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A semitone, also called a minor second, half step, or a half tone, 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]
is the smallest musical interval commonly used in Western tonal music,Miller, Michael. The Complete Idiot's Guide to Music Theory, 2nd ed. Indianapolis,: Alpha, 2005. . p. 19. and it is considered the most dissonant when sounded harmonically.
It is defined as the interval between two adjacent notes in a chromatic 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.
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 different , 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 Enharmonic 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 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.
. Here, middle C is followed by D, which is a tone 100 cents sharper than C, and then by both tones together.
Melody, this interval is very frequently used, and is of particular importance in cadences. In the perfect and deceptive cadences it appears as a resolution of the leading-tone 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.
Harmony, 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 chords.
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 music period, such as Modest Mussorgsky's Ballet of the Unhatched Chicks. More recently, the music to the movie Jaws exemplifies the minor second.
Melody, 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).
Harmony, augmented unisons are quite rare in tonal repertoire. In the example to the right, Franz 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.
In addition to this kind of usage, harmonic augmented unisons are frequently written in modern works involving tone clusters, such as Iannis Xenakis' Evryali for piano solo.
Though it would later become an integral part of the musical cadence, 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 to a unison, or an occursus having two notes at a major 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 remainder between the perfect fourth and the ditone ." 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."Carl Dahlhaus, trans. Gjerdingen, Robert O. Studies in the Origin of Harmonic Tonality. Princeton University Press: Princeton, 1990. .
However, beginning in the 13th century cadences 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). By the 16th century, the semitone had become a more versatile interval, sometimes even appearing as an augmented unison in very chromatic passages. Music semiotics, in the 16th century the repeated melodic semitone became associated with weeping, see: chromatic fourth, lament bass, and pianto.
By the Baroque music (1600 to 1750), the tonality harmonic framework was fully formed, and the various musical functions of the semitone were rigorously understood. Later in this period the adoption of 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 music period, and though it was used more frequently as the language of tonality became more chromatic in the Romantic music 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.
The chromatic semitone is usually smaller than the diatonic. In the common quarter-comma meantone, tuned as a cycle of tempered Perfect fifth 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 | |||||||||||||||||||
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.
All diatonic intervals can be expressed as an equivalent number of semitones. For instance a major sixth equals nine semitones.
There are many approximations, Rational number or otherwise, to the equal-tempered semitone. To cite a few:
For more examples, see Pythagorean and Just systems of tuning below.
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.
It can be thought of as the difference between three octaves and five perfect fifth, and functions as a diatonic semitone 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. .Hermann von Helmholtz (1885). On the Sensations of Tone as a Physiological Basis for the Theory of Music, p. 454.Benson, Dave (2006). Music: A Mathematical Offering, p. 369. . or the Pythagorean major semitone. ( See Pythagorean interval.)
It can be thought of as the difference between four perfect and seven perfect fifth, and functions as a chromatic semitone in a Pythagorean tuning.
The Pythagorean limma and Pythagorean apotome are enharmonic equivalents (chromatic semitones) and only a Pythagorean comma apart, in contrast to diatonic and chromatic semitones in meantone temperament and 5-limit just intonation.
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" (sharp) in just intonation is a different, smaller semitone, with frequency ratio 25:24 () or 1.0416... (approximately 70.7 cents). It is the interval between a major 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). Composer Ben 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. (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. A chromatic scale defines 12 semitones as the 12 intervals between the 13 adjacent notes, spanning a full octave (e.g. from C to C). The 12 semitones produced by a commonly 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 (, 16:15, and , 25:24): S occurs at 6 short intervals out of 12, 3 times, twice, and 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 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).
Under 11 limit tuning, there is a fairly common undecimal neutral second (12:11) (), 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.
In 13 limit tuning, there is a tridecimal tone (13:12 or 138.57 cents) and tridecimal 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, 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 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 use (diatonic semitone function is more prevalent).
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).
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