31 equal temperament
In music, 31 equal temperament, 31-ET, which can also be abbreviated 31-TET, 31-EDO (equal division of the octave), also known as tricesimoprimal, is the tempered scale derived by dividing the octave into 31 equal-sized steps (equal frequency ratios).
Play Each step represents a frequency ratio of 21/31, or 38.71 cents (
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31-ET is a very good approximation of quarter-comma meantone temperament. More generally, it is a tuning of the syntonic temperament in which the tempered perfect fifth is equal to 696.77 cents, as shown in Figure 1. On an isomorphic keyboard, the fingering of music composed in 31-ET is precisely the same as it is in any other syntonic tuning (such as 12-ET), so long as the notes are spelled properly -- that is, with no assumption of enharmonicity.
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