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Schismatic family: Difference between revisions

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Wikispaces>genewardsmith
**Imported revision 338060268 - Original comment: **
Wikispaces>genewardsmith
**Imported revision 344219610 - Original comment: **
Line 1: Line 1:
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-05-21 17:10:23 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-06-10 14:42:22 UTC</tt>.<br>
: The original revision id was <tt>338060268</tt>.<br>
: The original revision id was <tt>344219610</tt>.<br>
: The revision comment was: <tt></tt><br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
Line 13: Line 13:
The 5-limit version of the temperament is a [[Microtempering|microtemperament]], sometimes called **Helmholtz** or schismatic, which flattens the fifth by a fraction of a schisma, but some other members of the family are less accurate. As a 5-limit system, it is far more accurate than meantone but still with manageable complexity. [[53edo]] is a possible tuning for schismatic, but you need [[118edo]] if you want to get the full effect. In exact analogy with 1/4 comma meantone there is also 1/8 schisma schismatic, with pure major thirds and fifths flattened by 1/8 schisma. Since 1/8 of a schisma is 0.244 cents, this falls into the range of microtempering.
The 5-limit version of the temperament is a [[Microtempering|microtemperament]], sometimes called **Helmholtz** or schismatic, which flattens the fifth by a fraction of a schisma, but some other members of the family are less accurate. As a 5-limit system, it is far more accurate than meantone but still with manageable complexity. [[53edo]] is a possible tuning for schismatic, but you need [[118edo]] if you want to get the full effect. In exact analogy with 1/4 comma meantone there is also 1/8 schisma schismatic, with pure major thirds and fifths flattened by 1/8 schisma. Since 1/8 of a schisma is 0.244 cents, this falls into the range of microtempering.


[[POTE tuning|POTE generator]]: 701.736
[[POTE tuning|POTE generator]]: ~3/2 = 701.736
Mapping generator: ~3


Map: [&lt;1 0 15|, &lt;0 1 -8|]
Map: [&lt;1 0 15|, &lt;0 1 -8|]
Line 33: Line 34:
Eigenmonzos: 2, 9/7
Eigenmonzos: 2, 9/7


[[POTE tuning|POTE generator]]: 702.085
[[POTE tuning|POTE generator]]: ~3/2 = 702.085
Mapping generator: ~3


Map: [&lt;1 0 15 25|, &lt;0 1 -8 -14|]
Map: [&lt;1 0 15 25|, &lt;0 1 -8 -14|]
Line 48: Line 50:
Eigenmonzos: 2, 9/7
Eigenmonzos: 2, 9/7


[[POTE tuning|POTE generator]]: 702.157
[[POTE tuning|POTE generator]]: ~3/2 = 702.157
Mapping generator: ~3


Map: [&lt;1 0 15 25 -33|, &lt;0 1 -8 -14 23|]
Map: [&lt;1 0 15 25 -33|, &lt;0 1 -8 -14 23|]
Line 57: Line 60:
Commas: 225/224, 275/273, 325/324, 385/384
Commas: 225/224, 275/273, 325/324, 385/384


[[POTE tuning|POTE generator]]: 702.113
[[POTE tuning|POTE generator]]: ~3/2 = 702.113
Mapping generator: ~3


Map: [&lt;1 0 15 25 -33 -28|, &lt;0 1 -8 -14 23 20|]
Map: [&lt;1 0 15 25 -33 -28|, &lt;0 1 -8 -14 23 20|]
Line 66: Line 70:
Commas: 100/99, 225/224, 245/242
Commas: 100/99, 225/224, 245/242


[[POTE tuning|POTE generator]]: 702.321
[[POTE tuning|POTE generator]]: ~3/2 = 702.321
Mapping generator: ~3


Map: [&lt;1 0 15 25 32|, &lt;0 1 -8 -14 -18|]
Map: [&lt;1 0 15 25 32|, &lt;0 1 -8 -14 -18|]
Line 75: Line 80:
Commas: 100/99, 105/104, 196/195, 245/242
Commas: 100/99, 105/104, 196/195, 245/242


[[POTE tuning|POTE generator]]: 702.559
[[POTE tuning|POTE generator]]: ~3/2 = 702.559
Mapping generator: ~3


