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 In music, consonance and dissonance are categorizations of simultaneous or successive Sound, sounds. Within the Western tradition, some listeners associate consonance with sweetness, pleasantness, and acceptability, and dissonance with harshness ...

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 In Western music theory, a major second (sometimes also called whole tone or a whole step) is a second spanning two semitones (). A second is a musical interval encompassing two adjacent staff positions (see Interval number for more det ...

or major second is 2 semitones wide, a

major third In classical music, a third is a Interval (music), musical interval encompassing three staff positions (see Interval (music)#Number, Interval number for more details), and the major third () is a third spanning four semitones.Allen Forte, ...

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 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 when

twelve-tone equal temperament Twelve-tone equal temperament (12-TET) is the musical system that divides the octave into 12 parts, all of which are equally tempered (equally spaced) on a logarithmic scale, with a ratio equal to the 12th root of 2 ( ≈ 1.05946). That resultin ...

is used, but are not the same thing in

meantone temperament Meantone temperament is a musical temperament, that is a tuning system, obtained by narrowing the fifths so that their ratio is slightly less than 3:2 (making them ''narrower'' than a perfect fifth), in order to push the thirds closer to pure. M ...

, where the diatonic semitone is distinguished from and smaller than the chromatic semitone (augmented unison). See for more details about this terminology. In

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 In musical tuning, the Pythagorean comma (or ditonic comma), named after the ancient mathematician and philosopher Pythagoras, is the small interval (or comma) existing in Pythagorean tuning between two enharmonically equivalent notes such as ...

of ratio 531441:524288 or 23.5 cents. In

quarter-comma meantone Quarter-comma meantone, or -comma meantone, was the most common meantone temperament in the sixteenth and seventeenth centuries, and was sometimes used later. In this system the perfect fifth is flattened by one quarter of a syntonic comma (81:80 ...

, 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 Five-limit tuning, 5-limit tuning, or 5-prime-limit tuning (not to be confused with 5-odd-limit tuning), is any system for musical tuning, tuning a musical instrument that obtains the frequency of each note by multiplying the frequency of a given ...

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 In music theory, a scale is any set of musical notes ordered by fundamental frequency or pitch. A scale ordered by increasing pitch is an ascending scale, and a scale ordered by decreasing pitch is a descending scale. Often, especially in the ...

or chord containing semitones is called hemitonic; one without semitones is anhemitonic.

Minor second

The ''minor second'' occurs in the

major scale The major scale (or Ionian mode) is one of the most commonly used musical scales, especially in Western music. It is one of the diatonic scales. Like many musical scales, it is made up of seven notes: the eighth duplicates the first at double ...

, 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 In music from Western culture, a seventh is a musical interval encompassing seven staff positions (see Interval number for more details), and the major seventh is one of two commonly occurring sevenths. It is qualified as ''major'' because it i ...

'' (''M7'' or ''Ma7''). . 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 Western musical theory, a cadence (Latin ''cadentia'', "a falling") is the end of a phrase in which the melody or harmony creates a sense of full or partial resolution, especially in music of the 16th century onwards.Don Michael Randel (19 ...

. In the perfect and deceptive cadences it appears as a resolution of the

leading-tone In music theory, a leading-tone (also called a subsemitone, and a leading-note in the UK) is a note or pitch which resolves or "leads" to a note one semitone higher or lower, being a lower and upper leading-tone, respectively. Typically, ''t ...

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 In music, harmony is the process by which individual sounds are joined together or composed into whole units or compositions. Often, the term harmony refers to simultaneously occurring frequencies, pitches ( tones, notes), or chords. However, ...

, 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 chord An added tone chord, or added note chord, is a non- tertian chord composed of a triad and an extra "added" note. Any tone that is not a seventh factor is commonly categorized as an added tone. It can be outside the tertian sequence of ascendin ...

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 Modest Petrovich Mussorgsky ( rus, link=no, Модест Петрович Мусоргский, Modest Petrovich Musorgsky , mɐˈdɛst pʲɪˈtrovʲɪtɕ ˈmusərkskʲɪj, Ru-Modest Petrovich Mussorgsky version.ogg; – ) was a Russian compo ...

's '' Ballet of the Unhatched Chicks''. More recently, the music to the movie '' Jaws'' exemplifies the minor second.

