Semitone
Semitones are the smallest class of interval commonly used in Western music, and are among the most dissonant when sounded harmonically. The term refers to the interval between two adjacent notes in a 12-tone scale, visually seen on a keyboard as the distance between two adjacent keys. For example, C is adjacent to D; the interval between them is a semitone.
In a 12-note approximately equally divided scale, an appropriate number of semitones can realize a certain interval.
In music theory, a distinction is made between a diatonic semitone, or minor second and a chromatic semitone or augmented unison. These are enharmonically equivalent only if twelve-tone equal temperament is used; for example,
they are not the same size in Pythagorean tuning, where the diatonic semitone is distinguished from the larger chromatic semitone, or in quarter-comma meantone temperament, where the diatonic semitone is larger instead. See for more details about this terminology.
In twelve-tone equal temperament, all semitones are equal in size. In other tuning systems, "semitone" refers to a family of intervals that may vary both in size and name. 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.
Minor second
The minor second occurs in the major scale, between the third and fourth degree, and fa, and between the seventh and eighth degree and do. It is also called the diatonic semitone because it occurs between steps in the diatonic scale. The minor second is abbreviated m2. Its inversion is the major seventh.. 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 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.
Harmonically, 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.
File:Bach minor second smaller.png|thumb|center|400px|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.
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's "Ballet of the Unhatched Chicks" from Pictures at an Exhibition. 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 major scale between B & C and E & F, and is "the sharpest dissonance found in the scale."Augmented unison
The augmented unison, augmented prime, or chromatic semitone is the interval between two notes on the same staff position that differ by one chromatic alteration. For example, the interval between B and B, or between C and C, is an augmented unison.In 12-tone equal temperament and well temperaments, the augmented unison is realized as a semitone, making it enharmonically equivalent to the minor second. In other systems such as Pythagorean tuning and quarter-comma meantone, the intervals are acoustically distinct.
The term, in its French form unisson superflu, appears to have been coined by Jean-Philippe Rameau in 1722, who also called this interval a minor semitone. Historically, this interval, like the tritone, is described as being "mi contra fa" and was associated with the.
Definition
In terms of regular temperament theory, the augmented unison can be derived by ascending 7 perfect fifths and descending 4 octaves.Occurrence
, 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..File:Liszt augmented unison.png|thumb|right|Franz Liszt's second Transcendental Étude, 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.
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.
Diminished unison
The term diminished unison or diminished prime is also found occasionally. It is found once in Rameau's writings, for example, as well as subsequent French, German, and English sources.Other sources reject the possibility or utility of the diminished unison on the grounds that any alteration to the unison increases its size, thus augmenting rather than diminishing it. The term is sometimes justified as a negative-numbered interval, and also in terms of violin double-stopping technique on analogy to parallel intervals found on other strings. 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.
History
The semitone appeared in the music theory of Greek antiquity as part of a diatonic or chromatic tetrachord, 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 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."
File:Marenzio solo e pensoso chromatic.png|thumb|Dramatic chromatic scale in the opening measures of Luca Marenzio's Solo e pensoso, ca. 1580 |450x450px
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. 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, 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. 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 as a source of cacophony in their music. 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 system used. Meantone temperaments have two distinct types of semitones, but in the exceptional case of equal temperament, there is only one. The unevenly distributed well temperaments 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
In meantone systems, the diatonic and chromatic semitones are typically of different sizes. This results because of the break in the circle of fifths 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 quarter-comma meantone, tuned as a sequence of tempered fifths from E to G, the chromatic and diatonic semitones are 76.0 and 117.1 cents wide respectively. They differ by the lesser diesis of ratio 128:125 or 41.1 cents.
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.