5L 3s: Difference between revisions
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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 also [[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 also [[5L 3s#Tuning_ranges|Tuning ranges]]): | ||
# When the generator is between 457.14¢ (8\21) and 461.54¢ (5\13): [[ | # When the generator is between 457.14¢ (8\21) and 461.54¢ (5\13): [[Petrtri]] (13&21, a 2.5.9.11.13.17 temperament that mainly approximates the harmonic series chord 5:9:11:13) | ||
# 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) | # 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 [[step ratio]] (L/s) ranging from 3/2 to 3/1); [[13edo]] represents both temperaments, with a step 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 [[step ratio]] (L/s) ranging from 3/2 to 3/1); [[13edo]] represents both temperaments, with a step 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). | ||
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| | 184.615 | | | 184.615 | ||
| | 646.154 | | | 646.154 | ||
| | ...and ends here<br/>Boundary of propriety (generators smaller than this are proper)<br/>[[ | | | ...and ends here<br/>Boundary of propriety (generators smaller than this are proper)<br/>[[Petrtri]] starts here... | ||
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=== Petrtri (13&21) === | === Petrtri (13&21) === | ||
:''Main article: [[Petrtri]]'' | |||
=== Tridec (29&37) === | === Tridec (29&37) === | ||
In the broad sense, Tridec can be viewed as any oneirotonic tuning that equates three oneirotonic large steps to a [[4/3]] perfect fourth, i.e. equates the oneirotonic large step to a [[porcupine]] generator. [This identification may come in handy since many altered oneirotonic modes have three consecutive large steps.] Based on the JI interpretations of the [[29edo]] and [[37edo]] tunings, it can in fact be viewed as a 2.3.7/5.11/5.13/5 temperament, i.e. a [[Non-over-1 temperament|non-over-1 temperament]] that approximates the chord 5:7:11:13:15. Since it is the same as Petrtri when you only care about the 9:10:11:13 (R-M2-M3-M5), it can be regarded as a flatter variant of Petrtri (analogous to how septimal meantone and flattone are the same when you only consider how it maps 8:9:10:12). | In the broad sense, Tridec can be viewed as any oneirotonic tuning that equates three oneirotonic large steps to a [[4/3]] perfect fourth, i.e. equates the oneirotonic large step to a [[porcupine]] generator. [This identification may come in handy since many altered oneirotonic modes have three consecutive large steps.] Based on the JI interpretations of the [[29edo]] and [[37edo]] tunings, it can in fact be viewed as a 2.3.7/5.11/5.13/5 temperament, i.e. a [[Non-over-1 temperament|non-over-1 temperament]] that approximates the chord 5:7:11:13:15. Since it is the same as Petrtri when you only care about the 9:10:11:13 (R-M2-M3-M5), it can be regarded as a flatter variant of Petrtri (analogous to how septimal meantone and flattone are the same when you only consider how it maps 8:9:10:12). | ||