User:Zhenlige/EDO impressions

When talking about accuracy, assuming harmonic overtone.

• 0: A fancy way to say “pitchless”.
• 1: Equivalent to 2-limit JI. Not much about harmony. Possibly useful for a transition between different tunings.
• 2:
• 3: 12edo augmented chords.
• 4: 12edo diminished seventh chords.
• 5:
• 6: Incomplete 12edo.
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• 9: A subset of ennealimmal.
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• 11: Incomplete 22edo.
• 12: It deserves its position. A good tuning for almost all types of music, though not perfect. Very excellent 3/2 as well as prime 17 and 19 for its size. Easy to make accurate NEJIs.
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• 15: Better than it seems to be, tho still rough. A heavily stretched Carlos Alpha scale.
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• 17: Interesting sharp fifths.
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• 19: Meantone, but with a too flat fifth. Strangely large minor 2nds. Also a compressed Carlos Beta. 31edo is more preferable. The lower bound of a good fifth.
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• 22: Good superpyth and porcupine tuning. The higher bound of a good fifth.
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• 24: 12edo with neutral intervals. Good for prime 11. Accurate in subgroup 2.3.11.17.19.
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• 31: Ideal for pure-octave meantone, combining lots of 11-limit extensions in a single tuning. For other temperaments its flat fifth is a drawback.
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• 34: 17edo with prime 5. Also a stretched Carlos Gamma.
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• 36: Good for 2.3.7.13.17.19.23.29 subroup. Otherwise incomplete 72edo.
• 37: Everything but prime 3. Maybe interesting though.
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• 50: Good flatter meantone, but I usually just go for golden meantone at this level of precision.
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• 53: Almost just 3/2, and accurate 7-limit. Purely an approximation of JI.
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• 72: An excellent extension of 12- and 24edo. The relative error is within 1/3 steps for even large primes except a few including 13, 53 and 59. Suitable for octave stretching in 17-limit.
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