Quartismic family: Difference between revisions

The '''quartismic family''' is built up from temperaments that tempers out the [[quartisma]]- the unnoticeable comma with the ratio 117440512/117406179, and a monzo of {{monzo|24 -6 0 1 -5}}).  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, rendering them unsuitable for temperaments in this family.  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, yet, upon closer examination, actually fail to temper out the comma, and are thus unsuitable for temperaments in this family 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]], [[46edo]], [[68edo]], [[159edo]], [[224edo]] and [[3125edo]].