Map: [&lt;1 0 15 25 32 37|, &lt;0 1 -8 -14 -18 -21|]
Map: [&lt;1 0 15 25 32 37|, &lt;0 1 -8 -14 -18 -21|]
Line 85: Line 91:


POTE generator: ~3/2 = 701.725
POTE generator: ~3/2 = 701.725
Mapping generator: ~3


Map: [&lt;1 0 15 25 51|, &lt;0 1 -8 -14 -30|]
Map: [&lt;1 0 15 25 51|, &lt;0 1 -8 -14 -30|]
Line 94: Line 101:


POTE generator: ~3/2 = 701.747
POTE generator: ~3/2 = 701.747
Mapping generator: ~3


Map: [&lt;1 0 15 25 51 56|, &lt;0 1 -8 -14 -30 -33|]
Map: [&lt;1 0 15 25 51 56|, &lt;0 1 -8 -14 -30 -33|]
Line 102: Line 110:
Commas: 121/120, 225/224, 3125/3087
Commas: 121/120, 225/224, 3125/3087


POTE generator: ~220/189 = 248.918
POTE generator: ~63/55 = 248.918
Mapping generator: ~110/63


Map: [&lt;1 0 15 25 9|, &lt;0 2 -16 -28 -7|]
Map: [&lt;1 0 15 25 9|, &lt;0 2 -16 -28 -7|]
Line 111: Line 120:
Commas: 121/120, 169/168, 225/224, 275/273
Commas: 121/120, 169/168, 225/224, 275/273


POTE generator: ~52/45 = 248.918
POTE generator: ~15/13 = 248.918
Mapping generator: ~26/15


Map: [&lt;1 0 15 25 9 14|, &lt;0 2 -16 -28 -7 -13|]
Map: [&lt;1 0 15 25 9 14|, &lt;0 2 -16 -28 -7 -13|]
Line 125: Line 135:
[[Eigenmonzo|Eigenmonzos]]: 2, 5/4
[[Eigenmonzo|Eigenmonzos]]: 2, 5/4


[[POTE tuning|POTE generator]]: 233.930
[[POTE tuning|POTE generator]]: ~8/7 = 233.930
Mapping generator: ~8/7


Map: [&lt;1 1 7 3|, &lt;0 3 -24 -1|]
Map: [&lt;1 1 7 3|, &lt;0 3 -24 -1|]
Line 141: Line 152:
[[Eigenmonzo|Eigenmonzos]]: 2, 5/4
[[Eigenmonzo|Eigenmonzos]]: 2, 5/4


[[POTE tuning|POTE generator]]: 233.931
[[POTE tuning|POTE generator]]: ~8/7 = 233.931
Mapping generator: ~8/7


Map: [&lt;1 1 7 3 -2|, &lt;0 3 -24 -1 28|]
Map: [&lt;1 1 7 3 -2|, &lt;0 3 -24 -1 28|]
Line 151: Line 163:


POTE generator: ~8/7 = 233.890
POTE generator: ~8/7 = 233.890
Mapping generator: ~8/7


Map: [&lt;1 1 7 3 -2 0|, &lt;0 3 -24 -1 28 19|]
Map: [&lt;1 1 7 3 -2 0|, &lt;0 3 -24 -1 28 19|]
Line 160: Line 173:


POTE generator: ~9/7 = 433.901
POTE generator: ~9/7 = 433.901
Mapping generator: ~9/7


Map: [&lt;2 1 22 2|, &lt;0 3 -24 5|]
Map: [&lt;2 1 22 2|, &lt;0 3 -24 5|]
Line 169: Line 183:


POTE generator: ~9/7 = 433.911
POTE generator: ~9/7 = 433.911
Mapping generator: ~9/7


Map: [&lt;2 1 22 2 25|, &lt;0 3 -24 5 -25|]
Map: [&lt;2 1 22 2 25|, &lt;0 3 -24 5 -25|]
Line 178: Line 193:


POTE generator: ~3/2 = 701.556
POTE generator: ~3/2 = 701.556
Mapping generator: ~3


