In Western music, asemitone (also called ahalf step orhalf tone)[1] is aninterval between adjacent notes in achromatic scale, represented on akeyboard as the distance between two adjacent keys. For example, C is adjacent to D♭; the interval between them is a semitone.[2] Semitones are among the mostdissonant intervals when sounded harmonically.[3]
Inmusic theory, a distinction is made[4] between adiatonic semitone, or minor second (an interval encompassing two differentstaff positions, e.g. from C to D♭) and achromatic semitone or augmented unison (an interval between two notes at the same staff position, e.g. from C to C♯).
The modern system of12-tone equal temperament divides the octave into twelve equal semitones, each with a frequency ratio of thetwelfth root of two (100cents). In this system, diatonic and chromatic semitones have the same size. More generally, if the 12 notes of a chromatic scale are not equally spaced but form a closedcircle of fifths (as in various historicalwell temperaments), both diatonic and chromatic semitones still correspond to a single step in the chromatic scale. In either case, a given musical interval can be represented by a specific number of semitones from any starting note. For example, awhole tone or major second spans 2 semitones, amajor third 4 semitones, and aperfect fifth 7 semitones(see:Interval (music) § Number, for more on interval terminology).
In some other tuning systems, diatonic and chromatic semitones are distinct. For example, they are not the same size inPythagorean tuning, where the diatonic semitone is distinguished from the larger chromatic semitone (augmented unison), or inquarter-comma meantone temperament, where the diatonic semitone is larger instead.
In a more general sense, "semitone" refers to a family of intervals that may vary both in size and name(see:§ Semitones in different tunings, for more).
The condition of having semitones is called hemitonia; that of having no semitones isanhemitonia. Amusical scale orchord containing semitones is called hemitonic; one without semitones is anhemitonic.
| Inverse | Major seventh |
|---|---|
| Name | |
| Abbreviation | m2 |
| Size | |
| Semitones | 1 |
| Interval class | 1 |
| Just interval | 256:243, 16:15,[5] 27:25 |
| Cents | |
| 12-Tone equal temperament | 100.0 |
| Just intonation | 90.2, 111.7, 133.2 |
Theminor second occurs in themajor scale, between the third and fourth degree, (mi (E) andfa (F) in C major), and between the seventh and eighth degree (ti (B) anddo (C) in C major). It is also called thediatonic semitone because it occurs betweensteps in thediatonic scale. The minor second is abbreviated m2 (or −2). Its inversion is themajor seventh (M7 orMa7).
Melodically, this interval is very frequently used, and is of particular importance incadences. In theauthentic anddeceptive cadences it appears as a resolution of theleading-tone to thetonic. In theplagal cadence, it appears as the falling of thesubdominant to themediant. It also occurs in many forms of theimperfect cadence, wherever the tonic falls to the leading-tone.
Harmonically, the interval usually occurs as some form ofdissonance or anonchord tone that is not part of thefunctional harmony. It may also appear in inversions of amajor seventh chord, and in manyadded tone chords.
In unusual situations, the minor second can add a great deal of character to the music. For instance,Frédéric Chopin'sÉtude 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 theRomantic period, such asModest Mussorgsky's "Ballet of the Unhatched Chicks" fromPictures at an Exhibition. More recently, the music to the movieJaws exemplifies the minor second.
| Inverse | Diminished octave |
|---|---|
| Name | |
| Other names | Chromatic semitone, minor semitone |
| Abbreviation | A1 |
| Size | |
| Semitones | 1 |
| Interval class | 1 |
| Just interval | 2187:2048, 25:24 |
| Cents | |
| 12-Tone equal temperament | 100 |
| Just intonation | 114, 71 |
Theaugmented unison,augmented prime[6], orchromatic semitone[7] is theinterval between two notes on the samestaff position (same letter name) that differ by one chromatic alteration. For example, the interval between B♭ and B♮, or between C♮ and C♯, is an augmented unison.
The term, in itsFrench formunisson superflu, appears to have been coined byJean-Philippe Rameau in 1722, who also called this interval a minor semitone (semiton mineur).[8] Historically, this interval, like thetritone, is described as being"mi contra fa" and was associated with the"diabolus in musica" (Latin for 'theDevil in music').[9]
Melodically, an augmented unison very frequently occurs when proceeding to a chromatic chord, such as asecondary dominant, adiminished seventh chord, or anaugmented 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
).
Harmonically, augmented unisons are quite rare in tonal repertoire. In the example to the right,Liszt wrote 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 Fdominant seventh chord, and the augmented unison is the result of superimposing this harmony upon an Epedal point.
In addition to this kind of usage, harmonic augmented unisons are frequently written in modern works involvingtone clusters, such asIannis Xenakis'Evryali for solo piano.
