24576/24565: Difference between revisions

+"archagallic"
Temperaments: -srutal archagall (moved to diaschismic family)
Line 77: Line 77:


Badness: 9.335 × 10<sup>-6</sup>
Badness: 9.335 × 10<sup>-6</sup>
=== Srutal archagall ===
==== 2.3.5.17 subgroup (MVP srutal archagall) ====
Named because this lower-accuracy temperament is also an extension of (the 5-limit) [[srutal]] temperament that adds prime 17 (and which thereby is able to express the harmonics 75 and 85 in their appropriate prime subgroup). It achieves this by equating [[85/64]] with [[4/3]] by tempering their difference of S16 = [[256/255]]. Therefore it also tempers S17 = [[289/288]] and thus equates [[17/15]] with [[9/8]] due to tempering S16 × S17. It could be described as the 10 & 12 temperament (with strong emphasis on [[12edo]] being the better tuning) on the following prior-discussed subgroup:
Subgroup: 2.3.5.17
Comma list: 256/255, 289/288
Sval mapping: [{{val| 2 0 11 5 }}], {{val| 0 1 -2 1 }}]
Sval mapping generators: ~17/12, ~3
Optimal tuning (CTE): ~17/12 = 1\2, ~3/2 = 705.1272
Optimal GPV sequence: {{Val list| 10, 12, 22, 34, 80, 114, 194bc }}
Badness: 0.00575


[[Category:Mavka]]
[[Category:Mavka]]