate a note is lowered 70.6 cents.[10]

Two other kinds of semitones are produced by 5-limt tuning. A chromatic scale defines 12 semitones as the 12 intervals between the 13 adjacent notes forming a full octave (e.g. from C4 to C5). The 12 semitones produced by a commonly used version of 5-limit tuning have four different sizes, and can be classified as follows:

  •  S_1 = {25 \over 24} \approx 70.7 \ \hbox{cents}
    (Just augmented unison, or just chromatic semitone, e.g. between E and E)
  •  S_2 = {135 \over 128} \approx 92.2 \ \hbox{cents}
    (Augmented unison, or chromatic semitone, e.g. between D and D)
  •  S_3 = {16 \over 15} \approx 111.7 \ \hbox{cents}
    (Just minor second, or just diatonic semitone, e.g. between C and D)
  •  S_4 = {27 \over 25} \approx 133.2 \ \hbox{cents}
    (Minor second, or diatonic semitone, e.g. between A and B)

The most frequently occurring semitones are the just ones (S3 and S1): S3 occurs 6 times out of 12, S1 three times, S2 twice, and S1 only once.

Other ratios may function as a minor second. In 7-limit there is the septimal diatonic semitone of 15:14 (About this sound play ) available between the 5-limit major seventh (15:8) and the 7-limit minor seventh (7:4). There is also a smaller septimal chromatic semitone of 21:20 (About this sound play ) between a septimal minor seventh and a fifth (21:8) and an octave and a major third (5:2). Both are more rarely used than their 5-limit neighbours, although the former was often implemented by theorist Henry Cowell, while Harry Partch used the latter as part of his 43-tone scale.

Under 11-limit tuning, there is a fairly common undecimal neutral second (12:11) (About this sound play ), but it lies on the boundary between the minor and major second (150.6 cents). In just intonation there are infinitely many possibilities for intervals that fall within the range of the semitone (e.g. the Pythagorean semitones mentioned above), but most of them are impractical.


Other equal temperaments

19-tone equal temperament distinguishes between the chromatic and diatonic semitones; in this tuning, the chromatic semitone is one step of the scale (About this sound play 63.2 cents ), and the diatonic semitone is two (About this sound play 126.3 cents ). 31-tone equal temperament also distinguishes between these two intervals, which become 2 and 3 steps of the scale, respectively. 53-ET has an even closer match to the two semitones with 3 and 5 steps of its scale while 72-ET uses 4 (About this sound play 66.7 cents ) and 7 (About this sound play 116.7 cents ) steps of its scale.


See also


  1. ^ Semitone, half step, half tone, halftone, and half-tone are all variously used in sources.[1][2][3][4][5][6]
    Aaron Copland, Leonard Bernstein, and others use "half tone".[7] [8][9][10]
    One source says that step is "chiefly US",[11] and that half-tone is "chiefly N. Amer."[12]
  2. ^ Miller, Michael. The Complete Idiot's Guide to Music Theory, 2nd ed. [Indianapolis, IN]: Alpha, 2005. ISBN 1592574378. p. 19.
  3. ^ Capstick, John Walton (1913). Sound: An Elementary Text-book for Schools and Colleges. Cambridge University Press. 
  4. ^ Wharram, Barbara (2010). Elementary Rudiments of Music (2nd ed.). Mississauga, ON: Frederick Harris Music. p. 17. ISBN 9781554402830. 
  5. ^ a b Sembos (2006). Principles of Music Theory, p.51. ISBN 1430309555. online
  6. ^ a b Blood, Brian (2008 rev 2009). "Intervals". Music Theory Online. Dolmetsch Musical Instruments. Retrieved 25 December 2009. 
  7. ^ Kostka and Payne (2003). Tonal Harmony, p.21. ISBN 0072852607. "There is no such thing as a diminished unison."
  8. ^ Prout, Ebenezer (2004). Harmony, p.325. ISBN 1410219208.
  9. ^ a b Dahlhaus, Carl, trans. Gjerdingen, Robert O. Studies in the Origin of Harmonic Tonality. Princeton University Press: Princeton, 1990. ISBN 0-691-09135-8.
  10. ^ John Fonville. "Ben Johnston's Extended Just Intonation- A Guide for Interpreters", p.109, Perspectives of New Music, Vol. 29, No. 2 (Summer, 1991), pp. 106-137. "...the 25/24 ratio is the sharp (#) ratio...this raises a note approximately 70.6 cents."

Further reading


This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Semitone". Allthough most Wikipedia articles provide accurate information accuracy can not be guaranteed.

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