Semitone
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♯).
Harmonically, the interval usually occurs as some form of dissonance or a nonchord tone that is not part of the functional harmony.
This kind of usage of the minor second appears in many other works of the Romantic period, such as Modest Mussorgsky's Ballet of the Unhatched Chicks.
(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).
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.
The various modal scales of medieval music theory were all based upon this diatonic pattern of tones and semitones.
"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
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, and pianto.
By the Baroque era (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 temperaments for instrumental tuning and the more frequent use of enharmonic equivalences increased the ease with which a semitone could be applied.
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.
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.
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.
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.
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.
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.
It can be thought of as the difference between four perfect octaves and seven just fifths, and functions as a chromatic semitone in a Pythagorean tuning.
A minor second in just intonation typically corresponds to a pitch ratio of 16:15 (playⓘ) or 1.0666... (approximately 111.7 cents), called the just diatonic semitone.
[8] 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).
A chromatic 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 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 (S3, 16:15, and S1, 25:24): S3 occurs at 6 short intervals out of 12, S1 3 times, S2 twice, and S4 at only one interval (if diatonic D♭ replaces chromatic D♭ and sharp notes are not used).
Both are more rarely used than their 5 limit neighbours, although the former was often implemented by theorist Cowell, while Partch used the latter as part of his 43 tone scale.
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).
