300edo: Difference between revisions

{{EDO intro}}

300edo is the largest-number edo which [[tempering out|tempers out]] the [[pythagorean comma]], 531441/524288, in the [[patent val]].  

It is in[[consistent]] to the [[5-odd-limit]] and higher, with three mappings possible for the 5-limit: {{val| 300 475 697 }} (patent val), {{val| 300 '''476''' 697 }} (300b), and {{val| 300 475 '''696''' }} (300c).  

Using the patent val, it tempers out 531441/524288 and {{monzo| 47 7 -25 }} in the 5-limit; [[6144/6125]], [[50421/50000]], and 1594323/1568000 in the 7-limit.  

Using the 300b val, it tempers out [[393216/390625]] and {{monzo| 51 -38 4 }} in the 5-limit; 153664/151875, 179200/177147, and [[823543/819200]] in the 7-limit. Using the 300bd val, it tempers out [[10976/10935]], 65536/64827, and [[390625/388962]] in the 7-limit.  

 

Since 300 factors into {{factorization|300}}, 300edo has subset edos {{EDOs| 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, and 150 }}. [[600edo]], which doubles it, gives a good correction to its approximation of the 5-limit.