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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. For humans, a single cent is too small ...
The Pythagorean A ♭ (at the left) is at 792 cents, G ♯ (at the right) at 816 cents; the difference is the Pythagorean comma. Equal temperament by definition is such that A ♭ and G ♯ are at the same level. 1 ⁄ 4-comma meantone produces the "just" major third (5:4, 386 cents, a syntonic comma lower than the Pythagorean one of 408 cents).
For example, the just interval 7/6 may be referred to as a subminor third, since it is ~267 cents wide, which is narrower than a minor third (300 cents in 12-TET, ~316 cents for the just interval 6/5), or as the septimal minor third, since it is a 7-limit interval. These names refer just to the individual interval's size, and the interval ...
A cent is a measure of interval size. It is logarithmic in the musical frequency ratios. The octave is divided into 1200 steps, 100 cents for each semitone. Cents are often used to describe how much a just interval deviates from 12 TET. For example, the major third is 400 cents in 12 TET, but the 5th harmonic, 5:4 is 386.314 cents. Thus, the ...
A just perfect fifth has a size of 3:2 (about 701.96 cents), and four of them are equal to 81:16 (about 2807.82 cents). A just major third has a size of 5:4 (about 386.31 cents), and one of them plus two octaves (4:1 or exactly 2400 cents) is equal to 5:1 (about 2786.31 cents). The difference between these is the syntonic comma.
Each semitone is equal to one twelfth of an octave. This is a ratio of 2 1/12 (approximately 1.05946), or 100 cents, and is 11.7 cents narrower than the 16:15 ratio (its most common form in just intonation, discussed below). All diatonic intervals can be expressed as an equivalent number of semitones. For instance a major sixth equals nine ...
A narrower undecimal major fourth is found at 537 cents (the ratio 15:11). 31 equal temperament has an interval of 542 cents, which lies in between the two types of undecimal major fourth. The term may also be applied to the "comma-deficient major fourth" (or "chromatic major fourth" [3]), which is the ratio 25:18, or 568.72 cents (F ♯). [4]
22-TET contains an interval of 54.55 cents, slightly wider than a quarter-tone, whereas 53-TET has an interval of 45.28 cents, slightly smaller. 72-TET also has equally tempered quarter-tones, and indeed contains three quarter-tone scales, since 72 is divisible by 24.