Canou family: Difference between revisions

For tunings, a basic option would be [[80edo]]. Others such as [[94edo]], [[99edo]] and [[118edo]] are more accurate; [[19edo]] (perferably with stretched octaves) also provides a good trivial case, whereas the [[optimal patent val]] goes up to [[1131edo]], relating it to the [[amicable]] temperament.  

Badness: 1.122 × 10^-3

Still 80edo can be used as a tuning. Other options include 94edo, 118edo, and [[104edo]] in 104c val.  

Badness: 2.197 × 10^-3

This adds [[352/351]], the minthma, to the comma list. It is a natural extension to the 13-limit.  

Badness: 2.701 × 10^-3

Not supported by many patent vals, 80edo easily makes the optimal. Yet 104edo in 104c val and 118edo in 118f val are worth mentioning, and the temperament may be described as 80 & 104c & 118f.  

Badness: 3.511 × 10^-3

By adding [[896/891]], the pentacircle comma, [[33/32]] is equated with 28/27, so the scale is filled with this 33/32~28/27 mixture. This may be described as 75e & 80 & 99e, and 80edo makes the optimal.  

Badness: 4.523 × 10^-3

This adds [[351/350]], the ratwolfsma, to the comma list. Since 351/350 = (81/70)/(15/13). The 81/70-generator simultaneously represents 15/13, adding a lot of fun to the scale. Again 80edo makes the optimal.  

Badness: 3.470 × 10^-3

This adds [[352/351]], the minthma, as well as [[364/363]], the gentle comma, to the comma list. It is a natural extension of canta, as 896/891 factors neatly into (352/351)×(364/363). Again 80edo makes the optimal.  

Badness: 4.781 × 10^-3