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 <span style="display: block; text-align: right;">[[:de:Liese|Deutsch]]</span>
-[[Comma]]s: 81/80, 686/675
+Liese splits the twelfth interval of 3/1 into three generators of 10/7, using the comma 1029/1000. It also tempers out 686/675, the senga. [[74edo]] makes for a good liese tuning, though [[19edo]] can be used. The tuning is well-supplied with MOS: 7, 9, 11, 13, 15, 17, 19, 36, 55.
-Liese splits the twelfth interval of 3/1 into three generators of 10/7, using the comma 1029/1000. It also tempers out 686/675, the senga. [[74edo]] makes for a good liese tuning, though [[19edo]] can be used. The tuning is well-supplied with MOS: 7, 9, 11, 13, 15, 17, 19, 36, 55.
+Period: 1\1
+Optimal (POTE) generator: ~10/7 = 632.406
-and 9 limit minimax 1/4 comma
+EDO generators: [[17edo|9\17]], [[19edo|10\19]], [[36edo|19\36]], [[55edo|29\55]]
-[{{Monzo| 1 0 0 0 }}, {{Monzo| 1 0 1/4 0 }}, {{Monzo| 0 0 1 0 }}, {{Monzo| 2/3 0 11/12 0 }}]
+Scales (Scala files):
-[[Eigenmonzo]]s: 2, 5
+<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
+<div style="line-height:1.6;">Technical data</div>
+<div class="mw-collapsible-content">
-[[POTE generator]]: ~10/7 = 632.406
+[[Comma]] list: 81/80, 686/675
-Mapping generator: ~10/7
+Mapping: [{{val| 1 0 -4 -3 }}, {{val| 0 3 12 11 }}]
-Algebraic generator: Radix, the real root of ''x''<sup>5</sup> - 2''x''<sup>4</sup> + 2''x''<sup>3</sup> - 2''x''<sup>2</sup> + 2''x'' - 2, also a root of ''x''<sup>6</sup> - ''x''<sup>5</sup> - 2. The recurrence converges.
+Mapping generators: ~2, ~10/7
-Map: [&lt;1 0 -4 -3|, &lt;0 3 12 11|]
+Minimax tuning:
+* 7- and 9-odd-limit: 1/4 comma
+: [{{Monzo| 1 0 0 0 }}, {{Monzo| 1 0 1/4 0 }}, {{Monzo| 0 0 1 0 }}, {{Monzo| 2/3 0 11/12 0 }}]
+: [[Eigenmonzo]]s: 2, 5
-[[Generator]]s: 2, 10/7
+Algebraic generator: Radix, the real root of ''x''<sup>5</sup> - 2''x''<sup>4</sup> + 2''x''<sup>3</sup> - 2''x''<sup>2</sup> + 2''x'' - 2, also a root of ''x''<sup>6</sup> - ''x''<sup>5</sup> - 2. The recurrence converges.
-{{Vals|legend=1| 17c, 19, 36, 55, 74d }}
+{{Vals|legend=1| 17c, 19, 55, 74d }}
 [[Badness]]: 0.0467
+</div></div>
 == Liesel ==
-Commas: 56/55, 81/80, 540/539
-POTE generator: ~10/7 = 633.073
+Period: 1\1
+Optimal (POTE) generator: ~10/7 = 633.073
+EDO generators: [[17edo|9\17]], [[19edo|10\19]], [[36edo|19\36]]
+Scales (Scala files):
+<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
+<div style="line-height:1.6;">Technical data</div>
+<div class="mw-collapsible-content">
-Mapping generator: ~10/7
+Comma list: 56/55, 81/80, 540/539
-Map: [&lt;1 0 -4 -3 4|, &lt;0 3 12 11 -1|]
+Mapping: [{{val| 1 0 -4 -3 4 }}, {{val| 0 3 12 11 -1 }}]
-{{Vals|legend=1| 17c, 19, 36, 55e, 91cee }}
+Mapping generators: ~2, ~10/7
+{{Vals|legend=1| 17c, 19, 36, 91cee }}
 Badness: 0.0407
+</div></div>
 === 13-limit ===
 Liesel is a very natural 13-limit tuning, given the generator is so near 13/9.