In other temperaments

In just intonation a 16:15 minor second arises in the C

between B & C and E & F, and is, "the sharpest dissonance found in the ajor scale."Paul, Oscar (1885).
A manual of harmony for use in music-schools and seminaries and for self-instruction
', p. 165.

Theodore Baker Theodore Baker (June 3, 1851"Passed Away," ''Musical America'' (Nov. 10, 1934), p. 32."Dr. Theodore Baker," ''Musical Courier'' (Nov. 3, 1934), p. 20. – October 12, 1934) Mendelssohn dominants

The augmented unison, the interval produced by the augmentation, or widening by one half step, of the perfect 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''). The augmented unison is also the inversion of the augmented octave, because the interval of the diminished unison does not exist. This is because a unison is always made larger when one note of the interval is changed with an accidental. Melodically, an augmented unison very frequently occurs when proceeding to a chromatic chord, such as a secondary dominant, a

diminished seventh chord The diminished seventh chord is a four-note chord (a seventh chord) composed of a root note, together with a minor third, a diminished fifth, and a diminished seventh above the root: (1, 3, 5, 7). For example, the diminished seve ...

, or an

augmented sixth chord In music theory, an augmented sixth chord contains the interval of an augmented sixth, usually above its bass tone. This chord has its origins in the Renaissance, was further developed in the Baroque, and became a distinctive part of the musi ...

. 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). Liszt augmented unison

, augmented unisons are quite rare in tonal repertoire. In the example to the right,

Liszt Franz Liszt, in modern usage ''Liszt Ferenc'' . Liszt's Hungarian passport spelled his given name as "Ferencz". An orthographic reform of the Hungarian language in 1922 (which was 36 years after Liszt's death) changed the letter "cz" to simpl ...

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 In music theory, a dominant seventh chord, or major minor seventh chord, is a seventh chord, usually built on the fifth degree of the major scale, and composed of a root, major third, perfect fifth, and minor seventh. Thus it is a major triad t ...

chord, and the augmented unison is the result of superimposing this harmony upon an E pedal point. In addition to this kind of usage, harmonic augmented unisons are frequently written in modern works involving tone clusters, such as

Iannis Xenakis Giannis Klearchou Xenakis (also spelled for professional purposes as Yannis or Iannis Xenakis; el, Γιάννης "Ιωάννης" Κλέαρχου Ξενάκης, ; 29 May 1922 – 4 February 2001) was a Romanian-born Greek-French avant-garde c ...

' ''Evryali'' for piano solo.

History

The semitone appeared in the music theory of Greek antiquity as part of a diatonic or chromatic

tetrachord In music theory, a tetrachord ( el, τετράχορδoν; lat, tetrachordum) is a series of four notes separated by three intervals. In traditional music theory, a tetrachord always spanned the interval of a perfect fourth, a 4:3 frequency pr ...

, and it has always had a place in the diatonic scales of Western music since. The various modal scales of medieval music theory were all based upon this diatonic pattern of tones and semitones. Though it would later become an integral part of the musical

cadence In Western musical theory, a cadence (Latin ''cadentia'', "a falling") is the end of a phrase in which the melody or harmony creates a sense of full or partial resolution, especially in music of the 16th century onwards.Don Michael Randel (199 ...

, in the early polyphony of the 11th century this was not the case. Guido of Arezzo suggested instead in his '' Micrologus'' other alternatives: either proceeding by whole tone from a

major second In Western music theory, a major second (sometimes also called whole tone or a whole step) is a second spanning two semitones (). A second is a musical interval encompassing two adjacent staff positions (see Interval number for more de ...

to a unison, or an ''occursus'' having two notes at a

move by contrary motion toward a unison, each having moved a whole tone. "As late as the 13th century the half step was experienced as a problematic interval not easily understood, as the irrational remainder between the perfect fourth and the

ditone In music, a ditone (, from , "of two tones") is the interval of a major third. The size of a ditone varies according to the sizes of the two tones of which it is compounded. The largest is the Pythagorean ditone, with a ratio of 81:64, also cal ...

