Quartismic family: Difference between revisions

The '''quartismic family''' is built up from temperaments that temper 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 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, and are thus unsuitable for temperaments in this family.  Examples of edos that actually ''do'' temper out the quartisma are [[22edo]], [[24edo]], [[46edo]], [[68edo]], [[159edo]], [[224edo]] and [[3125edo]].