16ed5/3: Difference between revisions
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This shows the close relationships with [[srutal]] and [[pajara]] octave temperaments. In 16ed5/3's case, there is a close equivalence to [[22edo]]'s pajara tuning. | This shows the close relationships with [[srutal]] and [[pajara]] octave temperaments. In 16ed5/3's case, there is a close equivalence to [[22edo]]'s pajara tuning. | ||
As 3 semitones make a period-reduced octave, and it alludes to tritone tempering, [[User:Ayceman| | 16ed5/3 primes can be mapped on the 31-limit to the val ⟨65 103 151 183 225 241 266 276 294 316 322], using every 3 steps of a shrinked [[65edo]] (-2.431¢ per octave). It differs from the patent val of 65edo in the mapping of prime 7 (val 65d). | ||
As 3 semitones make a period-reduced octave, and it alludes to tritone tempering, [[User:Ayceman|Ayceman]] proposes the name '''tristone''' for the basic [[Diaschismic family|diaschismic temperament]], based on the 16/15 to 6/5 relationship, as well as the following variants and extensions: | |||
=== Tristone === | === Tristone === | ||
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'''16ed5/3''' also supports [[Blackcomb]] temperament which is built on [[5/4]] and [[3/2]] in a very similar way to octave-repeating [[meantone]] but is less accurate. Blackcomb tempers out the comma [[250/243]], the amount by which 3 [[3/2]]'s exceed [[5/4]] sixth-reduced, in the 5/3.2.3 subgroup (equal to the [[5-limit]]). | '''16ed5/3''' also supports [[Blackcomb]] temperament which is built on [[5/4]] and [[3/2]] in a very similar way to octave-repeating [[meantone]] but is less accurate. Blackcomb tempers out the comma [[250/243]], the amount by which 3 [[3/2]]'s exceed [[5/4]] sixth-reduced, in the 5/3.2.3 subgroup (equal to the [[5-limit]]). | ||
== See also == | |||
* [[Alpha, beta, and gamma family of equal divisions]] | |||
[[Category:Nonoctave]] | [[Category:Nonoctave]] | ||