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Twelve-tone equal temperament (12 TET) is obtained by making all semitones the same size, with each equal to one-twelfth of an octave; i.e. with ratios 12 √ 2 : 1. Relative to Pythagorean tuning , it narrows the perfect fifths by about 2 cents or 1 / 12 th of a Pythagorean comma to give a frequency ratio of 2 7 / 12 : 1 {\displaystyle ...
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This phenomenon gives rise to infinite shades of key-colors, which are lost in the modern standard version: 12-tone equal temperament (12-TET). Unlike meantone temperament, which alters the fifth to "temper out" the syntonic comma, 12-TET tempers out the Pythagorean comma, thus creating a cycle of fifths that repeats itself exactly after 12 steps.
12-tone Pythagorean temperament is based on a sequence of perfect fifths, each tuned in the ratio 3:2, the next simplest ratio after 2:1 (the octave). Starting from D for example (D-based tuning), six other notes are produced by moving six times a ratio 3:2 up, and the remaining ones by moving the same ratio down:
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 ...
This tuning uses mostly pure fifths, as in Pythagorean tuning, but each of the fifths C–G, G–D, D–A and B–F ♯ is made smaller, i.e. tempered by 1 / 4 comma. No matter if the Pythagorean comma or the syntonic comma is used, the resulting tempered fifths are for all practical purposes the same as meantone temperament fifths.
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).
In terms of frequency ratios, in order to close the circle of fifths, the product of the fifths' ratios must be 128 (since the twelve fifths, if closed in a circle, span seven octaves exactly; an octave is 2:1, and 2 7 = 128), and if f is the size of a fifth, 128 : f 11, or f 11 : 128, will be the size of the wolf.