5L 3s: Difference between revisions

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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,....

== 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".)

Thus the [[13edo]] gamut is as follows:

'''J''' J&/K@ '''K''' '''L''' L&/M@ '''M''' M&/N@ '''N''' '''O''' O&/P@ '''P''' P&/Q@ '''Q''' '''J'''

Note: N is close to standard C, since the reference pitch 360 Hz for J was chosen to be nearly a pure 11/8 above standard 12edo C.

== Oneirotonic rank-2 temperaments ==

The only notable harmonic entropy minimum is Vulture/[[Hemifamity_temperaments|Buzzard]], in which four generators make a 3/1 (and three generators approximate an octave plus 8/7). The rest of this region does not approximate low-complexity JI harmony well, but can be melodically interesting due to the distorted diatonic scale structure (see also [[oneirotonic]]).

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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,....
+== 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".)
+Thus the [[13edo]] gamut is as follows:
+'''J''' J&/K@ '''K''' '''L''' L&/M@ '''M''' M&/N@ '''N''' '''O''' O&/P@ '''P''' P&/Q@ '''Q''' '''J'''
+Note: N is close to standard C, since the reference pitch 360 Hz for J was chosen to be nearly a pure 11/8 above standard 12edo C.
 == Oneirotonic rank-2 temperaments ==
 The only notable harmonic entropy minimum is Vulture/[[Hemifamity_temperaments|Buzzard]], in which four generators make a 3/1 (and three generators approximate an octave plus 8/7). The rest of this region does not approximate low-complexity JI harmony well, but can be melodically interesting due to the distorted diatonic scale structure (see also [[oneirotonic]]).