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For the ordinary diatonic scales described here, the T-s are tones and the s-s are semitones which are half, or approximately half the size of the tone.But in the more general regular diatonic tunings, the two steps can be of any relation within the range between T = 171.43 ¢ (for s = T at the high extreme) and T = 240 ¢ (for s = 0 at the low extreme) in musical cents (fifth, p5, between 685 ...
If the generators are all the prime numbers up to a given prime p, we have what is called p-limit just intonation.Sometimes some irrational number close to one of these primes is substituted (an example of tempering) to favour other primes, as in twelve tone equal temperament where 3 is tempered to 2 19 ⁄ 12 to favour 2, or in quarter-comma meantone where 3 is tempered to 2 4 √ 5 to favor ...
17-ET is the tuning of the regular diatonic tuning in which the tempered perfect fifth is equal to 705.88 cents, as shown in Figure 1 (look for the label "17-TET"). History and use [ edit ]
31 EDO on the regular diatonic tuning continuum at p5 = 696.77 cents [1]. In music, 31 equal temperament, 31 ET, which can also be abbreviated 31 TET (31 tone ET) or 31 EDO (equal division of the octave), also known as tricesimoprimal, is the tempered scale derived by dividing the octave into 31 equally-proportioned steps (equal frequency ratios).
The most widely known example of this is the use of equal temperament to address problems of older temperaments, allowing for consistent tuning of keyboard and fretted instruments and enabling musical composition in, and modulation among, the various keys.
For other tuning schemes, refer to musical tuning. This list of frequencies is for a theoretically ideal piano. On an actual piano, the ratio between semitones is slightly larger, especially at the high and low ends, where string stiffness causes inharmonicity, i.e., the tendency for the harmonic makeup of each note to run sharp.
For example, Easley Blackwood, author of The Structure of Recognizable Diatonic Tunings (1985), wrote many etudes in equal temperament systems ranging from 12 to 24 tones. These etudes bring out connections and resemblances to twelve-tone music as well as various xenharmonic characteristics, reflected in Twelve Microtonal Etudes for Electronic ...
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).