5L 3s: Difference between revisions
m link to tuning ranges section before describing the temperaments |
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In terms of [[Tour of Regular Temperaments|regular temperament]]s, there are at least two melodically viable ways to interpret oneirotonic: (see [[5L 3s#Tuning_ranges|Tuning ranges]]): | In terms of [[Tour of Regular Temperaments|regular temperament]]s, there are at least two melodically viable ways to interpret oneirotonic: (see [[5L 3s#Tuning_ranges|Tuning ranges]]): | ||
# 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 2.5.9.11.13.17 temperament that approximates the harmonic series chord 4:5:9:11:13:17) | # 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 2.5.9.11.13.17 temperament that approximates the harmonic series chord 4:5:9:11:13:17) | ||
# When the generator is between 461.54¢ (5\13) and 466.67¢ (7\18): [[A-Team]] (13&18, a 2.9.5.21 temperament | # When the generator is between 461.54¢ (5\13) and 466.67¢ (7\18): [[A-Team]] (13&18, a 2.9.5.21 temperament where two major mosseconds or "whole tones" approximate a [[5/4]] classical major third) | ||
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, 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). | ||