Oneirotonic: Difference between revisions

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The generator size ranges from 450¢ (3\8) to 480¢ (2\5). Hence any edo with an interval between 450¢ and 480¢ has an oneirotonic scale. [[13edo]] is the smallest edo with a (non-degenerate) 5L3s oneirotonic scale and thus is the most commonly used oneirotonic tuning.

In terms of [[regular temperament]]s, there are at least two melodically viable ways to interpret oneirotonic (analogous to diatonic having multiple temperament interpretations depending on generator size):

# When the generator is between 461.54¢ (5\13) and 466.67¢ (7\18): [[A-Team]] (13&18, a 4:5:9:21 or 2.9.5.21 temperament)

# When the generator is between 457.14¢ (8\21) and 461.54¢ (5\13): [[Chromatic_pairs#Petrtri|Petrtri]] (13&21, a 4:5:9:11:13:17 or 2.5.9.11.13.17 temperament)

[[13edo]] represents both temperaments.

Some more extreme oneirotonic temperaments are:

* [[Chromatic pairs#Tridec|Tridec]] (a 5:7:11:13 or 2.7/5.11/5.13/5 subgroup temperament), when the generator is between 454.05c (14\37) and 457.14c (8\21). These have a L/s ratio of 5/4 to 3/2.

* [[Hemifamity_temperaments#Buzzard|Buzzard]], when the generator is between 471.42¢ (11\28) and 480¢ (2\5). While this is a harmonically accurate temperament, with 4 generators reaching [[3/2]] and -3 generators [[7/4]], it is relatively weak melodically, as the optimum size of the small steps is around 20-25 cents, making it difficult to distinguish from equal pentatonic.

== Tunings ==

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 The generator size ranges from 450¢ (3\8) to 480¢ (2\5). Hence any edo with an interval between 450¢ and 480¢ has an oneirotonic scale. [[13edo]] is the smallest edo with a (non-degenerate) 5L3s oneirotonic scale and thus is the most commonly used oneirotonic tuning.
+In terms of [[regular temperament]]s, there are at least two melodically viable ways to interpret oneirotonic (analogous to diatonic having multiple temperament interpretations depending on generator size):
+# When the generator is between 461.54¢ (5\13) and 466.67¢ (7\18): [[A-Team]] (13&18, a 4:5:9:21 or 2.9.5.21 temperament)
+# When the generator is between 457.14¢ (8\21) and 461.54¢ (5\13): [[Chromatic_pairs#Petrtri|Petrtri]] (13&21, a 4:5:9:11:13:17 or 2.5.9.11.13.17 temperament)
+[[13edo]] represents both temperaments.
+Some more extreme oneirotonic temperaments are:
+* [[Chromatic pairs#Tridec|Tridec]] (a 5:7:11:13 or 2.7/5.11/5.13/5 subgroup temperament), when the generator is between 454.05c (14\37) and 457.14c (8\21). These have a L/s ratio of 5/4 to 3/2.
+* [[Hemifamity_temperaments#Buzzard|Buzzard]], when the generator is between 471.42¢ (11\28) and 480¢ (2\5). While this is a harmonically accurate temperament, with 4 generators reaching [[3/2]] and -3 generators [[7/4]], it is relatively weak melodically, as the optimum size of the small steps is around 20-25 cents, making it difficult to distinguish from equal pentatonic.
 == Tunings ==