The Archipelago: Difference between revisions
→Subgroup temperaments: cleanup |
→Subgroup temperaments: cleanup; sorting; add some missing data |
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== Subgroup temperaments == | == Subgroup temperaments == | ||
=== Barbados === | === Barbados === | ||
Perhaps the simplest method of making use of the barbados triad and other characteristic island harmonies is to strip things down to essentials by tempering the 2.3.13/5 [[just intonation subgroup]]. The minimax tuning for this makes the generator the cube root of 20/13, or 248.5953 cents. | Perhaps the simplest method of making use of the barbados triad and other characteristic island harmonies is to strip things down to essentials by tempering the 2.3.13/5 [[just intonation subgroup]]. The [[minimax tuning]] for this makes the generator the cube root of 20/13, or 248.5953 cents. Edos which may be used for it are [[24edo]], [[29edo]], [[53edo]] and [[111edo]], with [[mos scale]]s of size 5, 9, 14, 19, 24 and 29 making for a good variety of scales. | ||
[[Subgroup]]: 2.3.13/5 | [[Subgroup]]: 2.3.13/5 | ||
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{{Val list|legend=1| 5, 24, 29, 53, 82, 111, 135 }} | {{Val list|legend=1| 5, 24, 29, 53, 82, 111, 135 }} | ||
Badness: ? | [[Badness]]: ? | ||
=== | ==== Tobago ==== | ||
{{See also| Chromatic pairs #Tobago }} | {{See also| Chromatic pairs #Tobago }} | ||
Tobago uses the semioctave period. It can be described as the 10 & 14 temperament and is related to [[neutral]] and [[barbados]]. | Tobago uses the semioctave period. It can be described as the 10 & 14 temperament and is related to [[neutral]] and [[barbados]]. | ||
Subgroup: 2.3.11.13/5 | [[Subgroup]]: 2.3.11.13/5 | ||
Comma list: 243/242, 676/675 | [[Comma list]]: 243/242 = {{monzo| -1 5 -2 }}, 676/675 = {{monzo| 2 -3 0 2 }} | ||
[[Sval]] [[mapping]]: [{{val| 2 0 -1 -2 }}, {{val| 0 2 5 3 }}] | [[Sval]] [[mapping]]: [{{val| 2 0 -1 -2 }}, {{val| 0 2 5 3 }}] | ||
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[[Tp tuning#T2 tuning|RMS error]]: 0.3533 cents | [[Tp tuning#T2 tuning|RMS error]]: 0.3533 cents | ||
=== Cata === | |||
{{Main| Catakleismic }} | |||
{{See also| Kleismic family #Cata }} | |||
Cata may be viewed as the [[restriction|"reduction"]] of [[catakleismic]] to the 2.3.5.13 subgroup. Another way to put it is that it is the rank-2 2.3.5.13 subgroup temperament tempering out 325/324, 625/624 and hence also 676/675. | |||
[[Subgroup]]: 2.3.5.13 | |||
[[Comma list]]: 325/324, 625/624 | |||
[[Sval]] [[mapping]]: [{{val| 1 0 1 0 }}, {{val| 0 6 5 14 }}] | |||
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~6/5 = 317.076 | |||
{{Val list|legend=1| 15, 19, 34, 53, 87, 140, 193, 246 }} | |||
[[Badness]]: 0.394 | |||
=== Parizekmic === | === Parizekmic === | ||
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{{Val list|legend=1| 5, 9, 10, 15, 19, 34, 53, 130, 140, 164, 183, 217, 270 }} | {{Val list|legend=1| 5, 9, 10, 15, 19, 34, 53, 130, 140, 164, 183, 217, 270 }} | ||
[[Badness]]: 0.00811 × 10<sup>-3</sup> | |||
; Music | ; Music | ||