User:Zhenlige/EDO impressions: Difference between revisions

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*[[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]]: ~~Tritones~~.

*[[2edo|2]]: Equally-divided tritones.

*[[3edo|3]]: 12edo augmented chords.

*[[4edo|4]]: 12edo diminished seventh chords.

*[[5edo|5]]: Equalized [[2L 3s|pentatonic]] scale. Kinda familiar but everything is warped. The first EDO containing an interval that roughly resembles [[3/2]].

*[[5edo|5]]: Equalized [[2L 3s|pentatonic]] scale. Kinda familiar but everything is warped. The first EDO containing an interval that roughly resembles [[3/2]]. Not very noticeable harmonically.

*[[6edo|6]]: Incomplete [[12edo]].

*...

*[[7edo|7]]: Equalized [[5L 2s|diatonic]] scale. Similar to 5edo.

*[[8edo|8]]: Incomplete [[24edo]].

*[[9edo|9]]: A subset of [[ennealimmal]].

*[[10edo|10]]: A stack of [[13/8]]. ~~Subset~~ of [[130edo]] and [[270edo]].

*[[10edo|10]]: A stack of [[13/8]]. A subset of [[130edo]] and [[270edo]].

*[[11edo|11]]: Incomplete [[22edo]].

*[[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, but inaccurate [[5/4]] and worse [[7/4]]. Suitable for symmetric scales. Easy to make [[../12neji|accurate NEJIs]]. Its 2.3.17.19 subgroup really deserves exploration.

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*[[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]]: A circle of fifths in [[34edo]]. Interesting sharp fifths. The fact that its thirds do not approximate any simple ratios well is a pity. (or benefit? I don't know)

*...

*[[18edo|18]]: Incomplete [[36edo]].

*[[19edo|19]]: Very different tradeoffs from 12edo. 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]].

*[[20edo|20]]: Does anyone really think an inconsistent 27 can be used with a 3 or 9?

*[[20edo|20]]: The fact that [[41edo]] is good indicates that 20- and 21edo are probably bad. Does anyone really think an inconsistent 27 can be used with a 3 or 9?

*...

*[[22edo|22]]: The simplest non-meantone EDO with reasonable 5-limit. Good [[superpyth]] and [[porcupine]] tuning. The upper bound of a good fifth.

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*...

*[[26edo|26]]: A stack of [[7/4]]. Incomplete [[130edo]].

*[[27edo|27]]: Worse than both 12- and 22edo for 7-limit. The fact that [[53edo]] is good indicates that 26- and 27edo are probably bad.

*...

*[[31edo|31]]: Ideal for pure-octave [[meantone]], combining lots of 11-limit extensions in a single tuning. IMO the best meantone EDO. For other temperaments its flat fifth may be a drawback.

*[[31edo|31]]: Ideal for pure-octave [[meantone]], combining lots of 11-limit extensions in a single tuning. Also [[valentine]]. IMO the best meantone EDO. For other temperaments its flat fifth may be a drawback.

*...

*[[34edo|34]]: 17edo with prime [[5/1|5]], but no [[7/1|7]]. Also a stretched [[Carlos Gamma]].

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*[[41edo|41]]: Prime octave and highly composite fifth, opposite from [[12edo]], thus good for fifth-dividing temperaments. Good for [[magic]]. The [[Kite guitar]] shows its elegance, with many simple intervals equidistantly spaced. Also good [[garibaldi]] and [[neutral]].

*...

*[[50edo|50]]: ~~Good flatter~~ meantone, but I usually ~~just go for~~ [[golden meantone]] at this ~~level of precision~~.

*[[46edo|46]]: Efficient [[gentle region|neogothic]] EDO.

*...

*[[50edo|50]]: Flatter meantone than [[31edo]], but I usually use [[golden meantone]] (with slight octave stretching) for this range.

*...

*[[53edo|53]]: Almost just [[3/2]], and accurate [[7-limit]]. Purely an approximation of JI and not many efficient temperaments are supported. Good for 5-limit [[schismatic]] with occasional [[garibaldi]] [[7/1|7]].

