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| == Tunings ==
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| === A-Team (13&18) ===
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| A-Team tunings (with generator between 5\13 and 7\18) have L/s ratios between 2/1 and 3/1.
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| EDOs that support A-Team include [[13edo]], [[18edo]], and [[31edo]].
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| * 18edo can be used for a large L/s ratio of 3, (thus 18edo oneirotonic is distorted 17edo diatonic), or for nearly pure 9/8 and 7/6.
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| * 31edo can be used to make the major mos3rd a near-just 5/4.
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| A-Team can be tuned by ear, by tuning a chain of pure harmonic sevenths and taking every other note. This corresponds to using a generator of 64/49 = 462.34819 cents. A chain of fourteen 7/4's are needed to tune the 8-note oneirotonic MOS. This produces a tuning close to 13edo.
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| The sizes of the generator, large step and small step of oneirotonic are as follows in various A-Team tunings.
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| {| class="wikitable right-2 right-3 right-4 right-5 right-6"
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| |-
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| !
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| ! [[13edo]]
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| ! [[18edo]]
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| ! [[31edo]]
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| ! 64/49 generator
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| ! [[POTE tuning]]
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| ! JI intervals represented (2.9.5.21 subgroup)
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| |-
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| | generator (g)
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| | 5\13, 461.54
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| | 7\18, 466.67
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| | 12\31, 464.52
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| | 462.35
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| | 464.14
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| | 21/16
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| |-
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| | L (3g - octave)
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| | 2\13, 184.62
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| | 3\18, 200.00
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| | 5\31, 193.55
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| | 187.04
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| | 192.42
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| | 9/8, 10/9
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| |-
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| | s (-5g + 2 octaves)
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| | 1\13, 92.31
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| | 1\18, 66.66
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| | 2\31, 77.42
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| | 88.26
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| | 79.30
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| | 21/20
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| |}
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| === Petrtri (13&21) ===
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| Petrtri tunings (with generator between 8\21 and 5\13) have less extreme L-to-s ratios than A-Team tunings, between 3/2 and 2/1. The 8\21-to-5\13 range of oneirotonic tunings remains relatively unexplored.
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| The three major edos 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.
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| The sizes of the generator, large step and small step of oneirotonic are as follows in various petrtri tunings.
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| {| class="wikitable right-2 right-3 right-4 right-5"
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| !
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| ! [[13edo]]
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| ! [[21edo]]
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| ! [[34edo]]
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| ! [[POTE tuning]]
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| ! JI intervals represented (2.5.9.11.13.17 subgroup)
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| |-
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| | generator (g)
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| | 5\13, 461.54
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| | 8\21, 457.14
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| | 13\34, 458.82
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| | 459.15
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| | 13/10, 17/13, 22/17
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| |-
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| | L (3g - octave)
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| | 2\13, 184.62
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| | 3\21, 171.43
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| | 5\34, 176.47
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| | 177.45
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| | 10/9, 11/10
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| |-
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| | s (-5g + 2 octaves)
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| | 1\13, 92.31
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| | 2\21, 114.29
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| | 3\34, 105.88
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| | 104.25
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| | 18/17, 17/16
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| |}
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| Trivia: One petrtri tuning is golden oneirotonic, which uses (2-φ)*1200 cents = 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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| == Notation== | | == Notation== |
| The notation used in this article is J Celephaïsian (LsLLsLLs) = JKLMNOPQJ, with reference pitch J = 360 Hz, unless specified otherwise. We denote raising and lowering by a chroma (L-s) by & "amp" and @ "at". (Mnemonics: & "and" means additional pitch. @ "at" rhymes with "flat".) | | The notation used in this article is J Celephaïsian (LsLLsLLs) = JKLMNOPQJ, with reference pitch J = 360 Hz, unless specified otherwise. We denote raising and lowering by a chroma (L-s) by & "amp" and @ "at". (Mnemonics: & "and" means additional pitch. @ "at" rhymes with "flat".) |