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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.
To go from A 4 up two semitones (one whole tone) to B 4, multiply 440 twice by the twelfth root of two (or once by the sixth root of two, approximately 1.122462). To go from A 4 up three semitones to C 5 (a minor third ), multiply 440 Hz three times by the twelfth root of two (or once by the fourth root of two, approximately 1.189207).
Chromatic scale: every key of one octave on the piano keyboard. 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.
A semitone is any interval between two adjacent notes in a chromatic scale, a whole tone is an interval spanning two semitones (for example, a major second), and a tritone is an interval spanning three tones, or six semitones (for example, an augmented fourth).
Example of piano tone clusters. The clusters in the upper staff—C ♯ D ♯ F ♯ G ♯ —are four successive black keys. The last two bars, played with overlapping hands, are a denser cluster. A tone cluster is a musical chord comprising at least three adjacent tones in a scale.
12-tone equal temperament chromatic scale on C, one full octave ascending, notated only with sharps. Play ascending and descending ⓘ. 12 equal temperament (12-ET) [a] 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).
Quarter tone on C. A quarter tone is a pitch halfway between the usual notes of a chromatic scale or an interval about half as wide (orally, or logarithmically) as a semitone, which itself is half a whole tone. Quarter tones divide the octave by 50 cents each, and have 24 different pitches.
The cent is a logarithmic unit of measure used for musical intervals. Twelve-tone equal temperament divides the octave into 12 semitones of 100 cents each. Typically, cents are used to express small intervals, to check intonation, or to compare the sizes of comparable intervals in different tuning systems.