Gamelismic clan: Difference between revisions

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 = Valentine =
-{{main|Valentine}}
+{{main| Valentine }}
-{{see also|Starling temperaments #Valentine}}
+{{see also| Starling temperaments #Valentine }}
 == 5-limit ==
-Comma: 1990656/1953125
+Comma list: 1990656/1953125
 POTE generator: ~25/24 = 78.039
-Map: [&lt;1 1 2|, &lt;0 9 5|]
+Mapping: [{{val| 1 1 2 }}, {{val| 0 9 5 }}]
-EDOs: 15, 31, 46, 77, 123
+{{Val list|legend=1| 15, 31, 46, 77, 123 }}
 Badness: 0.1228
 == 7-limit ==
-[[Comma]]s: 126/125, 1029/1024
+[[Comma list]]: 126/125, 1029/1024
-[[Minimax tuning]]:
+[[POTE generator]]: ~21/20 = 77.864
--limit: [|1 0 0 0&gt;, |5/2 3/4 0 -3/4&gt;,
+[[Mapping]]: [{{val| 1 1 2 3 }}, {{val| 0 9 5 -3 }}]
-|17/6 5/12 0 -5/12&gt;, [5/2 -1/4 0 1/4&gt;<nowiki>]</nowiki>
-[[Eigenmonzo]]s: 2, 7/6
+Mapping generators: ~2, ~21/20
--limit: [|1 0 0 0&gt;, |10/7 6/7 0 -3/7&gt;,
+[[Minimax tuning]]:
-|47/21 10/21 0 -5/21&gt;, |20/7 -2/7 0 1/7&gt;<nowiki>]</nowiki>
+* 7-odd-limit:
+: [{{monzo| 1 0 0 0 }}, {{monzo| 5/2 3/4 0 -3/4 }}, {{monzo| 17/6 5/12 0 -5/12 }}, {{monzo| 5/2 -1/4 0 1/4 }}]
-[[Eigenmonzo]]s: 2, 9/7
+: [[Eigenmonzo]]s: 2, 7/6
+* 9-odd-limit:
-[[POTE_tuning|POTE generator]]: ~21/20 = 77.864
+: [{{monzo| 1 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 }}, {{monzo| 47/21 10/21 0 -5/21 }}, {{monzo| 20/7 -2/7 0 1/7 }}]
+: [[Eigenmonzo]]s: 2, 9/7
-Algebraic generator: [[Algebraic_number|smaller root]] of x^2-89x+92, or (89-sqrt(7553))/2, at 77.8616 cents.
-Map: [&lt;1 1 2 3|, &lt;0 9 5 -3|]
-Mapping [[generator]]s: 2, 21/20
+Algebraic generator: [[Algebraic number|smaller root]] of ''x''<sup>2</sup> - 89''x'' + 92, or (89 - sqrt (7553))/2, at 77.8616 cents.
-EDOs: {{EDOs|15, 31, 46, 77, 185, 262cd}}
+{{Val list|legend=1| 15, 31, 46, 77, 185, 262cd }}
 Badness: 0.0311
-==11-limit==
+== 11-limit ==
-[[Comma|Commas]]: 121/120, 126/125, 176/175
+Comma list: 121/120, 126/125, 176/175
-[[Minimax_tuning|Minimax tuning]]:
+[[POTE generator]]: ~21/20 = 77.881
-[|1 0 0 0 0&gt;, |1 0 0 -9/10 9/10&gt;,
+Mapping: [{{val| 1 1 2 3 3 }}, {{val| 0 9 5 -3 7 }}]
-|2 0 0 -1/2 1/2&gt;, |3 0 0 3/10 -3/10&gt;, |3 0 0 -7/10 7/10&gt;<nowiki>]</nowiki>
-Eigenmonzos: 2, 11/7
+Mapping generators: 2, 21/20
-[[POTE_tuning|POTE generator]]: ~21/20 = 77.881
+Minimax tuning:
+* 11-odd-limit:
+: [{{monzo| 1 0 0 0 0 }}, {{monzo| 1 0 0 -9/10 9/10 }}, {{monzo| 2 0 0 -1/2 1/2 }}, {{monzo| 3 0 0 3/10 -3/10 }}, {{monzo| 3 0 0 -7/10 7/10 }}]
+: Eigenmonzos: 2, 11/7
-Algebraic generator: [[Algebraic_number|positive root]] of 4x^3+15x^2-21, or else Gontrand2, the smallest positive root of 4x^7-8x^6+5.
+Algebraic generator: [[Algebraic number|positive root]] of 4''x''<sup>3</sup> + 15''x''<sup>2</sup> - 21, or else Gontrand2, the smallest positive root of 4''x''<sup>7</sup> - 8''x''<sup>6</sup> + 5.
-Map: [&lt;1 1 2 3 3|, &lt;0 9 5 -3 7|]
-Mapping generators: 2, 21/20
-[[EDO|EDOs]]: {{EDOs|15, 31, 46, 77, 262cdee, 339cdeee}}
+{{Val list|legend=1| 15, 31, 46, 77, 262cdee, 339cdeee }}
 Badness: 0.0167
-{{see also|Chords of valentine}}
+{{see also| Chords of valentine }}
 = Unidec =