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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.
Just (black) major and parallel minor triad, compared to its equal temperament (gray) approximations, within the chromatic circle. Pythagorean tuning has been attributed to both Pythagoras and Eratosthenes by later writers, but may have been analyzed by other early Greeks or other early cultures as well.
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 musical tuning, a temperament is a tuning system that slightly compromises the pure intervals of just intonation to meet other requirements. Most modern Western musical instruments are tuned in the equal temperament system. Tempering is the process of altering the size of an interval by making it narrower or wider than pure.
In the quarter-tone scale, also called 24-tone equal temperament (24-TET), the quarter tone is 50 cents, or a frequency ratio of 24 √ 2 or approximately 1.0293, and divides the octave into 24 equal steps (equal temperament). In this scale the quarter tone is the smallest step.
Since the average size of the 12 fifths must equal exactly 700 cents (as in equal temperament), the other one must have a size of 700 − 11ε cents, which is about 678.495 cents (the wolf fifth). As shown in the table, the latter interval, although enharmonically equivalent to a fifth, is more properly called a diminished sixth ( d6 ).
The numbers above the harmonic indicate the difference – in cents – from equal temperament (rounded to the nearest integer). Blue notes are very flat and red notes are very sharp. Listeners accustomed to more tonal tuning, such as meantone and well temperaments, notice many other notes are "off".
Ascending by fifths in equal temperament leads to a return to the starting pitch class—starting with a C and ascending by fifths leads to another C after a certain number of iterations. This does not occur if an exact 3:2 ratio is used (just intonation). The adjustment made in equal temperament tuning is called the Pythagorean comma.
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