No-fives subgroup temperaments: Difference between revisions

{{Main| Squares }}

[[Subgroup]]: 2.3.7

=== Harrison ===

{{Optimal ET sequence|legend=1| 12, 19, 31, 112b, 143b, 174b }}

=== Leapfrog ===

: ''For extensions, see [[Leapday]], [[Leapweek]], [[Supermean]], and [[Srutal]].''

{{See also| Gentle region }}

In regular [[13-limit]] [[leapday]], the mapping for prime 5 is very complex at +21 generator steps. Furthermore, adding prime 5 to rank-3 [[parapythic]] is arguably against the original vision of it as a 2.3.7.11.13-subgroup temperament, so avoiding prime 5 may be preferred for this reason also. This results in no-5's leapday, or leapfrog, which as aforementioned is much lower in badness, but it also allows more tunings to be used: a notable [[patent val]] tuning not appearing in the [[optimal ET sequence]] is [[80edo]], which is approximately the just-13's tuning (as [[10edo]] is used as a [[consistent circle]] of [[~]][[16/13]]'s therein), with 13/8 still tuned slightly flat so qualifying a reasonable tuning for the 2.3.13 subgroup (as evidenced by appearing in the sequence for [[tetris]]). In other words, the only reason 80edo was "disqualified" from leapday is that the mapping for prime 5 constrains the tuning range which is naturally more flexible as a no-5's 13-limit temperament, which is also a sign of leapfrog being very efficient.

{{Mapping|legend=2| 1 0 -21 | 0 1 15 }}

[[Optimal tuning]]s:  

==== 2.3.7.11 ====

==== 2.3.7.11.13 ====

===== Skidoo =====

====== 2.3.7.11.13.23.29 ======

; Music

** I. Prelude

** II. Allemande

=== Doublehearted ===

Subgroup: 2.3.7