Map: [&lt;1 0 15 6|, &lt;0 1 -8 -2|]
Map: [&lt;1 0 15 6|, &lt;0 1 -8 -2|]
Line 188: Line 204:


POTE generator ~3/2 = 702.136
POTE generator ~3/2 = 702.136
Mapping generator: ~3


Map: [&lt;1 0 15 6 13|, &lt;0 1 -8 -2 -6|]
Map: [&lt;1 0 15 6 13|, &lt;0 1 -8 -2 -6|]
Line 207: Line 224:


[[POTE tuning|POTE generator]]: 701.757
[[POTE tuning|POTE generator]]: 701.757
Mapping generator: ~3


Map: [&lt;1 0 15 -59|, &lt;0 1 -8 39|]
Map: [&lt;1 0 15 -59|, &lt;0 1 -8 39|]
Line 223: Line 241:


[[POTE tuning|POTE generator]]: 701.239
[[POTE tuning|POTE generator]]: 701.239
Mapping generator: ~3


Map: [&lt;1 0 15 -44|, &lt;0 1 -8 -26|]
Map: [&lt;1 0 15 -44|, &lt;0 1 -8 -26|]
Line 239: Line 258:


[[POTE tuning|POTE generator]]: 701.592
[[POTE tuning|POTE generator]]: 701.592
Mapping generator: ~3


Map: [&lt;2 0 30 69|, &lt;0 1 -8 -20|]
Map: [&lt;2 0 30 69|, &lt;0 1 -8 -20|]
Line 249: Line 269:


POTE generator: ~3/2 = 701.612
POTE generator: ~3/2 = 701.612
Mapping generator: ~3


Map: [&lt;2 0 30 69 102|, &lt;0 1 -8 -20 -30|]
Map: [&lt;2 0 30 69 102|, &lt;0 1 -8 -20 -30|]
Line 258: Line 279:


POTE generator: ~3/2 = 701.590
POTE generator: ~3/2 = 701.590
Mapping generator: ~3


Map: [&lt;2 0 30 69 102 -75|, &lt;0 1 -8 -20 -30 26|]
Map: [&lt;2 0 30 69 102 -75|, &lt;0 1 -8 -20 -30 26|]
Line 267: Line 289:


POTE generator: ~36/35 = 50.920
POTE generator: ~36/35 = 50.920
Mapping generator: ~35/24


Map: [&lt;2 1 22 -15|, &lt;0 2 -16 19|]
Map: [&lt;2 1 22 -15|, &lt;0 2 -16 19|]
Line 277: Line 300:


POTE generator: ~36/35 = 50.918
POTE generator: ~36/35 = 50.918
Mapping generator: ~16/11


Map: [&lt;2 1 22 -15 8|, &lt;0 2 -16 19 -1|]
Map: [&lt;2 1 22 -15 8|, &lt;0 2 -16 19 -1|]
Line 286: Line 310:


POTE generator: ~36/35 = 50.938
POTE generator: ~36/35 = 50.938
Mapping generator: ~16/11


Map: [&lt;2 1 22 -15 8 15|, &lt;0 2 -16 19 -1 -7|]
Map: [&lt;2 1 22 -15 8 15|, &lt;0 2 -16 19 -1 -7|]
Line 300: Line 325:
Eigenmonzos: 2, 9/7
Eigenmonzos: 2, 9/7


[[POTE tuning|POTE generator]]: 701.742
[[POTE tuning|POTE generator]]: ~3/2 = 701.742
Mapping generator: ~3


Map: [&lt;3 0 45 94|, &lt;0 1 -8 -18|]
Map: [&lt;3 0 45 94|, &lt;0 1 -8 -18|]
Line 316: Line 342:
Eigenmonzos: 2, 9/7
Eigenmonzos: 2, 9/7


[[POTE tuning|POTE generator]]: 175.434
[[POTE tuning|POTE generator]]: ~448/405 = 175.434
Mapping generator: ~448/405


Map: [&lt;1 1 7 5|, &lt;0 4 -32 -15|]
Map: [&lt;1 1 7 5|, &lt;0 4 -32 -15|]
Line 327: Line 354:


POTE generator: ~256/231 = 175.406
POTE generator: ~256/231 = 175.406
Mapping generator: ~256/231


