5L 3s: Difference between revisions

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

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 the past, 5L 3s has been viewed as a MOS of the low-accuracy 5-limit temperament [[father]]. This viewpoint is increasingly considered obsolete, but "father" is still sometimes used for both the 5L 3s oneirotonic and the 3L 2s oneiro-pentatonic.)

More extreme oneirotonic temperaments include:

* [[Chromatic pairs#Tridec|Tridec]] (a 2.3.7/5.11/5.13/5 subgroup temperament that approximates 5:7:11:13:15), when the generator is between 453.33¢ (17\45) and 457.14¢ (8\21). These have near-equal L/s ratios of 6/5 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.

In the past, 5L 3s has been viewed as a MOS of the low-accuracy 5-limit temperament [[father]]. This viewpoint is increasingly considered obsolete, but "father" is still sometimes used for both the 5L 3s oneirotonic and the 3L 2s oneiro-pentatonic.

== Scale tree ==

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 # When the generator is between 461.54¢ (5\13) and 466.67¢ (7\18): [[A-Team]] (13&18, a 2.9.5.21 temperament that approximates 4:5:9:21)
 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 the past, 5L 3s has been viewed as a MOS of the low-accuracy 5-limit temperament [[father]]. This viewpoint is increasingly considered obsolete, but "father" is still sometimes used for both the 5L 3s oneirotonic and the 3L 2s oneiro-pentatonic.)
 More extreme oneirotonic temperaments include:
 * [[Chromatic pairs#Tridec|Tridec]] (a 2.3.7/5.11/5.13/5 subgroup temperament that approximates 5:7:11:13:15), when the generator is between 453.33¢ (17\45) and 457.14¢ (8\21). These have near-equal L/s ratios of 6/5 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.
+In the past, 5L 3s has been viewed as a MOS of the low-accuracy 5-limit temperament [[father]]. This viewpoint is increasingly considered obsolete, but "father" is still sometimes used for both the 5L 3s oneirotonic and the 3L 2s oneiro-pentatonic.
 == Scale tree ==