Comparisons of similar tunings - Revision history

Ground at 04:16, 6 January 2026

2026-01-06T04:16:05Z

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 edo misses a relatively good approximation of prime 3 well but has accurate 5.7.11.13.(17).(19), whereas 57edo missed both 3 and 5 but has 7.11.13.17.19.23.29.37. For most purposes, 37edo has the advantage because it is significantly smaller and has a good 5, which simplifies the choices in how to approximate 4:5:6 and provides harmonic stability. Few composers tend to have much use for tempered approximations of primes above 13 anyway. However, 57edo also contains 19edo as a subset, which simplifies the somewhat difficult learning curve present in 37edo and offers equal or better stability than 37edo's best 4:5:6. Both tunings share the 2.7.11.13 Bossier temperament generated by a sharp 14/11.
-== 81, 86, 100, and 117edo ==
+== Contorted Dual-3 ==
 These are some of the recommendations for dual-3 systems with contortion, which have promising ~2.3.5 blackdye and ~2.3.7 scales.
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 !2.>3.5
 !2.>3.>5
 |-
 |81
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 |86
 |43x2
+|
+|
@@ Line 42: / Line 62: @@
 |100
 |25x4, 50x2
+|
+|

Ground: /* 37 and 57edo */

2026-01-06T04:04:10Z

37 and 57edo

← Older revision		Revision as of 04:04, 6 January 2026
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	22 and 27edo are comparable because both are good representations of Superpyth temperament, but neither is obviously better. 37 is the obvious edo for Ultrapyth, which is tuned similarly to 22edo due to Porcupine.		22 and 27edo are comparable because both are good representations of Superpyth temperament, but neither is obviously better. 37 is the obvious edo for Ultrapyth, which is tuned similarly to 22edo due to Porcupine.

	22edo has 5/4, 9/7, and 11/8; neutral seconds (Porcupine). It also supports Pajara.		For notable Superpyth approximations, 22edo has 5/4, 9/7, and 11/8; neutral seconds (Porcupine). It also supports Pajara. 27edo has 6/5, 7/4, and 13/8. It also supports Augene. Both of the two have 7/6.

	~~27edo has 6/5, 7/4, and 13/8~~		37edo has all 5.7.11.13 but the 3 is the sharpest of the set so 7/6 and 9/7 are bad, the patent val 81/80 is huge, but good unusual scales and temperaments are unusually abundant.

	~~Both have 7/6~~

	37edo has all 5.7.11.13 but the 3 is the sharpest so 7/6 and 9/7 are bad, the 81/80 is huge, but ~~there are a bunch of~~ unusual temperaments

	32edo is halfway between 27 and 37 with its melodically strong blackdye, but begins to leave Superpyth mappings behind in favor of Ultrapyth. It is generally lacking in LCJI approximations due to being between temperaments, but is melodically promising, especially since it's unique in the group for having a middle neutral second.		32edo is halfway between 27 and 37 with its melodically strong blackdye, but begins to leave Superpyth mappings behind in favor of Ultrapyth. It is generally lacking in LCJI approximations due to being between temperaments, but is melodically promising, especially since it's unique in the group for having a middle neutral second.
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	== 37 and 57edo ==		== 37 and 57edo ==

	37edo misses a relatively good approximation of prime 3 well but has accurate 5.7.11.13.(17).(19), whereas 57edo missed both 3 and 5 but has 7.11.13.17.19.23.29.37. For most purposes, 37edo has the advantage because it is significantly smaller and has a good 5, which simplifies the choices in how to approximate 4:5:6. ~~Most~~ composers ~~don't~~ have much use for primes above 13 anyway. However, ~~its accurate primes are 2.5.7.11.13, whereas 57edo manages 2.7.11.13.17.19.23.29.37.~~ 57edo also contains 19edo as a subset, which simplifies the somewhat difficult learning curve present in 37edo. Both tunings share the 2.7.11.13 Bossier temperament generated by a sharp 14/11.		37edo misses a relatively good approximation of prime 3 well but has accurate 5.7.11.13.(17).(19), whereas 57edo missed both 3 and 5 but has 7.11.13.17.19.23.29.37. For most purposes, 37edo has the advantage because it is significantly smaller and has a good 5, which simplifies the choices in how to approximate 4:5:6 and provides harmonic stability. Few composers tend to have much use for tempered approximations of primes above 13 anyway. However, 57edo also contains 19edo as a subset, which simplifies the somewhat difficult learning curve present in 37edo and offers equal or better stability than 37edo's best 4:5:6. Both tunings share the 2.7.11.13 Bossier temperament generated by a sharp 14/11.

	== 81, 86, 100, and 117edo ==		== 81, 86, 100, and 117edo ==

Ground at 03:59, 6 January 2026

2026-01-06T03:59:01Z

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 This page is intended to show the differences between multiple tunings that have a major purpose in common.
-== 22edo, 27edo, 37edo ==
+== 22, 27, 32, and 37edo ==
 and 27edo are comparable because both are good representations of Superpyth temperament, but neither is obviously better. 37 is the obvious edo for Ultrapyth, which is tuned similarly to 22edo due to Porcupine.
@@ Line 15: / Line 15: @@
 edo has all 5.7.11.13 but the 3 is the sharpest so 7/6 and 9/7 are bad, the 81/80 is huge, but there are a bunch of unusual temperaments
-== 37edo and 57edo ==
+edo is halfway between 27 and 37 with its melodically strong blackdye, but begins to leave Superpyth mappings behind in favor of Ultrapyth. It is generally lacking in LCJI approximations due to being between temperaments, but is melodically promising, especially since it's unique in the group for having a middle neutral second.
-and 57edo are comparable because both miss one or two low primes and are very accurate for several primes after. For most purposes, 37edo has the advantage because it is significantly smaller and has a good 5, which simplifies the choices in how to approximate 4:5:6. Most composers don't have much use for primes above 13 anyway. However, its accurate primes are 2.5.7.11.13, whereas 57edo manages 2.7.11.13.17.19.23.29.37. 57edo also contains 19edo as a subset, which simplifies the somewhat difficult learning curve present in 37edo.
+== 37 and 57edo ==

