Star and Nova: Difference between revisions

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=== Notes of Star ===

By tempering out 126/125, leading to [[Starling_family#~~x7-limit starling~~|7-limit starling temperament]] we add the 7-limit intervals 8/7, 7/6, 7/5 and their inversions to the mix, and by tempering by 385/384 also, leading to [[Starling_family#~~x7-limit starling-11-limit~~|~~11-limit starling~~]], the 11/8 interval also. There is no significant tuning advantage to 11-limit starling, a planar temperament, over the linear temperament [[~~Starling_temperaments~~#Valentine ~~temperament-11-limit~~|valentine]], so we may consider Star to be a scale of valentine. In valentine, with generator a tempered 21/20 of 78 cents, the notes of Star are -4, 0, 1, 4, 5, 8, 9 and 13 generators; in the ordering of the scale itself, that's 0, 1, 4, 5, 8, 9, -4, 13.

By tempering out 126/125, leading to [[Starling_family#Starling|7-limit starling temperament]] we add the 7-limit intervals 8/7, 7/6, 7/5 and their inversions to the mix, and by tempering by 385/384 also, leading to [[Starling_family#Starnova|starnova]] (formerly known as ''undecimal starling''), the 11/8 interval also. There is no significant tuning advantage to 11-limit starling, a planar temperament, over the linear temperament [[Gamelismic clan#Valentine|valentine]], so we may consider Star to be a scale of valentine. In valentine, with generator a tempered 21/20 of 78 cents, the notes of Star are -4, 0, 1, 4, 5, 8, 9 and 13 generators; in the ordering of the scale itself, that's 0, 1, 4, 5, 8, 9, -4, 13.

Since there are a finite number of 11-limit 8-note [[Lesfip_scales|lesfip scales]], we may consider the [[star-lesfip|lesfip version of Star]], star-lesfip, to be canonical. It can be reached from a variety of starting points. Lesfiping the 5-limit transversal in the range 14 to 17 cents of tolerance leads to Star; so does lesfiping the 46et version in the range from 9 to 17 cents or the 77et version in the range 6 to 16 cents. Another tuning for Star, not very different, is [[star|Star in 77et]]; 77 giving the optimal patent val for both 11-limit starling and valentine.

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 === Notes of Star ===
-By tempering out 126/125, leading to [[Starling_family#x7-limit starling|7-limit starling temperament]] we add the 7-limit intervals 8/7, 7/6, 7/5 and their inversions to the mix, and by tempering by 385/384 also, leading to [[Starling_family#x7-limit starling-11-limit|11-limit starling]], the 11/8 interval also. There is no significant tuning advantage to 11-limit starling, a planar temperament, over the linear temperament [[Starling_temperaments#Valentine temperament-11-limit|valentine]], so we may consider Star to be a scale of valentine. In valentine, with generator a tempered 21/20 of 78 cents, the notes of Star are -4, 0, 1, 4, 5, 8, 9 and 13 generators; in the ordering of the scale itself, that's 0, 1, 4, 5, 8, 9, -4, 13.
+By tempering out 126/125, leading to [[Starling_family#Starling|7-limit starling temperament]] we add the 7-limit intervals 8/7, 7/6, 7/5 and their inversions to the mix, and by tempering by 385/384 also, leading to [[Starling_family#Starnova|starnova]] (formerly known as ''undecimal starling''), the 11/8 interval also. There is no significant tuning advantage to 11-limit starling, a planar temperament, over the linear temperament [[Gamelismic clan#Valentine|valentine]], so we may consider Star to be a scale of valentine. In valentine, with generator a tempered 21/20 of 78 cents, the notes of Star are -4, 0, 1, 4, 5, 8, 9 and 13 generators; in the ordering of the scale itself, that's 0, 1, 4, 5, 8, 9, -4, 13.
 Since there are a finite number of 11-limit 8-note [[Lesfip_scales|lesfip scales]], we may consider the [[star-lesfip|lesfip version of Star]], star-lesfip, to be canonical. It can be reached from a variety of starting points. Lesfiping the 5-limit transversal in the range 14 to 17 cents of tolerance leads to Star; so does lesfiping the 46et version in the range from 9 to 17 cents or the 77et version in the range 6 to 16 cents. Another tuning for Star, not very different, is [[star|Star in 77et]]; 77 giving the optimal patent val for both 11-limit starling and valentine.