Breedsmic temperaments: Difference between revisions

=Hemififths=

Hemififths tempers out 5120/5103, the hemifamity comma, and 10976/10935, hemimage. It has a neutral third as a generator, with [[99edo]] and [[140edo]] providing good tunings, and [[239edo]] an even better one; and other possible tunings are (160)^(1/25), giving just 5s, the 7 and 9 limit minimax tuning, or 14^(1/13), giving just 7s. It may be called the 41&58 temperament and has wedgie <<2 25 13 35 15 -40||, which tells us that it requires 25 generator steps to get to the class for major thirds, whereas the 7 is half as complex, and hence hemififths makes for a good no-fives temperament, to which the 17 and 24 note MOS are suited. The full force of this highly accurate temperament can be found using the 41 note MOS or even the 34 note 2MOS.

=Harry=

Commas: 2401/2400, 19683/19600

=Decoid=

In addition to 2401/2400, decoid tempers out 67108864/66976875 to temper 15/14 into one degree of [[10edo]]. Either 8/7 or 16/15 can be used its generator. It may be described as the 10&270 temperament, and as one might expect, 181\940 or 233\1210 makes for an excellent tuning choice. It is also described as an extension of the [[Qintosec family|qintosec temperament]].

EDOs: 37, 72, 109, 181f