The term diminished unison or diminished prime is also found occasionally. It is found once inRameau's writings, for example,[8] as well as subsequent French, German, and English sources.[diminished 1]Other sources reject the possibility or utility of the diminished unison on the grounds that any alteration to the unison increases its size, thusaugmenting rather thandiminishing it.[augmented 1] The term is sometimes justified as a negative-numbered interval,[10][11] and also in terms of violin double-stopping technique on analogy to parallel intervals found on other strings.[12] Some theoreticians make a distinction for this diminished form of the unison, stating it is only valid as a melodic interval, not a harmonic one.[melodic 1]
The semitone appeared in the music theory of Greek antiquity as part of a diatonic or chromatictetrachord, and it has always had a place in the diatonic scales of Western music since. The variousmodal scales ofmedieval music theory were all based upon this diatonic pattern oftones and semitones.
Though it would later become an integral part of the musicalcadence, in the early polyphony of the 11th century this was not the case.Guido of Arezzo suggested instead in hisMicrologus other alternatives: either proceeding by whole tone from amajor second to a unison, or anoccursus having two notes at amajor third 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 [sic] remainder between the perfect fourth and theditone." 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 inclausulae because it lacked clarity as an interval."[13]
However, beginning in the 13th centurycadences begin to require motion in one voice by half step and the other a whole step in contrary motion.[13] 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 asmusica ficta). By the 16th century, the semitone had become a more versatile interval, sometimes even appearing as an augmented unison in verychromatic passages.Semantically, in the 16th century the repeated melodic semitone became associated with weeping, see:passus duriusculus,lament bass, andpianto.
By theBaroque era (1600 to 1750), thetonal harmonic framework was fully formed, and the various musical functions of the semitone were rigorously understood. Later in this period the adoption ofwell temperaments for instrumental tuning and the more frequent use ofenharmonic equivalences increased the ease with which a semitone could be applied. Its function remained similar through theClassical period, and though it was used more frequently as the language of tonality became more chromatic in theRomantic period, the musical function of the semitone did not change.
In the 20th century, however, composers such asArnold Schoenberg,Béla Bartók, andIgor 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 ofHenry Cowell). By now, enharmonic equivalence was a commonplace property ofequal 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.
The exact size of a semitone depends on thetuning system used.Pythagorean tuning has two distinct types of semitones.Meantone temperaments have two distinct types of semitones, but in the exceptional case of12-tone equal temperament, there is only one. The unevenly distributedwell temperaments contain many different semitones. In systems ofjust intonation, several types of semitones are encountered.
Pythagorean tuning, or 3-limit just intonation, is generated by a sequence ofperfect fifths, which creates two distinct semitones.
 |  |
| Pythagorean limma on C | Pythagorean apotome on C |
 |  |
| As five descending fifths from C (the inverse is B) | As seven ascending fifths from C (the inverse is C♭) |
ThePythagorean diatonic semitone has a ratio of 256/243 (playⓘ), and is often called thePythagorean limma. It is also sometimes called thePythagorean minor semitone. It is about 90.2 cents.
It can be thought of as the difference between threeoctaves and fivejust fifths, and functions as adiatonic semitone in aPythagorean tuning.
ThePythagorean chromatic semitone has a ratio of 2187/2048 (playⓘ). It is about 113.7cents. It may also be called thePythagorean apotome[14][15][16] or thePythagorean major semitone. (SeePythagorean interval.)
It can be thought of as the difference between four perfectoctaves and sevenjust fifths, and functions as achromatic semitone in aPythagorean tuning.
The Pythagorean limma and Pythagorean apotome are only aPythagorean comma apart, and may be consideredenharmonic equivalents, in contrast to the diatonic and chromatic semitones inmeantone temperament and 5-limitjust intonation, which are farther apart.
Meantone temperaments are generated by a sequence oftemperedperfect fifths of thesame size, similarly to Pythagorean tuning, where the perfect fifths are pure instead. Likewise, the diatonic and chromatic semitones depend on the size of the fifth, where the diatonic semitone is derived by descending 5 fifths, and the chromatic semitone is derived by ascending 7 fifths. These are typically of different sizes, with the exception of12 equal temperament, discussed below. Unlike in Pythagorean tuning, the chromatic semitone is usually smaller than the diatonic.
In the commonquarter-comma meantone, the chromatic and diatonic semitones are 76.0 and 117.1 cents wide respectively. They differ by the lesserdiesis of ratio 128:125 or 41.1 cents.
Quarter-comma meantone is largely used to create a 12-tone tuning, usually via a sequence of fifths from E♭ to G♯. There is a break in thecircle of fifths in this tuning; the interval between G♯ and E♭ does not represent a perfect fifth, but rather adiminished sixth. Such intervals are referred to aswolf intervals. Ascending by a semitone from an arbirary pitch, the resulting interval depends on this break: diatonic semitones derive from a descending chain of 5 fifths that does not cross the break, and chromatic semitones come from one that does, where the note is instead derived by an ascending chain of 7 fifths.
| 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 | |||||||||||||||||||
Extended tunings 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[dubious –discuss] flexible of these, which makes an unbroken circle of 31 fifths, allowing the choice of semitone to be made for any pitch.
