Comparisons of similar tunings

This page or section is a work in progress. It may lack sufficient justification, content, or organization, and is subject to future overhaul.

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

22, 27, 32, and 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.

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.

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.

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.

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 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.

Contorted Dual-3

64, 74, 81, 86, 93, 100, 105, 108, and 117edo

These are some of the recommendations for dual-3 systems with contortion, which have promising ~2.3.5 blackdye and ~2.3.7 scales.

Table that's about to get really annoying

Edo	Subset(s)	2.<3.7	2.>3.5	2.>3.>5
64	32x2
74	37x2
81	27x3
86	43x2
93	31x3
100	25x4, 50x2
105	35x3
108	27x4, 36x3, 54x2
117	39x3