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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 ...
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 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).
12 tone equal temperament chromatic scale on C, one full octave ascending, notated only with sharps. Play ascending and descending ⓘ. An equal temperament is a musical temperament or tuning system that approximates just intervals by dividing an octave (or other interval) into steps such that the ratio of the frequencies of any adjacent pair of notes is the same.
The twelve-tone technique—also known as dodecaphony, twelve-tone serialism, and (in British usage) twelve-note composition—is a method of musical composition.The technique is a means of ensuring that all 12 notes of the chromatic scale are sounded equally often in a piece of music while preventing the emphasis of any one note [3] through the use of tone rows, orderings of the 12 pitch classes.
In twelve-tone music and serialism complementation (in full, literal pitch class complementation) is the separation of pitch-class collections into complementary sets, each containing pitch classes absent from the other [2] or rather, "the relation by which the union of one set with another exhausts the aggregate". [3]
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 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.