Gamelismic clan: Difference between revisions
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The 2.3.7 [[Just_intonation_subgroups|subgroup]] comma for the '''gamelismic clan''' is the gamelisma, [[1029/1024]], with monzo {{monzo|-10 1 0 3}}. For any member of the clan, for the rank three [[Gamelismic family #Gamelan|gamelan temperament]] itself, and for the rank two 2.3.7 temperament [[slendric]], this means three [[8/7]] intervals give a fifth, [[3/2]]. In fact, we find that 3/2 = (8/7)<sup>3</sup> × 1029/1024. From this it follows that gamelismic temperaments tend to flatten both the fifth and the 7/4, or if they do not, the other of the pair must be flattened even more. [[36edo]] is a good tuning for gamelismic itself, though if the full 7-limit is desired, [[72edo]], [[77edo]] or [[118edo]] might be preferred. | The 2.3.7 [[Just_intonation_subgroups|subgroup]] comma for the '''gamelismic clan''' is the gamelisma, [[1029/1024]], with monzo {{monzo|-10 1 0 3}}. For any member of the clan, for the rank three [[Gamelismic family #Gamelan|gamelan temperament]] itself, and for the rank two 2.3.7 temperament [[slendric]], this means three [[8/7]] intervals give a fifth, [[3/2]]. In fact, we find that 3/2 = (8/7)<sup>3</sup> × 1029/1024. From this it follows that gamelismic temperaments tend to flatten both the fifth and the 7/4, or if they do not, the other of the pair must be flattened even more. [[36edo]] is a good tuning for gamelismic itself, though if the full 7-limit is desired, [[72edo]], [[77edo]] or [[118edo]] might be preferred. | ||
= Slendric = | |||
{{main| Slendric }} | |||
Subgroup: 2.3.7 | |||
Comma list: 1029/1024 | |||
[[POTE generator]]: ~8/7 = 233.688 | |||
[|1 | Sval mapping: [{{val| 1 1 3 }}, {{val| 0 3 -1 }}] | ||
Mapping generators: ~2, ~8/7 | |||
Gencom mapping: [{{val| 1 1 0 3 }}, {{val| 0 3 0 -1 }}] | |||
Gencom: [2 8/7; 1029/1024] | |||
{{Val list|legend=1| 36, 77, 113, 190 }} | |||
== Full seven limit children == | == Full seven limit children == | ||