\left(\begin \frac \end /  = \begin \frac \end\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." Dahlhaus, Carl, trans. Gjerdingen, Robert O. ''Studies in the Origin of Harmonic Tonality''. Princeton University Press: Princeton, 1990. . Marenzio solo e pensoso chromatic

However, beginning in the 13th century

begin to require motion in one voice by half step and the other a whole step in contrary motion. These cadences would become a fundamental part of the musical language, even to the point where the usual accidental accompanying the minor second in a cadence was often omitted from the written score (a practice known as

musica ficta ''Musica ficta'' (from Latin, "false", "feigned", or "fictitious" music) was a term used in European music theory from the late 12th century to about 1600 to describe pitches, whether notated or added at the time of performance, that lie outside ...

). By the 16th century, the semitone had become a more versatile interval, sometimes even appearing as an augmented unison in very chromatic passages. Semantically, in the 16th century the repeated melodic semitone became associated with weeping, see: passus duriusculus,

lament bass In music, the lament bass is a ground bass, built from a descending perfect fourth from tonic to dominant, with each step harmonized.Brover-Lubovsky, Bella (2008). ''Tonal Space in the Music of Antonio Vivaldi'', p.151-52. . The diatonic versi ...

, and

pianto In music, the ''pianto'' (en:crying) is the motif of a descending minor second, has represented laments and been associated textually with weeping, sighing (called the Mannheim sigh by Hugo Riemann); or pain, grief, etc.; since the 16th centur ...

. By the

Baroque era The Baroque (, ; ) is a style of architecture, music, dance, painting, sculpture, poetry, and other arts that flourished in Europe from the early 17th century until the 1750s. In the territories of the Spanish and Portuguese empires including th ...

(1600 to 1750), the tonal harmonic framework was fully formed, and the various musical functions of the semitone were rigorously understood. Later in this period the adoption of

well temperament Well temperament (also good temperament, circular or circulating temperament) is a type of tempered tuning described in 20th-century music theory. The term is modeled on the German word ''wohltemperiert''. This word also appears in the title of ...

s for instrumental tuning and the more frequent use of enharmonic equivalences increased the ease with which a semitone could be applied. Its function remained similar through the Classical period, and though it was used more frequently as the language of tonality became more chromatic in the Romantic period, the musical function of the semitone did not change. In the 20th century, however, composers such as Arnold Schoenberg, Béla Bartók, and Igor Stravinsky sought alternatives or extensions of tonal harmony, and found other uses for the semitone. Often the semitone was exploited harmonically as a caustic dissonance, having no resolution. Some composers would even use large collections of harmonic semitones ( tone clusters) as a source of cacophony in their music (e.g. the early piano works of Henry Cowell). By now, enharmonic equivalence was a commonplace property of equal temperament, and instrumental use of the semitone was not at all problematic for the performer. The composer was free to write semitones wherever he wished.

Semitones in different tunings

The exact size of a semitone depends on the

tuning Tuning can refer to: Common uses * Tuning, the process of tuning a tuned amplifier or other electronic component * Musical tuning, musical systems of tuning, and the act of tuning an instrument or voice ** Guitar tunings ** Piano tuning, adjusti ...

system used.

Meantone temperament Meantone temperament is a musical temperament, that is a tuning system, obtained by narrowing the fifths so that their ratio is slightly less than 3:2 (making them ''narrower'' than a perfect fifth), in order to push the thirds closer to pure. M ...

s have two distinct types of semitones, but in the exceptional case of equal temperament, there is only one. The unevenly distributed

s contain many different semitones. Pythagorean tuning, similar to meantone tuning, has two, but in other systems of just intonation there are many more possibilities.

Meantone temperament

meantone Meantone temperament is a musical temperament, that is a tuning system, obtained by narrowing the fifths so that their ratio is slightly less than 3:2 (making them ''narrower'' than a perfect fifth), in order to push the thirds closer to pure. Me ...

systems, there are two different semitones. This results because of the break in the

circle of fifths In music theory, the circle of fifths is a way of organizing the 12 chromatic pitches as a sequence of perfect fifths. (This is strictly true in the standard 12-tone equal temperament system — using a different system requires one interval of ...

that occurs in the tuning system: diatonic semitones derive from a chain of five fifths that does not cross the break, and chromatic semitones come from one that does. The chromatic semitone is usually smaller than the diatonic. In the common

, 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. Extended meantone temperaments with more than 12 notes still retain the same two semitone sizes, but there is more flexibility for the musician about whether to use an augmented unison or minor second. 31-tone equal temperament is the most flexible of these, which makes an unbroken circle of 31 fifths, allowing the choice of semitone to be made for any pitch.

