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; these tunings have a L/s step ratio between 3/2 and 2/1. The three major edo tunings in this range, [[13edo]], [[21edo]] and [[34edo]] all nominally support ~~Petrtri~~, but [[34edo]] is close to optimal for the temperament, with a generator only .33c flat of 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. The three major edo tunings in this range, [[13edo]], [[21edo]] and [[34edo]] all nominally support petrtri, but [[34edo]] is close to optimal for the temperament, with a generator only .33c flat of 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,....)

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,....)

{| class="wikitable right-2 right-3 right-4"

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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; these tunings have a L/s step ratio between 3/2 and 2/1. The three major edo tunings in this range, [[13edo]], [[21edo]] and [[34edo]] all nominally support Petrtri, but [[34edo]] is close to optimal for the temperament, with a generator only .33c flat of 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. The three major edo tunings in this range, [[13edo]], [[21edo]] and [[34edo]] all nominally support petrtri, but [[34edo]] is close to optimal for the temperament, with a generator only .33c flat of 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,....)
+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,....)
 {| class="wikitable right-2 right-3 right-4"