Werckismic temperaments: Difference between revisions

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 __FORCETOC__
-=Rank four=
+This is a collection of rank-3 temperaments tempering out [[441/440]], but we can begin by looking at the rank-4 temperament.
-These are rank three temperaments tempering out 441/440, but we can began by looking at the rank four temperament.
-Minimax tuning
+== Werckismic ==
+Subgroup: 2.3.5.7.11
-[|1 0 0 0 0&gt;, |1/2 2/3 1/6 -1/3 1/6&gt;, |0 0 1 0 0&gt;,
+[[Mapping]]: [{{val| 1 0 0 0 -3 }}, {{val| 0 1 0 0 2 }}, {{val| 0 0 1 0 -1 }}, {{val| 0 0 0 1 2 }}]
-|1 -2/3 1/3 1/3 1/3&gt;, |0 0 0 0 1&gt;]
-Eigenmonzos: 2, 5, 11, 9/7
+[[Minimax tuning]]:
+* [[11-odd-limit]]
+: [{{monzo| 1 0 0 0 0 }}, {{monzo| 1/2 2/3 1/6 -1/3 1/6 }}, {{monzo| 0 0 1 0 0 }}, {{monzo| 1 -2/3 1/3 1/3 1/3 }}, {{monzo| 0 0 0 0 1 }}]
+: Eigenmonzos: 2, 5, 11, 9/7
-Map: [&lt;1 0 0 0 -3|, &lt;0 1 0 0 2|, &lt;0 0 1 0 -1|, &lt;0 0 0 1 2|]
+{{Val list|legend=1| 72, 118, 130, 159, 171, 190, 248, 289, 320 }}
-EDOs: 72, 118, 130, 159, 171, 190, 248, 289, 320
+== History ==
+Subgroup: 2.3.5.7.11
-=History=
+[[Comma list]]: 441/400, 4000/3993
-Commas: 441/400, 4000/3993
-Minimax tuning
+[[Mapping]]: [{{val| 1 2 0 0 1 }}, {{val| 0 -6 0 7 2 }}, {{val| 0 0 1 1 1 }}]
-[|1 0 0 0 0&gt;, |4/17 12/17 0 -6/17 6/17&gt;,
+Mapping generators: ~2, ~21/20, ~5
-|-27/17 4/17 0 -2/17 19/17&gt;,
-|8/17 -10/17 0 5/17 12/17&gt;, |0 0 0 0 1&gt;]
-Eigenmonzos: 2, 11, 9/7
+[[Minimax tuning]]:
+: [[11-odd-limit]]
+: [{{monzo| 1 0 0 0 0 }}, {{monzo| 4/17 12/17 0 -6/17 6/17 }}, {{monzo| -27/17 4/17 0 -2/17 19/17 }}, {{monzo| 8/17 -10/17 0 5/17 12/17 }}, {{monzo| 0 0 0 0 1 }}]
+: Eigenmonzos: 2, 11, 9/7
-Map: [&lt;1 2 0 0 1|, &lt;0 -6 0 7 2|, &lt;0 0 1 1 1|]
+{{Val list|legend=1| 58, 72, 130, 202, 217, 289, 491 }}
-Generators: 2, 21/20, 5
+[[Badness]]: 0.604 × 10<sup>-3</sup>
-EDOs: 58, 72, 130, 202, 217, 289, 491
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
-Badness: 0.000604
+Comma list: 364/363, 441/440, 1001/1000
-==13-limit==
+Mapping: [{{val| 1 2 0 0 1 2 }}, {{val| 0 -6 0 7 2 -9 }}, {{val| 0 0 1 1 1 1 }}]
-Commas: 364/363, 441/440, 1001/1000
-Minimax tuning
+Mapping generators: ~2, ~21/20, ~5
-[|1 0 0 0 0 0&gt;, |5/4 0 0 -3/8 0 3/8&gt;, |0 0 1 0 0 0&gt;,
+Minimax tuning:
-|7/8 0 1 7/16 0 -7/16&gt;, |5/4 0 1 1/8 0 -1/8&gt;,
+* 13-odd-limit
-|7/8 0 1 -9/16 0 9/16&gt;]
+: [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 5/4 0 0 -3/8 0 3/8 }}, {{monzo| 0 0 1 0 0 0 }}, {{monzo| 7/8 0 1 7/16 0 -7/16 }}, {{monzo| 5/4 0 1 1/8 0 -1/8 }}, {{monzo| 7/8 0 1 -9/16 0 9/16 }}]
+: Eigenmonzos: 2, 5, 13/7
-Eigenmonzos: 2, 5, 13/7
+Vals: {{Val list| 58, 72, 87, 130, 217, 289 }}
-Map: [&lt;1 2 0 0 1 2|, &lt;0 -6 0 7 2 -9|, &lt;0 0 1 1 1 1|]
+Badness: 0.540 × 10<sup>-3</sup>
-Generators: 2, 21/20, 5
+Complexity spectrum: 11/10, 15/13, 14/11, 4/3, 7/5, 5/4, 11/8, 18/13, 15/11, 13/12, 13/10, 6/5, 8/7, 16/15, 12/11, 13/11, 9/8, 16/13, 15/14, 10/9, 7/6, 11/9, 14/13, 9/7
-EDOs: 58, 72, 87, 130, 217, 289
+== Varuna ==
+Subgroup: 2.3.5.7.11
-Badness: 0.000540
+[[Comma list]]: 441/440, 8019/8000
-[[Spectrum_of_a_temperament|Spectrum]]: 11/10, 15/13, 14/11, 4/3, 7/5, 5/4, 11/8, 18/13, 15/11, 13/12, 13/10, 6/5, 8/7, 16/15, 12/11, 13/11, 9/8, 16/13, 15/14, 10/9, 7/6, 11/9, 14/13, 9/7
+[[Mapping]]: [{{val| 2 0 0 9 12 }}, {{val| 0 1 0 -4 -6 }}, {{val| 0 0 1 2 3 }}]
-= Varuna =
+Mapping generators: ~99/70, ~3, ~5
-Commas: 441/440, 8019/8000
-Map: [&lt;2 0 0 9 12|, &lt;0 1 0 -4 -6|, &lt;0 0 1 2 3|]
+{{Val list|legend=1| 12, 26, 46, 58, 72, 118, 130, 248, 320 }}
-EDOs: 12, 26, 46, 58, 72, 118, 130, 248, 320
+[[Badness]]: 0.419 × 10<sup>-3</sup>
-Generators: 99/70, 3, 5
-Badness: 0.000419
 [[Category:Regular temperament theory]]
 [[Category:Temperament collection]]
-[[Category:Werckismic]]
+[[Category:Werckismic temperaments| ]] <!-- main article -->
+[[Category:Rank 3]]
 [[Category:Varuna]]
-[[Category:Rank 3]]