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.

16ed5/3 primes can be mapped on the 31-limit to the val ⟨65 103 151 ~~177~~ 225 ~~235~~ 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 ~~mappings~~ of ~~primes~~ 7 ~~and 13~~.

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|I]] ~~propose~~ 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:

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 ===

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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.
-ed5/3 primes can be mapped on the 31-limit to the val ⟨65 103 151 177 225 235 266 276 294 316 322], using every 3 steps of a shrinked 65edo (-2.431¢ per octave). It differs from the patent val of 65edo in the mappings of primes 7 and 13.
+ed5/3 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|I]] propose 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:
+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 ===