The Archipelago: Difference between revisions
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[[24edo|24edo]] approximates this triad to within an error of four cents, and [[29edo|29edo]] does even better, getting it to within 1.5 cents; either may be used as a tuning for the barbados temperament discussed below. | [[24edo|24edo]] approximates this triad to within an error of four cents, and [[29edo|29edo]] does even better, getting it to within 1.5 cents; either may be used as a tuning for the barbados temperament discussed below. | ||
= | =Rank five temperament= | ||
==Island== | |||
Comma: 676/675 | Comma: 676/675 | ||
Map: | Map:<br> | ||
<1 0 0 0 0 -1|<br> | |||
<1 0 0 0 0 -1| | <0 2 0 0 0 3|<br> | ||
<0 0 1 0 0 1|<br> | |||
<0 2 0 0 0 3| | <0 0 0 1 0 0|<br> | ||
<0 0 1 0 0 1| | |||
<0 0 0 1 0 0| | |||
<0 0 0 0 1 0| | <0 0 0 0 1 0| | ||
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[[Optimal_patent_val|Optimal patent val]]: [[940edo|940edo]] | [[Optimal_patent_val|Optimal patent val]]: [[940edo|940edo]] | ||
=Rank four temperaments= | =Rank four temperaments= | ||
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===Music=== | ===Music=== | ||
[http://micro.soonlabel.com/gene_ward_smith/Others/Sevish/Sevish%20-%20Desert%20Island%20Rain.mp3 Desert Island Rain] in 313et tuned Barbados[9], by [https://soundcloud.com/sevish/desert-island-rain Sevish] | [http://micro.soonlabel.com/gene_ward_smith/Others/Sevish/Sevish%20-%20Desert%20Island%20Rain.mp3 Desert Island Rain] in 313et tuned Barbados[9], by [https://soundcloud.com/sevish/desert-island-rain Sevish] | ||
==Trinidad== | ==Trinidad== | ||
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==[[Chromatic_pairs#Tobago|Tobago]]== | ==[[Chromatic_pairs#Tobago|Tobago]]== | ||
Subgroup: 2.3.11.13/5 | |||
Commas: 243/242, 676/675 | |||
POT2 generator: ~15/13 = 249.312 | |||
Map: [<2 0 -1 -2], <0 2 5 3]] | |||
EDOs: 10, 14, 24, 58, 82, 130 | |||
==Parizekmic== | ==Parizekmic== | ||
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Closely related to barbados temperament is parizekmic, the rank three 2.3.5.13 subgroup temperament tempering out 676/675. This is generated by 2, 5, and 15/13, where the minimax tuning makes 2 and 5 pure, and 15/13 sharp by sqrt(676/675), or 1.28145 cents. This is, in other words, the same sqrt(4/3) generator as the minimax tuning for barbados, and it gives parizekmic a just 5-limit, with barbados triads where the 13/10 is a cent flat. | Closely related to barbados temperament is parizekmic, the rank three 2.3.5.13 subgroup temperament tempering out 676/675. This is generated by 2, 5, and 15/13, where the minimax tuning makes 2 and 5 pure, and 15/13 sharp by sqrt(676/675), or 1.28145 cents. This is, in other words, the same sqrt(4/3) generator as the minimax tuning for barbados, and it gives parizekmic a just 5-limit, with barbados triads where the 13/10 is a cent flat. | ||
[[Smonzos_and_Svals|Sval map]] | [[Smonzos_and_Svals|Sval map]]: [<1 0 0 -1|, <0 2 0 3|, <0 0 1 1|] | ||
<1 0 0 -1| | |||
<0 2 0 3| | |||
<0 0 1 1| | |||
===Music=== | ===Music=== | ||
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EDOs: 5, 9, 10, 15, 19, 34, 53, 130, 140, 164, 183, 217, 270 | EDOs: 5, 9, 10, 15, 19, 34, 53, 130, 140, 164, 183, 217, 270 | ||
[[Category:archipelago]] | [[Category:archipelago]] | ||
[[Category:listen]] | [[Category:listen]] | ||
[[Category:overview]] | [[Category:overview]] | ||
[[Category: | [[Category:temperament]] | ||
[[Category:theory]] | [[Category:theory]] | ||