Oneirotonic: Difference between revisions

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== Petrtri (13&21, 4:5:9:11:13:17) interpretation ==

The 8\21-to-5\13 range of oneirotonic tunings is relatively underexplored. [[13edo]], [[21edo]] and [[34edo]] all nominally represent petrtri, but [[34edo]] is close to optimal for the temperament, with a generator only -.33c off from the optimal ([[POTE]]) petrtri generator of 459.1502c. Close-to-optimal petrtri tunings such as 34edo may be particularly useful for the Sarnathian mode, as Sarnathian in these tunings uniquely approximates four over-2 harmonics plausibly, namely 17/16, 5/4, 11/8, and 13/8.

The 8\21-to-5\13 range of oneirotonic tunings is relatively underexplored; these tunings have a L/s step ratio between 3/2 and 2/1. [[13edo]], [[21edo]] and [[34edo]] all nominally represent petrtri, but [[34edo]] is close to optimal for the temperament, with a generator only -.33c off from the optimal ([[POTE]]) petrtri generator of 459.1502c. Close-to-optimal petrtri tunings such as 34edo may be particularly useful for the Sarnathian mode, as Sarnathian in these tunings uniquely approximates four over-2 harmonics plausibly, namely 17/16, 5/4, 11/8, and 13/8.

The sizes of the generator, large step and small step of oneirotonic are as follows in various Petrtri tunings. (Golden oneirotonic uses 1200*(2-φ) = 458.3592135¢ as generator and has L/s = φ; it is the limit of taking generators in Fibonacci number edos 5\13, 8\21, 13\34, 21\55, 34\89,....)

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 == Petrtri (13&21, 4:5:9:11:13:17) interpretation ==
-The 8\21-to-5\13 range of oneirotonic tunings is relatively underexplored. [[13edo]], [[21edo]] and [[34edo]] all nominally represent petrtri, but [[34edo]] is close to optimal for the temperament, with a generator only -.33c off from the optimal ([[POTE]]) petrtri generator of 459.1502c. Close-to-optimal petrtri tunings such as 34edo may be particularly useful for the Sarnathian mode, as Sarnathian in these tunings uniquely approximates four over-2 harmonics plausibly, namely 17/16, 5/4, 11/8, and 13/8.
+The 8\21-to-5\13 range of oneirotonic tunings is relatively underexplored; these tunings have a L/s step ratio between 3/2 and 2/1. [[13edo]], [[21edo]] and [[34edo]] all nominally represent petrtri, but [[34edo]] is close to optimal for the temperament, with a generator only -.33c off from the optimal ([[POTE]]) petrtri generator of 459.1502c. Close-to-optimal petrtri tunings such as 34edo may be particularly useful for the Sarnathian mode, as Sarnathian in these tunings uniquely approximates four over-2 harmonics plausibly, namely 17/16, 5/4, 11/8, and 13/8.
 The sizes of the generator, large step and small step of oneirotonic are as follows in various Petrtri tunings. (Golden oneirotonic uses 1200*(2-φ) = 458.3592135¢ as generator and has L/s = φ; it is the limit of taking generators in Fibonacci number edos 5\13, 8\21, 13\34, 21\55, 34\89,....)