24576/24565: Difference between revisions
→Temperaments: added 2.75.85.9/7 and 2.3.5.7.17 subgroup extension of archagall with latter mapping prime 5 at +13 fourths and former mapping 9/7 at two 17/15's aka +4 fifths |
m →Srutal archagall: correct temperament hierarchy |
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Some good (relative to their size) EDOs supporting it: 22, 149, 171, 193, 215, 320, 364 | Some good (relative to their size) EDOs supporting it: 22, 149, 171, 193, 215, 320, 364 | ||
=== | == 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: | 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: | ||