Subgroup temperaments: Difference between revisions
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== 2.3.… subgroups == | == 2.3.… subgroups == | ||
=== Shrub === | === Shrub === | ||
Named by [[User: VectorGraphics|Vector]] in 2026, shrub is a [[restriction]] of [[diaschismic family #Diaschismic|diaschismic]] which omits the tritone to produce a [[5L 2s|diatonic]] scale. True to its name, it generates a [[neogothic major and minor|shrubmajor]]{{idio}} third (~425{{c}}) in quarter-comma tuning. It has an equal-temperament join of 12 & 17. | Named by [[User: VectorGraphics|Vector]] in 2026, shrub is a [[restriction]] of [[diaschismic family #Diaschismic|diaschismic]] which omits the tritone to produce a [[5L 2s|diatonic]] scale. True to its name, it generates a [[neogothic major and minor|shrubmajor]]{{idio}} third (~425{{c}}) in quarter-comma tuning. Specifically, the diatonic major third in shrub temperament is [[32/25]]. It has an equal-temperament join of 12 & 17. | ||
It can also admit a [[41/1|41st harmonic]] by tempering out [[82/81]] (same mapping as [[reversed meantone]]). However, its tuning tends to be flat, and with the rest of the harmonics tending sharp, this will increase the overall error. | It can also admit a [[41/1|41st harmonic]] by tempering out [[82/81]] (same mapping as [[reversed meantone]]). However, its tuning tends to be flat, and with the rest of the harmonics tending sharp, this will increase the overall error. | ||
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=== Barbados === | === Barbados === | ||
Barbados | Barbados tempers out [[676/675]] alone in the 2.3.13/5 subgroup. It melodically resembles [[semaphoresmic clan #Semaphore|semaphore]], but targets specifically the interseptimal intervals like [[13/10]] and [[15/13]]. [[#Bridgetown|Bridgetown]], which adds 11/5, is a notable extension of it. | ||
The {1, 3, 13/5} and {1, 3, 9, 13/5} [[minimax tuning]]s have 13/5 and 3 tuned pure, respectively. Edos which may be used for it include but are not limited to [[24edo]], [[29edo]], and [[53edo]], with [[mos scale]]s of size 5, 9, 14, 19, 24 and 29 making for a good variety of scales. If tuned near-optimally, it is just barely a [[microtemperament]], with errors of under one cent for 3 and 13/5, and given its ultra-low complexity, this makes barbados an extremely [[badness|low-badness]] temperament within its subgroup. | |||
Several related temperaments, all tempering out 676/675, can be found in [[The Archipelago]]. | Several related temperaments, all tempering out 676/675, can be found in [[The Archipelago]]. | ||
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[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[Tp tuning|Subgroup]] [[WE]]: ~2 = 1199.9502{{c}}, ~26/15 = 951.0713{{c}} | * [[Tp tuning|Subgroup]] [[WE]]: ~2 = 1199.9502{{c}}, ~26/15 = 951.0713{{c}} | ||
: [[error map]]: {{val| -0.050 +0.188 -0.950 }} | |||
* [[Tp tuning|Subgroup]] [[CWE]]: ~2 = 1200.0000{{c}}, ~26/15 = 951.0933{{c}} | * [[Tp tuning|Subgroup]] [[CWE]]: ~2 = 1200.0000{{c}}, ~26/15 = 951.0933{{c}} | ||
: error map: {{val| 0.000 +0.232 -0.934 }} | |||
{{Optimal ET sequence|legend=1| 5, 14, 19, 24, 29, 53, 82, 135 }} | {{Optimal ET sequence|legend=1| 5, 14, 19, 24, 29, 53, 82, 135 }} | ||
[[Badness]] ( | [[Badness]] (Sintel): 0.022 | ||
; Music | ; Music | ||