No-threes subgroup temperaments: Difference between revisions

=== Mabilic ===

{{Main| Mabilic and trismegistus }}

{{See also| Chromatic pairs #Mabilic }}

Mabilic is the no-3 [[restriction]] of [[mavila family #Armodue|armodue]] (7 & 16), [[magic family #Trismegistus|trismegistus]] (16 & 25), and [[mabila family #Semabila|semabila]] (25 & 34). It is the 7 & 9 temperament in the [[2.5.7 subgroup]], and tempers out [[1071875/1048576]], the mabilisma. [[Weak extension]]s of mabilic include [[archytas clan #Sixix|sixix]] (7 & 25), [[vishnu family #Vishnean|vishnean]] (16 & 34), [[marvel temperaments #Septimin|septimin]] (9 & 41) and [[tetracot family #Monkey|monkey]] (7 & 34).  

[[Comma list]]: 1071875/1048576

{{Mapping|legend=3| 1 1 5 | 0 3 -5 }}

{{Mapping|legend=5| 1 0 1 5 | 0 0 3 -5 }}

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1201.2543{{c}}, ~175/128 = 527.7872{{c}}

: [[error map]]: {{val| +1.254 -1.698 -1.491 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~175/128 = 527.2041{{c}}

: error map: {{val| 0.000 -4.701 -4.846 }}

{{Optimal ET sequence|legend=1| 7, 9, 16, 25, 41, 66, 305ccdd, 371ccddd }}

[[Badness]] (Sintel): 1.70

Wizz, the 6 & 16 temperament in the 2.5.11 subgroup, tempers out [[15625/15488]], and is the common [[restriction]] of [[astrology]] and [[wizard]].  

This temperament has a structure very similar to [[mavila]] but is somewhat more accurate because the generator is a flat [[11/8]] rather than a sharp [[4/3]]. The major third is still ~[[5/4]], but the minor third is now ~[[64/55]] instead of ~[[6/5]].

{{Mapping|legend=3| 1 2 3 | 0 1 2 }}

: mapping generators, ~2, ~5/4

Argument tempers out [[1372/1331]] in the 2.7.11 subgroup. It is the no-3 [[restriction]] of [[#Augment|augment]].  

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

Gencom mapping: {{mapping|| 1 0 0 0 1 3 | 0 0 0 8 7 2 }}

{{Mapping|legend=3| 1 3 3 | 0 2 3 }}

{{Mapping|legend=5| 1 0 0 0 3 3 | 0 0 0 0 2 3 }}

: mapping generators, ~2, ~13/11