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 2^1/12 (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). All diatonic intervals can be expressed as an equivalent number of semitones. For instance a

equals two semitones. There are many approximations,

rational Rationality is the quality of being guided by or based on reasons. In this regard, a person acts rationally if they have a good reason for what they do or a belief is rational if it is based on strong evidence. This quality can apply to an abi ...

or otherwise, to the equal-tempered semitone. To cite a few: :*

18 / 17 \approx 99.0 \text

suggested by

Vincenzo Galilei Vincenzo Galilei (born 3 April 1520, Santa Maria a Monte, Italy died 2 July 1591, Florence, Italy) was an Italian lutenist, composer, and music theorist. His children included the astronomer and physicist Galileo Galilei and the lute virtuoso and ...

and used by luthiers of the

Renaissance The Renaissance ( , ) , from , with the same meanings. is a period in European history The history of Europe is traditionally divided into four time periods: prehistoric Europe (prior to about 800 BC), classical antiquity (800 BC to AD ...

, :*

\approx 100.4 \text

suggested by Marin Mersenne as a constructible and more accurate alternative, :*

(139 / 138 )^8  \approx 99.9995 \text

used by Julián Carrillo as part of a sixteenth-tone system. For more examples, see Pythagorean and Just systems of tuning below.

Well temperament

There are many forms of

, but the characteristic they all share is that their semitones are of an uneven size. Every semitone in a well temperament has its own interval (usually close to the equal-tempered version of 100 cents), and there is no clear distinction between a ''diatonic'' and ''chromatic'' semitone in the tuning. Well temperament was constructed so that enharmonic equivalence could be assumed between all of these semitones, and whether they were written as a minor second or augmented unison did not effect a different sound. Instead, in these systems, each key had a slightly different sonic color or character, beyond the limitations of conventional notation.

Pythagorean tuning

Like meantone temperament, Pythagorean tuning is a broken

. This creates two distinct semitones, but because Pythagorean tuning is also a form of 3-limit just intonation, these semitones are rational. Also, unlike most meantone temperaments, the chromatic semitone is larger than the diatonic. The Pythagorean diatonic semitone has a ratio of 256/243 (), and is often called the Pythagorean limma. It is also sometimes called the ''Pythagorean minor semitone''. It is about 90.2 cents. :

\frac = \frac \approx 90.2 \text

It can be thought of as the difference between three octaves and five just fifths, and functions as a

diatonic semitone A semitone, also called a half step or a half tone, is the smallest interval (music), musical interval commonly used in Western tonal music, and it is considered the most Consonance and dissonance#Dissonance, dissonant when sounded harmonically ...

in a Pythagorean tuning. The Pythagorean chromatic semitone has a ratio of 2187/2048 (). It is about 113.7 cents. It may also be called the Pythagorean apotomeRashed, Roshdi (ed.) (1996). ''Encyclopedia of the History of Arabic Science, Volume 2'', pp. 588, 608. Routledge. . or the ''Pythagorean major semitone''. (''See Pythagorean interval''.) :

\frac = \frac \approx 113.7\text

It can be thought of as the difference between four perfect octaves and seven just fifths, and functions as a

chromatic semitone In modern Western tonal music theory an augmented unison or augmented prime is the interval between two notes on the same staff position, or denoted by the same note letter, whose alterations cause them, in ordinary equal temperament, to be one ...

in a Pythagorean tuning. The Pythagorean limma and Pythagorean apotome are enharmonic equivalents (chromatic semitones) and only a

apart, in contrast to diatonic and chromatic semitones in

and 5-limit just intonation.

Just 5-limit intonation

A minor second in just intonation typically corresponds to a pitch

ratio In mathematics, a ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ...

of 16:15 () or 1.0666... (approximately 111.7 cents), called the just diatonic semitone. This is a practical just semitone, since it is the difference between a

perfect fourth A fourth is a musical interval encompassing four staff positions in the music notation of Western culture, and a perfect fourth () is the fourth spanning five semitones (half steps, or half tones). For example, the ascending interval from C to ...

and

(

\tfrac \div \tfrac = \tfrac

). The 16:15 just minor second arises in the C major scale between B & C and E & F, and is, "the sharpest dissonance found in the scale." An augmented unison in just intonation is another semitone of 25:24 () or 1.0416... (approximately 70.7 cents). It is the difference between a 5:4 major third and a 6:5 minor third. Composer Ben Johnston uses a sharp () to indicate a note is raised 70.7 cents, or a flat () to indicate a note is lowered 70.7 cents. 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." Two other kinds of semitones are produced by 5-limit tuning. A

chromatic scale The chromatic scale (or twelve-tone scale) is a set of twelve pitches (more completely, pitch classes) used in tonal music, with notes separated by the interval of a semitone. Chromatic instruments, such as the piano, are made to produce th ...

