Hyperpyth: Difference between revisions

'''Hyperpyth temperament''' is a pentave-based 5.9.13 subgroup temperament which tempers out 28561/28125 (quadtho-aquingu comma).

== Hyperreich? ==

Looking at the primes, 7 and 11 (and 19) are "conspicuously absent" which begs comparison to the Meantone/Orgone dichotomy. The search being on, in the context of simple scales, 11/5 is close enough to the square root of 5, that one might as well just use it (1393 v the real 11/5 at 1365 cents); eventually as step sizes get closer to 60 cents or so, better approximations will abound. This would make a good period for a scale. The pure 7/5 then is around 582 cents, and among the simpler temperaments 557-cent (from 5ED5, 10ED5, 15ED5) and 596-cent (from [[14ed5|14ED5]], which is a slightly compressed [[6edo|6EDO]]) intervals are the closest approximations. That is, until [[19ed5|19ED5]] (14+5) which is a very slightly stretched [[13edt|13EDT]] (Bohlen-Pierce) scale, and [[24ed5|24ED5]] which is something completely different.