Map: [&lt;1 1 7 5 2|, &lt;0 4 -32 -15 10|]
Map: [&lt;1 1 7 5 2|, &lt;0 4 -32 -15 10|]
Line 336: Line 364:


POTE generator: ~21/20 = 83.053
POTE generator: ~21/20 = 83.053
Mapping generator: ~21/20


Map: [&lt;1 2 -1 -1|, &lt;0 -6 48 55|]
Map: [&lt;1 2 -1 -1|, &lt;0 -6 48 55|]
Line 345: Line 374:


POTE generator: ~21/20 = 83.049
POTE generator: ~21/20 = 83.049
Mapping generator: ~21/20


Map: [&lt;1 2 -1 -1 0|, &lt;0 -6 48 55 50|]
Map: [&lt;1 2 -1 -1 0|, &lt;0 -6 48 55 50|]
Line 354: Line 384:


POTE generator: ~21/20 = 83.049
POTE generator: ~21/20 = 83.049
Mapping generator: ~21/20


Map: [&lt;1 2 -1 -1 0 1|, &lt;0 -6 48 55 50 39|]
Map: [&lt;1 2 -1 -1 0 1|, &lt;0 -6 48 55 50 39|]
Line 363: Line 394:


POTE generator: ~243/224 = 140.350
POTE generator: ~243/224 = 140.350
Mapping generator: ~243/224


Map: [&lt;1 1 7 0|, &lt;0 5 -40 24|]
Map: [&lt;1 1 7 0|, &lt;0 5 -40 24|]
Line 373: Line 405:


POTE generator: ~56/45 = 380.355
POTE generator: ~56/45 = 380.355
Mapping generator: ~56/45


Map: [&lt;1 0 15 12|, &lt;0 5 -40 -29|]
Map: [&lt;1 0 15 12|, &lt;0 5 -40 -29|]
Line 383: Line 416:


POTE generator: ~56/45 = 380.352
POTE generator: ~56/45 = 380.352
Mapping generator: ~56/45


Map: [&lt;1 0 15 12 -7|, &lt;0 5 -40 -29 33|]
Map: [&lt;1 0 15 12 -7|, &lt;0 5 -40 -29 33|]
Line 392: Line 426:


POTE generator: ~3/2 = 701.713
POTE generator: ~3/2 = 701.713
Mapping generator: ~3


Map: [&lt;8 0 120 -117|, &lt;0 1 -8 11|]
Map: [&lt;8 0 120 -117|, &lt;0 1 -8 11|]
Line 402: Line 437:


POTE generator: ~3/2 = 701.713
POTE generator: ~3/2 = 701.713
Mapping generator: ~3


Map: [&lt;8 0 120 -117 15|, &lt;0 1 -8 11 1|]
Map: [&lt;8 0 120 -117 15|, &lt;0 1 -8 11 1|]
Line 411: Line 447:


POTE generator: ~3/2 = 701.725
POTE generator: ~3/2 = 701.725
Mapping generator: ~3


