User:Userminusone/Goldis comma: Difference between revisions

The 5 limit parent temperament, Goldis, has a generator of approximately 458 cents. The major third is reached by -7 generators, and the perfect fifth is reached by +12 generators, making this a rather complex temperament. It should be noted that there is an alternate major third, reached by +27 generators, which is more accurate than the -7 generator major third whenever the generator is between 458.6314 cents and 458.8235 cents (or 13 steps of [[34edo]]). Generators in this range generate Tetracot (which is contorted by order 3) rather than Goldis.

Perhaps the most accurate 7 limit extension of this temperament, which I call Semigoldis, splits the generator in half and maps one step to 8/7. Semigoldis tempers out the [[breedsma]] in addition to the goldis comma. The only downside is that this drastically increases the complexity. This temperament is supported by [[21edo]], [[68edo]], [[89edo]], [[136edo]], and [[157edo]].

Curiously enough, Semigoldis naturally extends to the 11 limit by adding the one and only [[quartisma]], which doesn't require the generator to be further split into any number of parts. In addition, 11-limit Semigoldis tempers out the [[valinorsma]]. High complexity is the downside for this temperament, as is the case with 7-limit Semigoldis. (The exception is 7/4, which is reached by only -1 generators). 5/4 is reached by -14 generators, 3/2 is reached by +24 generators, and 11/8 is reached by -29 generators. 89edo is a really good tuning for 11-limit Semigoldis, but all the EDOs that support 7-limit Semigoldis also support 11-limit Semigoldis.