@@ 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]]: Tritones.
+*[[2edo|2]]: Equally-divided tritones.
 *[[3edo|3]]: 12edo augmented chords.
 *[[4edo|4]]: 12edo diminished seventh chords.
-*[[5edo|5]]: Equalized [[2L 3s|pentatonic]] scale. Kinda familiar but everything is warped. The first EDO containing an interval that roughly resembles [[3/2]].
+*[[5edo|5]]: Equalized [[2L 3s|pentatonic]] scale. Kinda familiar but everything is warped. The first EDO containing an interval that roughly resembles [[3/2]]. Not very noticeable harmonically.
 *[[6edo|6]]: Incomplete [[12edo]].
-*...
+*[[7edo|7]]: Equalized [[5L 2s|diatonic]] scale. Similar to 5edo.
+*[[8edo|8]]: Incomplete [[24edo]].
 *[[9edo|9]]: A subset of [[ennealimmal]].
-*[[10edo|10]]: A stack of [[13/8]]. Subset of [[130edo]] and [[270edo]].
+*[[10edo|10]]: A stack of [[13/8]]. A subset of [[130edo]] and [[270edo]].
 *[[11edo|11]]: Incomplete [[22edo]].
 *[[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, but inaccurate [[5/4]] and worse [[7/4]]. Suitable for symmetric scales. Easy to make [[../12neji|accurate NEJIs]]. Its 2.3.17.19 subgroup really deserves  exploration.
@@ Line 15: / Line 16: @@
 *[[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]]: A circle of fifths in [[34edo]]. Interesting sharp fifths. The fact that its thirds do not approximate any simple ratios well is a pity. (or benefit? I don't know)
-*...
+*[[18edo|18]]: Incomplete [[36edo]].
 *[[19edo|19]]: Very different tradeoffs from 12edo. 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]].
-*[[20edo|20]]: Does anyone really think an inconsistent 27 can be used with a 3 or 9?
+*[[20edo|20]]: The fact that [[41edo]] is good indicates that 20- and 21edo are probably bad. Does anyone really think an inconsistent 27 can be used with a 3 or 9?
 *...
 *[[22edo|22]]: The simplest non-meantone EDO with reasonable 5-limit. Good [[superpyth]] and [[porcupine]] tuning. The upper bound of a good fifth.
@@ Line 25: / Line 26: @@
 *...
 *[[26edo|26]]: A stack of [[7/4]]. Incomplete [[130edo]].
+*[[27edo|27]]: Worse than both 12- and 22edo for 7-limit. The fact that [[53edo]] is good indicates that 26- and 27edo are probably bad.
 *...
-*[[31edo|31]]: Ideal for pure-octave [[meantone]], combining lots of 11-limit extensions in a single tuning. IMO the best meantone EDO. For other temperaments its flat fifth may be a drawback.
+*[[31edo|31]]: Ideal for pure-octave [[meantone]], combining lots of 11-limit extensions in a single tuning. Also [[valentine]]. IMO the best meantone EDO. For other temperaments its flat fifth may be a drawback.
 *...
 *[[34edo|34]]: 17edo with prime [[5/1|5]], but no [[7/1|7]]. Also a stretched [[Carlos Gamma]].
@@ Line 36: / Line 38: @@
 *[[41edo|41]]: Prime octave and highly composite fifth, opposite from [[12edo]], thus good for fifth-dividing temperaments. Good for [[magic]]. The [[Kite guitar]] shows its elegance, with many simple intervals equidistantly spaced. Also good [[garibaldi]] and [[neutral]].
 *...
-*[[50edo|50]]: Good flatter meantone, but I usually just go for [[golden meantone]] at this level of precision.
+*[[46edo|46]]: Efficient [[gentle region|neogothic]] EDO.
+*...
+*[[50edo|50]]: Flatter meantone than [[31edo]], but I usually use [[golden meantone]] (with slight octave stretching) for this range.
 *...
 *[[53edo|53]]: Almost just [[3/2]], and accurate [[7-limit]]. Purely an approximation of JI and not many efficient temperaments are supported. Good for 5-limit [[schismatic]] with occasional [[garibaldi]] [[7/1|7]].