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In music theory, the circle of fifths (sometimes also cycle of fifths) is a way of organizing pitches as a sequence of perfect fifths. Starting on a C, and using the standard system of tuning for Western music (12-tone equal temperament), the sequence is: C, G, D, A, E, B, F ♯ /G ♭, C ♯ /D ♭, G ♯ /A ♭, D ♯ /E ♭, A ♯ /B ♭, F ...
The Oxford Companion to Music describes three interrelated uses of the term "music theory": The first is the "rudiments", that are needed to understand music notation (key signatures, time signatures, and rhythmic notation); the second is learning scholars' views on music from antiquity to the present; the third is a sub-topic of musicology ...
In the case of Pythagorean tuning, all the fifths are 701.96 cents wide, in the exact ratio 3:2, except the wolf fifth, which is only 678.49 cents wide, nearly a quarter of a semitone flatter. If the notes G ♯ and E ♭ need to be sounded together, the position of the wolf fifth can be changed.
In music theory, a perfect fifth is the musical interval corresponding to a pair of pitches with a frequency ratio of 3:2, or very nearly so. In classical music from Western culture , a fifth is the interval from the first to the last of the first five consecutive notes in a diatonic scale . [ 2 ]
The frequency ratio of the semitone then becomes the twelfth root of two (12 √ 2 ≈ 1.059463, 100 cents). The tone is the sum of two semitone. Its ratio is the sixth root of two (6 √ 2 ≈ 1.122462, 200 cents). Equal temperament can be produced by a succession of tempered fifths, each of them with the ratio of 2 7 ⁄ 12 ≈ 1.498307, 700 ...
The terms quartal and quintal imply a contrast, either compositional or perceptual, with traditional harmonic constructions based on thirds: listeners familiar with music of the common practice period are guided by tonalities constructed with familiar elements: the chords that make up major and minor scales, all in turn built from major and minor thirds.
Interval class Play ⓘ.. In musical set theory, an interval class (often abbreviated: ic), also known as unordered pitch-class interval, interval distance, undirected interval, or "(even completely incorrectly) as 'interval mod 6'" (Rahn 1980, 29; Whittall 2008, 273–74), is the shortest distance in pitch class space between two unordered pitch classes.
In meantone temperament, this effect is even more pronounced (the fifth over the break in the circle is known as the Wolf interval, as its intense beating was likened to a "howling"). 53 equal temperament provides an extension of Pythagorean tuning, and 31 equal temperament is used nowadays to extend quarter-comma meantone.
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