User:Zhenlige/EDO impressions: Difference between revisions
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When talking about accuracy, assuming harmonic overtone. | |||
*[[0edo|0]]: A fancy way to say “pitchless”. | *[[0edo|0]]: A fancy way to say “pitchless”. | ||
*[[1edo|1]]: Equivalent to [[2-limit]] JI. Not much about harmony. Possibly useful for a transition between different tunings. | *[[1edo|1]]: Equivalent to [[2-limit]] JI. Not much about harmony. Possibly useful for a transition between different tunings. | ||
*[[2edo|2]]: | *[[2edo|2]]: | ||
*[[3edo|3]]: | *[[3edo|3]]: 12edo augmented chords. | ||
* | *[[4edo|4]]: 12edo diminished seventh chords. | ||
*[[5edo|5]]: | *[[5edo|5]]: | ||
*[[6edo|6]]: Incomplete 12edo. | *[[6edo|6]]: Incomplete 12edo. | ||
| Line 10: | Line 11: | ||
*... | *... | ||
*[[11edo|11]]: Incomplete 22edo. | *[[11edo|11]]: Incomplete 22edo. | ||
*[[12edo|12]]: It deserves its position. A good tuning for almost all music, | *[[12edo|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 [[17/1|17]] and [[19/1|19]] for its size. Easy to make [[../12neji|accurate NEJIs]]. | ||
*... | *... | ||
*[[15edo|15]]: Better than it seems to be, tho still rough. A heavily stretched [[Carlos Alpha]] scale. | *[[15edo|15]]: Better than it seems to be, tho still rough. A heavily stretched [[Carlos Alpha]] scale. | ||
| Line 23: | Line 24: | ||
*... | *... | ||
*[[31edo|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. | *[[31edo|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. | ||
*.. | *... | ||
*[[34edo|34]]: 17 with prime [[5/1|5]]. | *[[34edo|34]]: 17 with prime [[5/1|5]]. | ||
*... | *... | ||
Revision as of 03:11, 13 December 2024
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.
- ...
- 9: A subset of ennealimmal.
- ...
- 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.
- ...
- 15: Better than it seems to be, tho still rough. A heavily stretched Carlos Alpha scale.
- ...
- 17: Interesting sharp fifths.
- ...
- 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.
- ...
- 22: Good superpyth and porcupine tuning. The higher bound of a good fifth.
- ...
- 24: 12edo with neutral intervals. Good for prime 11. Accurate in subgroup 2.3.11.17.19.
- ...
- 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.
- ...
- 34: 17 with prime 5.
- ...
- 36: Good for 2.3.7.13.17.19.23.29 subroup. Otherwise incomplete 72edo.
- 37: Everything but prime 3. Maybe interesting though.
- ...
- 50: Good flatter meantone, but I usually just go for golden meantone at this level of precision.
- ...
- 53: Almost just 3/2, and accurate 7-limit. Purely an approximation of JI.
- ...
- 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.
- ...