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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 ...
Pythagorean tuning also had a second problem, which non-extended meantone temperaments do not solve, which is the problem of modulation (see below), which is restricted because being limited to 12 pitches per octave results in a broken circle of fifths.
English: Graph showing the frequencies and value in cents of the notes of the equal-tempered diatonic scale tuned to concert pitch (A4 = 440Hz), starting with C1 and ending with C5 (middle C = C4). Vertical grid lines correspond to equal-tempered semitones.
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).
15-ET is the smallest tuning that matches the 11th harmonic at all and still has a usable perfect fifth, but its match to intervals utilizing the 11th harmonic is poorer than 22-ET, which also has more in-tune fifths and major thirds.
The whole chromatic scale (a subset of which is the diatonic scale), can be constructed by starting from a given base note, and increasing or decreasing its frequency by one or more fifths. This method is identical to Pythagorean tuning, except for the size of the fifth, which is tempered as explained above.
Solo tuning is a system of choosing the reeds for a diatonic wind instrument (such as a harmonica or accordion) to fit a pattern where blow notes repeat a sequence of C E G C (perhaps shifted to begin with E or with G) and draw notes follow a repeating sequence of D F A B (perhaps correspondingly shifted).
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.