No-threes subgroup temperaments: Difference between revisions

Scaevola is the 2.7.11-subgroup temperament tempering out 14641/14336, with a generator of [[11/8]] and mapping +4 generators is to [[7/4]]. Two strong extensions are [[score]] to 2.7.11.13 and [[joan]] to 2.9.7.11. Scaevola has a structure that is very similar to [[mavila]], but whereas Mavila has a "fifth" of [[3/2]], "major third" of [[5/4]], and "minor third" of [[6/5]], scaevola has a "fifth" of [[16/11]], "major third" of [[14/11]], and "minor third" of [[8/7]], substituting Mavila's 4:5:6 for 11:14:16. Essentially, Scaevola can be seen as a counterpart of Mavila for fifths even flatter than [[9edo]], such as [[11edo]]'s fifth. It was named by [[User:CompactStar|CompactStar]] in 2026, referring to ''Scaevola'' (the genus of flowering plants), which is meant to sound reminiscent of "score" and "mavila" (the score and joan temperaments were actually named prior to this temperament).

* [[WE]]: ~2 = 1201.248{{c}}, ~11/8 = 542.116{{c}}

* [[CWE]]: ~2 = 1200.000{{c}}, ~11/8 = 541.940{{c}}

{{Optimal ET sequence|legend=1| TBA}}

Score is an extension of scaevola that equates [[13/8]] to +6 generators.

[[Subgroup]]: 2.7.11.13

[[Comma list]]: 343/338, 847/832

{{Mapping|legend=3| 1 1 3 1 | 0 4 1 6 }}

{{Mapping|legend=5| 1 0 0 1 3 1 | 0 0 0 4 1 6 }}

[[Optimal tuning]]s:  

* [[WE]]: ~2 = 1201.5484{{c}}, ~11/8 = 540.7963{{c}}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~11/8 = 540.5091{{c}}

{{Optimal ET sequence|legend=1| 9, 11, 20 }}

[[Badness]] (Sintel): 0.368