12-tone equal temperament is a form of meantone tuning in which the diatonic and chromatic semitones are exactly the same. Each semitone is equal to one twelfth of an octave. This is a ratio of21/12 (approximately 1.05946), or 100 cents, and is 11.7 cents narrower than the 16:15 ratio (its most common form injust intonation,discussed below).
There are many approximations,rational or otherwise, to the equal-tempered semitone. To cite a few:
There are many forms ofwell temperament, 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 adiatonic andchromatic semitone in the tuning. Well temperament was constructed so thatenharmonic 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, eachkey had a slightly different sonic color or character, beyond the limitations of conventional notation.
A minor second injust intonation typically corresponds to a pitchratio of 16:15 (playⓘ) or 1.0666... (approximately 111.7 cents), called thejust diatonic semitone.[17] This is a practical just semitone, since it is the interval that occurs twice within the diatonic scale between a:
The 16:15 just minor second arises inPtolemy's intense diatonic scale. Given amajor scale starting on C, it occurs between B & C and E & F, and is "the sharpest dissonance found in the scale".[18]Play B & Cⓘ
An "augmented unison" (sharp) in just intonation is a different, smaller semitone, with frequency ratio 25:24 (playⓘ) or 1.0416... (approximately 70.7 cents). It is the interval between amajor third (5:4) and a minor third (6:5). In fact, it is the spacing between the minor and major thirds, sixths, and sevenths (but not necessarily the major and minor second). ComposerBen Johnston used a sharp (♯) to indicate a note is raised 70.7 cents, or a flat (♭) to indicate a note is lowered 70.7 cents.[19] (This is the standard practice for just intonation, but not for all other microtunings.)
Two other kinds of semitones are produced by 5 limit tuning. Achromatic scale defines 12 semitones as the 12 intervals between the 13 adjacent notes, spanning a full octave (e.g. from C4 to C5). The 12 semitones produced by acommonly used version of 5 limit tuning have four different sizes, and can be classified as follows:
The most frequently occurring semitones are the just ones (S3, 16:15, andS1, 25:24): S3 occurs at 6 short intervals out of 12,S1 3 times,S2 twice, andS4 at only one interval (if diatonic D♭ replaces chromatic D♭ and sharp notes are not used).
The smaller chromatic and diatonic semitones differ from the larger by thesyntonic 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 thediaschisma (2048:2025 or 19.6 cents), the outer differ by the greater diesis (648:625 or 62.6 cents).
In7 limit tuning there is theseptimal diatonic semitone of 15:14 (playⓘ) available in between the 5 limitmajor seventh (15:8) and the7 limit minor seventh /harmonic seventh (7:4). There is also a smallerseptimal chromatic semitone of 21:20 (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 theoristCowell, whilePartch used the latter as part ofhis 43 tone scale.
Under 11 limit tuning, there is a fairly commonundecimalneutral second (12:11) (playⓘ), but it lies on the boundary between the minor andmajor 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.
In 13 limit tuning, there is a tridecimal2/3 tone (13:12 or 138.57 cents) and tridecimal1/3 tone (27:26 or 65.34 cents).
In 17 limit just intonation, the major diatonic semitone is 15:14 or 119.4 cents (Playⓘ), and the minor diatonic semitone is 17:16 or 105.0 cents,[20][21] and septendecimal limma is 18:17 or 98.95 cents.
Though the namesdiatonic andchromatic are often used for these intervals, their musical function is not the same as the meantone semitones. For instance, 15:14 would usually be written as an augmented unison, functioning as thechromatic counterpart to adiatonic 16:15. These distinctions are highly dependent on the musical context, and just intonation is not particularly well suited to chromatic use (diatonic semitone function is more prevalent).
19-tone equal temperament distinguishes between the chromatic and diatonic semitones; in this tuning, the chromatic semitone is one step of the scale (play 63.2 centsⓘ), and the diatonic semitone is two (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 while72-ET uses 4 (play 66.7 centsⓘ) and 7 (play 116.7 centsⓘ) 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).
digitized 26 Feb 2008; Harvard University
... the25/24 ratio is the sharp (♯) ratio ... this raises a note approximately 70.6 cents.(p109)
| Twelve- semitone (post-Bach Western) |
| ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Other tuning systems |
| ||||||||||||||
| Other intervals |
| ||||||||||||||
| Fundamentals |  | |
|---|---|---|
| Permutations | ||
| Notable composers | ||
| Related articles | ||
