Talk:Kite's thoughts on pergens: Difference between revisions

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 ==Pergens for no-3 temperaments?==
 Hey TallKite, I was just wondering if you could explain how to use pergens to describe no-3 temperaments. Also, how do I determine tunings such as 3/7-comma mintaka? Thanks! [[User:MisterShafXen|MisterShafXen]] ([[User talk:MisterShafXen|talk]]) 11:57, 10 May 2026 (UTC)
+: Glad to help! For no-3 temps, see https://en.xen.wiki/w/Kite%27s_thoughts_on_pergens#Notating_non-8ve_and_no-5ths_pergens. Analogous to imperfect 2.3 pergens like (P8/2, M2/4), there are imperfect 2.5 pergens that would use A5, defined as 25/16. And likewise d4, A7, etc.
+: For mintaka, the period is P12 = 3/1 and the generator is 11/7. The 3.7.11 mapping is [(1 3 3)(0 -3 -2)]. Thus prime 7 equals 3 periods minus 3 generators. Thus the multigen is 27/7. The pergen is #9 in the 3.7 column (P12, cM7/3), where cM7 means P12 = 3/1 plus a M3 = 9/7.
+: 3/7-comma mintaka means the multigen 27/7 is sharpened or flattened by 3/7 of a comma, 4.473¢. The mintaka comma has 7 in the denominator, so tempering it out implies sharpening prime 7. Thus prime 7 is sharpened by 4.473¢, and the multigen 27/7 is flattened by 4.473¢. (We're assuming a just prime 3.)
+: If you're into temps that don't use 2 and/or 3, you might find pergen squares useful, since they apply to all JI subgroups.
+: --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 10:26, 14 May 2026 (UTC)