Ground at 21:30, 24 December 2025

2025-12-24T21:30:47Z

← Older revision		Revision as of 21:30, 24 December 2025
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			{{problematic}}

	This page is intended to show the differences between multiple tunings that have a major purpose in common.		This page is intended to show the differences between multiple tunings that have a major purpose in common.

	===22edo, 27edo, 37edo===		== 22edo, 27edo, 37edo ==

	22 and 27edo are comparable because both are good representations of Superpyth temperament, but neither is obviously better. 37 is the obvious edo for Ultrapyth, which is tuned similarly to 22edo due to Porcupine.		22 and 27edo are comparable because both are good representations of Superpyth temperament, but neither is obviously better. 37 is the obvious edo for Ultrapyth, which is tuned similarly to 22edo due to Porcupine.
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	37edo has all 5.7.11.13 but the 3 is the sharpest so 7/6 and 9/7 are bad, the 81/80 is huge, but there are a bunch of unusual temperaments		37edo has all 5.7.11.13 but the 3 is the sharpest so 7/6 and 9/7 are bad, the 81/80 is huge, but there are a bunch of unusual temperaments

			== 37edo and 57edo ==

			37 and 57edo are comparable because both miss one or two low primes and are very accurate for several primes after. For most purposes, 37edo has the advantage because it is significantly smaller and has a good 5, which simplifies the choices in how to approximate 4:5:6. Most composers don't have much use for primes above 13 anyway. However, its accurate primes are 2.5.7.11.13, whereas 57edo manages 2.7.11.13.17.19.23.29.37. 57edo also contains 19edo as a subset, which simplifies the somewhat difficult learning curve present in 37edo.

Vector at 02:33, 11 December 2025

2025-12-11T02:33:54Z

← Older revision		Revision as of 02:33, 11 December 2025
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	22 and 27edo are comparable because both are good representations of Superpyth temperament, but neither is obviously better. 37 is the obvious edo for Ultrapyth, which is tuned similarly to 22edo due to Porcupine.		22 and 27edo are comparable because both are good representations of Superpyth temperament, but neither is obviously better. 37 is the obvious edo for Ultrapyth, which is tuned similarly to 22edo due to Porcupine.

	22edo has 5/4, 9/7, and 11/8; neutral seconds (Porcupine)		22edo has 5/4, 9/7, and 11/8; neutral seconds (Porcupine). It also supports Pajara.

	27edo has 6/5, 7/4, and 13/8~~; leans neogothic~~		27edo has 6/5, 7/4, and 13/8

	Both have 7/6		Both have 7/6

	37edo has all 5.7.11.13 but the 3 is the sharpest so 7/6 and 9/7 are bad, the 81/80 is huge, but there are a bunch of unusual temperaments		37edo has all 5.7.11.13 but the 3 is the sharpest so 7/6 and 9/7 are bad, the 81/80 is huge, but there are a bunch of unusual temperaments

Ground at 01:30, 27 October 2025

2025-10-27T01:30:34Z

← Older revision		Revision as of 01:30, 27 October 2025
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	~~===22edo and 27edo===~~		This page is intended to show the differences between multiple tunings that have a major purpose in common.

	~~These two~~ are comparable because both are good representations of Superpyth temperament, but neither is obviously better.		===22edo, 27edo, 37edo===

			22 and 27edo are comparable because both are good representations of Superpyth temperament, but neither is obviously better. 37 is the obvious edo for Ultrapyth, which is tuned similarly to 22edo due to Porcupine.

	22edo has 5/4, 9/7, and 11/8; neutral seconds (Porcupine)		22edo has 5/4, 9/7, and 11/8; neutral seconds (Porcupine)
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	Both have 7/6		Both have 7/6

			37edo has all 5.7.11.13 but the 3 is the sharpest so 7/6 and 9/7 are bad, the 81/80 is huge, but there are a bunch of unusual temperaments

Ground: Created page with "===22edo and 27edo=== These two are comparable because both are good representations of Superpyth temperament, but neither is obviously better. 22edo has 5/4, 9/7, and 11/8; neutral seconds (Porcupine) 27edo has 6/5, 7/4, and 13/8; leans neogothic Both have 7/6"

2025-10-27T00:33:33Z

Created page with "===22edo and 27edo=== These two are comparable because both are good representations of Superpyth temperament, but neither is obviously better. 22edo has 5/4, 9/7, and 11/8; neutral seconds (Porcupine) 27edo has 6/5, 7/4, and 13/8; leans neogothic Both have 7/6"

New page

===22edo and 27edo===

These two are comparable because both are good representations of Superpyth temperament, but neither is obviously better.

22edo has 5/4, 9/7, and 11/8; neutral seconds (Porcupine)

27edo has 6/5, 7/4, and 13/8; leans neogothic

Both have 7/6