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| 1 | +# source https://en.wikipedia.org/wiki/Quarter-comma_meantone and https://it.wikipedia.org/wiki/Temperamento_mesotonico#La_scala_diatonica |
| 2 | +# The following is a list of 12 frequencies ratios for the chromatic scale of the chosen key |
| 3 | +# Optionally, after a comma, the corresponding value in cents can be specified, which will be used as a check |
| 4 | + |
| 5 | +# T = sqrt(5) / 2 ~ 1.118 # ratio of most whole tones |
| 6 | +# S = 8 / sqrt(sqrt(5 ** 5)) = |
| 7 | +# = 8 / (5 * sqrt(sqrt(5))) ~ 1.070 # ratio of the diatonic semitone (greater) |
| 8 | +# X = 5 ** (7/4) / 16 = |
| 9 | +# = 5 * sqrt(sqrt(125)) / 16 ~ 1.045 # ratio of the chromatic semitone (lesser) |
| 10 | +# P = S * T ** 3 = |
| 11 | +# = (8 / (5 * sqrt(sqrt(5)))) * |
| 12 | +# * (5 * sqrt(5) / 8) = |
| 13 | +# = sqrt(5) / sqrt(sqrt(5)) = |
| 14 | +# = sqrt(sqrt(5)) ~ 1.495 # ratio of most fifths |
| 15 | + |
| 16 | +1 , 0 # (tonic) |
| 17 | +5 * sqrt(sqrt(125)) / 16, 76 # X = chromatic semitone = |
| 18 | + # = augmented first |
| 19 | +sqrt(5) / 2 , 193 # T = whole tone = |
| 20 | + # = second |
| 21 | +4 * sqrt(sqrt(5)) / 5 , 310 # T * S = sqrt(5) * 8 / (2 * 5 * sqrt(sqrt(5))) = |
| 22 | + # = 4 * sqrt(sqrt(5)) / 5 = |
| 23 | + # = whole tone and diatonic semitone = |
| 24 | + # = minor third |
| 25 | +5/4 , 386 # T ** 2 = two whole tones = |
| 26 | + # = major third |
| 27 | +2 / sqrt(sqrt(5)) , 503 # S * T ** 2 = 5 * 8 / (4 * 5 * sqrt(sqrt(5))) = |
| 28 | + # = 2 whole tones and 1 diatonic semitone = |
| 29 | + # = forth |
| 30 | +5 * sqrt(5) / 8 , 580 # T ** 3 = 3 whole tones = |
| 31 | + # = augmented forth |
| 32 | +sqrt(sqrt(5)) , 697 # P = fifth |
| 33 | +25 / 16 , 773 # P * X = sqrt(sqrt(5)) * 5 * sqrt(sqrt(125)) / 16 = |
| 34 | + # = 25 / 16 = |
| 35 | + # = a fifth and a chromatic semitone = |
| 36 | + # = augmented fifth |
| 37 | +sqrt(sqrt(125)) / 2 , 890 # P * T = fifth and a whole tone = |
| 38 | + # = sixth |
| 39 | +4 * sqrt(5) / 5 , 1007 # P * T * S = sqrt(sqrt(5)) * sqrt(5) * 8 / (2 * 5 * sqrt(sqrt(5))) = |
| 40 | + # = 4 * sqrt(5) / 5 = |
| 41 | + # = fifth and a whole tone and a diatonic semitone = |
| 42 | + # = diminished seventh |
| 43 | +5 * sqrt(sqrt(5)) / 4 , 1083 # P * T ** 2 = fifth and two whole tones = |
| 44 | + # = seventh |
| 45 | +# 2 , 1200 # octave (automatically assumed by temperanotes) |
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