User:Zhenlige/EDO impressions: Difference between revisions

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Revision as of 18:24, 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: Tritones.
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. The fact that its thirds do not approximate any simple ratios well is a pity. (or benefit? I don't know)
...
19: Usable but imperfect for many temperaments. Meantone, but with a too flat fifth. Strangely large minor 2nds. Also a compressed Carlos Beta. For meantone 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.
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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.
...
41: Good for magic. The Kite guitar shows its elegance, with many simple intervals equidistantly spreaded.
...
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 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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171: Ideal for approximating 7-limit JI. At this size level, EDOs are more like free pitch, rather than either JI or a stable temperament.

@@ Line 2: / Line 2: @@
 *[[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.
-*[[2edo|2]]:
+*[[2edo|2]]: Tritones.
 *[[3edo|3]]: 12edo augmented chords.
 *[[4edo|4]]: 12edo diminished seventh chords.
@@ Line 15: / Line 15: @@
 *[[15edo|15]]: Better than it seems to be, tho still rough. A heavily stretched [[Carlos Alpha]] scale.
 *...
-*[[17edo|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.
+*[[17edo|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)
 *...
-*[[19edo|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.
+*[[19edo|19]]: Usable but imperfect for many temperaments. [[Meantone]], but with a too flat fifth. Strangely large minor 2nds. Also a compressed [[Carlos Beta]]. For meantone 31edo is more preferable. The lower bound of a good fifth.
 *...
 *[[22edo|22]]: Good [[superpyth]] and [[porcupine]] tuning. The higher bound of a good fifth.
@@ Line 25: / Line 25: @@
 *[[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]]: 17edo with prime [[5/1|5]]. Also a stretched [[Carlos Gamma]].
+*[[34edo|34]]: 17edo with prime [[5/1|5]], but no [[7/1|7]]. Also a stretched [[Carlos Gamma]].
 *...
 *[[36edo|36]]: Good for 2.3.7.13.17.19.23.29 subroup. Otherwise incomplete 72edo.
 *[[37edo|37]]: Everything but prime [[3/1|3]]. Maybe interesting though.
+*...
+*[[41edo|41]]: Good for [[magic]]. The [[Kite guitar]] shows its elegance, with many simple intervals equidistantly spreaded.
 *...
 *[[50edo|50]]: Good flatter meantone, but I usually just go for [[golden meantone]] at this level of precision.
@@ Line 34: / Line 36: @@
 *[[53edo|53]]: Almost just [[3/2]], and accurate [[7-limit]]. Purely an approximation of JI.
 *...
-*[[72edo|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.
+*[[72edo|72]]: An excellent extension of 12- and 24edo. 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.
 *...
 *[[77edo|77]]: Good [[valentine]] and [[boethius]].
+*...
+*[[171edo|171]]: Ideal for approximating 7-limit JI. At this size level, EDOs are more like free pitch, rather than either JI or a stable temperament.

User:Zhenlige/EDO impressions: Difference between revisions

Revision as of 18:24, 13 December 2024

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