-Commas: 56/55, 78/77, 81/80, 91/90
+Period: 1\1
-POTE generator: ~10/7 = ~13/9 = 633.042
+Optimal (POTE) generator: ~10/7 = 633.042
-Mapping generator: ~10/7
+EDO generators: [[17edo|9\17]], [[19edo|10\19]], [[36edo|19\36]]
-Map: [&lt;1 0 -4 -3 4 0|, &lt;0 3 12 11 -1 7|]
+Scales (Scala files):
-{{Vals|legend=1| 17c, 19, 36, 55ef, 91ceef }}
+<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
+<div style="line-height:1.6;">Technical data</div>
+<div class="mw-collapsible-content">
+Comma list: 56/55, 78/77, 81/80, 91/90
+Mapping: [{{val| 1 0 -4 -3 4 0 }}, {{val| 0 3 12 11 -1 7 }}]
+Mapping generators: ~2, ~10/7
+{{Vals|legend=1| 17c, 19, 36, 91ceef }}
 Badness: 0.0273
+</div></div>
 == Elisa ==
-Commas: 77/75, 81/80, 99/98
-POTE generator: ~10/7 = 633.061
+Period: 1\1
+Optimal (POTE) generator: ~10/7 = 633.061
+EDO generators: [[17edo|9\17]], [[19edo|10\19]], [[36edo|19\36]]
-Mapping generator: ~10/7
+Scales (Scala files):
-Map: [&lt;1 0 -4 -3 -5|, &lt;0 3 12 11 16|]
+<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
+<div style="line-height:1.6;">Technical data</div>
+<div class="mw-collapsible-content">
+Comma list: 77/75, 81/80, 99/98
+Mapping: [{{val| 1 0 -4 -3 -5 }}, {{val| 0 3 12 11 -1 16 }}]
+Mapping generators: ~2, ~10/7
 {{Vals|legend=1| 17c, 19e, 36e }}
 Badness: 0.0416
+</div></div>
 == Lisa ==
-Commas: 45/44, 81/80, 343/330
-POTE generator: ~10/7 = 631.370
+Period: 1\1
+Optimal (POTE) generator: ~10/7 = 631.370
+EDO generators: [[19edo|10\19]]
+Scales (Scala files):
+<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
+<div style="line-height:1.6;">Technical data</div>
+<div class="mw-collapsible-content">
+Comma list: 45/44, 81/80, 343/330
-Mapping generator: ~10/7
+Mapping: [{{val| 1 0 -4 -3 -6 }}, {{val| 0 3 12 11 -1 18 }}]
-Map: [&lt;1 0 -4 -3 -6|, &lt;0 3 12 11 18|]
+Mapping generators: ~2, ~10/7
-{{Vals|legend=1| 19 }}
+{{Vals|legend=1| 17cee, 19 }}
 Badness: 0.0548
+</div></div>
 === 13-limit ===
-Commas: 45/44, 81/80, 91/88, 147/143
-POTE generator: ~10/7 = 631.221
+Period: 1\1
-Map: [&lt;1 0 -4 -3 -6 0|, &lt;0 3 12 11 18 7|]
+Optimal (POTE) generator: ~10/7 = 631.221
-{{Vals|legend=1| 19 }}
+EDO generators: [[19edo|10\19]]
+Scales (Scala files):
+<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
+<div style="line-height:1.6;">Technical data</div>
+<div class="mw-collapsible-content">
+Comma list: 45/44, 81/80, 91/88, 147/143
+Mapping: [{{val| 1 0 -4 -3 -6 0 }}, {{val| 0 3 12 11 -1 18 7 }}]
+Mapping generators: ~2, ~10/7
+{{Vals|legend=1| 17cee, 19 }}
 Badness: 0.0361
+</div></div>
 = Jerome =