Quartismic family: Difference between revisions

The '''quartisma''' or '''Saquinlu-azo comma''' is a comma with a ratio of '''117440512/117406179''' and a [[monzo]] of {{monzo|24 -6 0 1 -5}}.  It is an [[unnoticeable comma]] of the [[11-limit]]- specifically one of the the 2.9.7.11 subgroup- with a value of approximately 0.50619 cents.  The quartisma is significant on account of it being the difference between a stack of five [[33/32]] quartertones and one [[7/6]] subminor third in Just Intonation.  Despite that fact that the quartisma is an unnoticeable comma in JI, a number of reasonably well known EDOs (such as [[17edo]], [[26edo]] and [[34edo]]) actually fail to temper it out.  In fact, there are even some EDOs such as [[23edo]] and [[70edo]] that seem to temper out the comma when one merely examines the patent vals for 33/32 and 7/6, yet, upon closer examination, actually fail to temper out the comma, as [https://www.wolframalpha.com/input/?i=dot+product+of+%2823%2C+round%28log%283%29%2Flog%282%29*23%29%2C+round%28log%285%29%2Flog%282%29*23%29%2C+round%28log%287%29%2Flog%282%29*23%29%2C+round%28log%2811%29%2Flog%282%29*23%29%29++and+%2824%2C+-6%2C+0%2C+1%2C+-5%29 these] [https://www.wolframalpha.com/input/?i=dot+product+of+%2870%2C+round%28log%283%29%2Flog%282%29*70%29%2C+round%28log%285%29%2Flog%282%29*70%29%2C+round%28log%287%29%2Flog%282%29*70%29%2C+round%28log%2811%29%2Flog%282%29*70%29%29++and+%2824%2C+-6%2C+0%2C+1%2C+-5%29 calculations] prove.  Examples of edos that actually ''do'' temper out the quartisma are [[22edo]], [[24edo]], [[68edo]], [[90edo]], [[91edo]], [[92edo]], [[159edo]], and [[3125edo]].