5L 3s: 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~~):

In terms of [[regular temperament]]s, there are at least two melodically viable ways to interpret oneirotonic:

# When the generator is between 457.14¢ (8\21) and 461.54¢ (5\13): [[5L_3s#Petrtri_.2813.2621.2C_2.5.9.11.13.17.29|Petrtri]] (13&21, a 4:5:9:11:13:17 or 2.5.9.11.13.17 temperament)

# 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): [[5L_3s#Petrtri_.2813.2621.2C_2.5.9.11.13.17.29|Petrtri]] (13&21, a 4:5:9:11:13:17 or 2.5.9.11.13.17 temperament)~~

In a sense, these two temperaments represent the middle of the oneirotonic spectrum (with the L/s ratio ranging from 3/2 to 3/1); [[13edo]] represents both temperaments, with a L/s ratio of 2/1. This is analogous to how in the diatonic spectrum, the [[19edo]]-to-[[17edo]]-range has the least extreme ratio of large to small step sizes, with [[12edo]] representing both [[meantone]] (19edo to 12edo) and [[pythagorean]]/[[neogothic]] (12edo to 17edo) in a sense.

In a sense, these two temperaments represent the middle of the oneirotonic spectrum; [[13edo]] represents both temperaments, with a L/s ratio of 2/1.

More extreme oneirotonic temperaments include:

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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):
+In terms of [[regular temperament]]s, there are at least two melodically viable ways to interpret oneirotonic:
+# When the generator is between 457.14¢ (8\21) and 461.54¢ (5\13): [[5L_3s#Petrtri_.2813.2621.2C_2.5.9.11.13.17.29|Petrtri]] (13&21, a 4:5:9:11:13:17 or 2.5.9.11.13.17 temperament)
 # 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): [[5L_3s#Petrtri_.2813.2621.2C_2.5.9.11.13.17.29|Petrtri]] (13&21, a 4:5:9:11:13:17 or 2.5.9.11.13.17 temperament)
+In a sense, these two temperaments represent the middle of the oneirotonic spectrum (with the L/s ratio ranging from 3/2 to 3/1); [[13edo]] represents both temperaments, with a L/s ratio of 2/1. This is analogous to how in the diatonic spectrum, the [[19edo]]-to-[[17edo]]-range has the least extreme ratio of large to small step sizes, with [[12edo]] representing both [[meantone]] (19edo to 12edo) and [[pythagorean]]/[[neogothic]] (12edo to 17edo) in a sense.
-In a sense, these two temperaments represent the middle of the oneirotonic spectrum; [[13edo]] represents both temperaments, with a L/s ratio of 2/1.
 More extreme oneirotonic temperaments include: