Gamelismic clan: Difference between revisions

+slendric (replace old incomplete data)
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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.


7-limit minimax
= Slendric =
{{main| Slendric }}


[|1 0 0 0&gt;, |5/2 3/4 0 -3/4&gt;,
Subgroup: 2.3.7
|5/2 -1/4 1 -3/4&gt;, |5/2 -1/4 0 1/4&gt;<nowiki>]</nowiki>


Eigenmonzos: 2, 7/6, 6/5
Comma list: 1029/1024


9-limit minimax
[[POTE generator]]: ~8/7 = 233.688


[|1 0 0 0&gt;, |10/7 6/7 0 -3/7&gt;,
Sval mapping: [{{val| 1 1 3 }}, {{val| 0 3 -1 }}]  
|10/7 -1/7 1 -3/7&gt;, |20/7 -2/7 0 1/7&gt;<nowiki>]</nowiki>


Eigenmonzos: 2, 6/5, 9/7
Mapping generators: ~2, ~8/7


Lattice basis: 8/7 0.5192 5/4 2.3219
Gencom mapping: [{{val| 1 1 0 3 }}, {{val| 0 3 0 -1 }}]


Angle(8/7, 5/4) = 90 degrees
Gencom: [2 8/7; 1029/1024]


Map to lattice: [&lt;0 3 0 -1|, &lt;0 0 1 0|]
{{Val list|legend=1| 36, 77, 113, 190 }}
 
No-five map: [&lt;1 1 0 3|, &lt;0 3 0 -1|]
 
No-five mapping generators: 2, 8/7
 
No-five [[POTE_tuning|POTE generator]]: ~8/7 = 233.688
 
No-five EDOs: {{EDOs|5, 36, 77, 190}}


== Full seven limit children ==
== Full seven limit children ==