User:Zhenlige/EDO impressions: Difference between revisions

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

*...

*[[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. 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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*[[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.

*[[38edo|38]]: 19edo with neutrals. Near pure [[11/9]]. The acceptable error of 19edo really becomes a problem at this size.

*...

*[[38edo|38]]: 19edo with neutrals. Near pure [[11/9]]. The acceptable error of 19edo becomes really a problem at this size.

*[[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]].

*...

*[[41edo|41]]: Prime octave and highly composite fifth. 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.

*...

*[[53edo|53]]: Almost just [[3/2]], and accurate [[7-limit]]. Purely an approximation of JI.

*[[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]].

*...

*[[72edo|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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*[[77edo|77]]: Good for [[valentine]] and accurate [[boethius]].

*...

*[[99edo|99]]: Efficient near-[[Logarithmic approximants#Argent temperament|argent]] EDO. Suggests slight compression.

*[[99edo|99]]: Efficient near-[[Logarithmic approximants#Argent temperament|argent]] EDO. Suggests slight compression. Good for [[hemififths]].

*...

*[[118edo|118]]: The relationship of 53-118-171edo for [[schismatic]] is similar to 12-19-31edo for meantone. 53 and 12 are the simplest reasonable EDO 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.

@@ Line 26: / Line 26: @@
 *[[26edo|26]]: A stack of [[7/4]]. Incomplete [[130edo]].
 *...
-*[[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. 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 32: / Line 32: @@
 *[[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.
+*[[38edo|38]]: 19edo with neutrals. Near pure [[11/9]]. The acceptable error of 19edo really becomes a problem at this size.
 *...
-*[[38edo|38]]: 19edo with neutrals. Near pure [[11/9]]. The acceptable error of 19edo becomes really a problem at this size.
+*[[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]].
-*...
-*[[41edo|41]]: Prime octave and highly composite fifth. 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.
 *...
-*[[53edo|53]]: Almost just [[3/2]], and accurate [[7-limit]]. Purely an approximation of JI.
+*[[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]].
 *...
 *[[72edo|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.
@@ Line 45: / Line 44: @@
 *[[77edo|77]]: Good for [[valentine]] and accurate [[boethius]].
 *...
-*[[99edo|99]]: Efficient near-[[Logarithmic approximants#Argent temperament|argent]] EDO. Suggests slight compression.
+*[[99edo|99]]: Efficient near-[[Logarithmic approximants#Argent temperament|argent]] EDO. Suggests slight compression. Good for [[hemififths]].
 *...
 *[[118edo|118]]: The relationship of 53-118-171edo for [[schismatic]] is similar to 12-19-31edo for meantone. 53 and 12 are the simplest reasonable EDO 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.