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: Tritones.
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, but inaccurate 5/4 and worse 7/4. Suitable for symmetric scales. 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. The fact that its thirds do not approximate any simple ratios well is a pity. (or benefit? I don't know)
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19: Usable but imperfect for many temperaments. Meantone or magic, but with a too flat fifth. Strangely large minor 2nds. Also a compressed Carlos Beta. For meantone 31edo is more preferable, and for magic 41edo. The lower bound of a good fifth. Good as a subset of enneadecal.
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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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26: A stack of 7/4. Incomplete 130edo.
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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, but no 7. 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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41: Good for magic. The Kite guitar shows its elegance, with many simple intervals equidistantly spreaded. Also good garibaldi and neutral.
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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. Good for miracle. The relative error of primes is within 1/3 steps up to large primes except a few including 13, 53 and 59. Suitable for octave stretching in 17-limit.
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77: Good valentine and boethius.
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118: The relationship of 53-118-171edo for schismatic is similar to 12-19-31edo for meantone. 53 and 12 are the simplest with very mildly tempered fifths, 118 and 19 are better over all but a bit overtempered (outside 5-odd-limit diamond tradeoff), and 171 and 31 are ideal. So like 19, I won't use it much.
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171: Ideal for approximating 7-limit JI Good as schismatic, gammic, ennealimmal and enneadecal. At this size level, EDOs are more like free pitch, rather than either JI or a stable temperament.
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224: like 171 but with a slightly sharper (and closer to just) fifth, worse 7-limit but better 13-limit.

User:Zhenlige/EDO impressions

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