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: *Just, or smaller, or minor, chromatic semitone, e.g. between E and E (6/5 and 5/4): :

S_1 =  \approx 70.7 \ \hbox

*Larger, or major, chromatic semitone, or larger limma, or major chroma, e.g. between C and C (1/1 and 135/128): :

S_2 =  \approx 92.2 \ \hbox

*Just, or smaller, or minor, diatonic semitone, e.g. between C and D (1/1 and 16/15): :

S_3 =  \approx 111.7 \ \hbox

*Larger, or major, diatonic semitone, e.g. between A and B (5/3 and 16/9): :

S_4 =  \approx 133.2 \ \hbox

The most frequently occurring semitones are the just ones (S₃ and S₁): S₃ occurs six times out of 12, S₁ three times, S₂ twice, and S₄ only once. The smaller chromatic and diatonic semitones differ from the larger by the

syntonic comma In music theory, the syntonic comma, also known as the chromatic diesis, the Didymean comma, the Ptolemaic comma, or the diatonic comma is a small comma type interval between two musical notes, equal to the frequency ratio 81:80 (= 1.0125) ...

(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).

Extended just intonations

7-limit 7-limit or septimal tunings and intervals are musical instrument tunings that have a limit of seven: the largest prime factor contained in the interval ratios between pitches is seven. Thus, for example, 50:49 is a 7-limit interval, but 14 ...

there is the

septimal diatonic semitone In music, a septimal diatonic semitone (or major diatonic semitoneHaluska, Jan (2003). ''The Mathematical Theory of Tone Systems'', p.xxiv & 25. .) is the interval 15:14 . It is about 119.44 cents. The septimal diatonic semitone may be derived f ...

of 15:14 () available between the 5-limit

(15:8) and the 7-limit minor seventh (7:4). There is also a smaller septimal chromatic semitone of 21:20 () 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 Harry Partch (June 24, 1901 – September 3, 1974) was an American composer, music theorist, and creator of unique musical instruments. He composed using scales of unequal intervals in just intonation, and was one of the first 20th-century com ...

used the latter as part of his 43-tone scale. Under 11-limit tuning, there is a fairly common ''undecimal

neutral second In music theory, a neutral interval is an interval that is neither a major nor minor, but instead in between. For example, in equal temperament, a major third is 400 cents, a minor third is 300 cents, and a neutral third is 350 cents. A neutral ...

'' (12:11) (), but it lies on the boundary between the minor and

(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. In 13-limit tuning, there is a tridecimal 2/3 tone (13:12 or 138.57 cents) and tridecimal 1/3 tone (27:26 or 65.34 cents). 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, Prout, Ebenezer (2004). ''Harmony'', p. 325. . and septendecimal limma is 18:17 or 98.95 cents. Though the names ''diatonic'' and ''chromatic'' are often used for these intervals, their musical function is not the same as the two meantone semitones. For instance, 15:14 would usually be written as an augmented unison, functioning as the ''chromatic'' counterpart to a ''diatonic'' 16:15. These distinctions are highly dependent on the musical context, and just intonation is not particularly well suited to chromatic usage (diatonic semitone function is more prevalent).

Other equal temperaments

19-tone equal temperament In music, 19 Tone Equal Temperament, called 19 TET, 19 EDO ("Equal Division of the Octave"), or 19 ET, is the tempered scale derived by dividing the octave into 19 equal steps (equal frequency ratios). Each step represent ...

distinguishes between the chromatic and diatonic semitones; in this tuning, the chromatic semitone is one step of the scale (), and the diatonic semitone is two (). 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 () and 7 () steps of its scale. In general, because the smaller semitone can be viewed as the difference between a minor third and a major third, and the larger as the difference between a major third and a perfect fourth, tuning systems that closely match those just intervals (6/5, 5/4, and 4/3) will also distinguish between the two types of semitones and closely match their just intervals (25/24 and 16/15).