Hyperpyth: Difference between revisions
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* [[22ed5|22ED5]] | * [[22ed5|22ED5]] | ||
* [[27ed5|27ED5]] | * [[27ed5|27ED5]] | ||
* [[29ed5|29ED5]] | |||
* [[39ed5|39ED5]] | * [[39ed5|39ED5]] | ||
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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. | 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. | ||
[[Category:Hyperpyth| ]] | |||
[[Category:Fifth harmonic]] | [[Category:Fifth harmonic]] | ||
[[Category:Temperament]] | [[Category:Temperament]] | ||
[[Category:Nonoctave]] | [[Category:Nonoctave]] | ||