Map: [&lt;8 0 120 -117 15 93|, &lt;0 1 -8 11 1 -5|]
Map: [&lt;8 0 120 -117 15 93|, &lt;0 1 -8 11 1 -5|]
EDOs: 24, 224, 472, 696
EDOs: 24, 224, 472, 696
Badness: 0.0304
Badness: 0.0304
</pre></div>
</pre></div>
<h4>Original HTML content:</h4>
<h4>Original HTML content:</h4>
Line 463: Line 499:
The 5-limit version of the temperament is a &lt;a class="wiki_link" href="/Microtempering"&gt;microtemperament&lt;/a&gt;, sometimes called &lt;strong&gt;Helmholtz&lt;/strong&gt; or schismatic, which flattens the fifth by a fraction of a schisma, but some other members of the family are less accurate. As a 5-limit system, it is far more accurate than meantone but still with manageable complexity. &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt; is a possible tuning for schismatic, but you need &lt;a class="wiki_link" href="/118edo"&gt;118edo&lt;/a&gt; if you want to get the full effect. In exact analogy with 1/4 comma meantone there is also 1/8 schisma schismatic, with pure major thirds and fifths flattened by 1/8 schisma. Since 1/8 of a schisma is 0.244 cents, this falls into the range of microtempering.&lt;br /&gt;
The 5-limit version of the temperament is a &lt;a class="wiki_link" href="/Microtempering"&gt;microtemperament&lt;/a&gt;, sometimes called &lt;strong&gt;Helmholtz&lt;/strong&gt; or schismatic, which flattens the fifth by a fraction of a schisma, but some other members of the family are less accurate. As a 5-limit system, it is far more accurate than meantone but still with manageable complexity. &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt; is a possible tuning for schismatic, but you need &lt;a class="wiki_link" href="/118edo"&gt;118edo&lt;/a&gt; if you want to get the full effect. In exact analogy with 1/4 comma meantone there is also 1/8 schisma schismatic, with pure major thirds and fifths flattened by 1/8 schisma. Since 1/8 of a schisma is 0.244 cents, this falls into the range of microtempering.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 701.736&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~3/2 = 701.736&lt;br /&gt;
Mapping generator: ~3&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 15|, &amp;lt;0 1 -8|]&lt;br /&gt;
Map: [&amp;lt;1 0 15|, &amp;lt;0 1 -8|]&lt;br /&gt;
Line 483: Line 520:
Eigenmonzos: 2, 9/7&lt;br /&gt;
Eigenmonzos: 2, 9/7&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 702.085&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~3/2 = 702.085&lt;br /&gt;
Mapping generator: ~3&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 15 25|, &amp;lt;0 1 -8 -14|]&lt;br /&gt;
Map: [&amp;lt;1 0 15 25|, &amp;lt;0 1 -8 -14|]&lt;br /&gt;
Line 498: Line 536:
Eigenmonzos: 2, 9/7&lt;br /&gt;
Eigenmonzos: 2, 9/7&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 702.157&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~3/2 = 702.157&lt;br /&gt;
Mapping generator: ~3&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 15 25 -33|, &amp;lt;0 1 -8 -14 23|]&lt;br /&gt;
Map: [&amp;lt;1 0 15 25 -33|, &amp;lt;0 1 -8 -14 23|]&lt;br /&gt;
Line 507: Line 546:
Commas: 225/224, 275/273, 325/324, 385/384&lt;br /&gt;
Commas: 225/224, 275/273, 325/324, 385/384&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 702.113&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~3/2 = 702.113&lt;br /&gt;
Mapping generator: ~3&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 15 25 -33 -28|, &amp;lt;0 1 -8 -14 23 20|]&lt;br /&gt;
Map: [&amp;lt;1 0 15 25 -33 -28|, &amp;lt;0 1 -8 -14 23 20|]&lt;br /&gt;
Line 516: Line 556:
Commas: 100/99, 225/224, 245/242&lt;br /&gt;
Commas: 100/99, 225/224, 245/242&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 702.321&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~3/2 = 702.321&lt;br /&gt;
Mapping generator: ~3&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 15 25 32|, &amp;lt;0 1 -8 -14 -18|]&lt;br /&gt;
Map: [&amp;lt;1 0 15 25 32|, &amp;lt;0 1 -8 -14 -18|]&lt;br /&gt;
Line 525: Line 566:
Commas: 100/99, 105/104, 196/195, 245/242&lt;br /&gt;
Commas: 100/99, 105/104, 196/195, 245/242&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 702.559&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~3/2 = 702.559&lt;br /&gt;
Mapping generator: ~3&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 15 25 32 37|, &amp;lt;0 1 -8 -14 -18 -21|]&lt;br /&gt;
Map: [&amp;lt;1 0 15 25 32 37|, &amp;lt;0 1 -8 -14 -18 -21|]&lt;br /&gt;
Line 535: Line 577:
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~3/2 = 701.725&lt;br /&gt;
POTE generator: ~3/2 = 701.725&lt;br /&gt;
Mapping generator: ~3&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 15 25 51|, &amp;lt;0 1 -8 -14 -30|]&lt;br /&gt;
Map: [&amp;lt;1 0 15 25 51|, &amp;lt;0 1 -8 -14 -30|]&lt;br /&gt;
Line 544: Line 587:
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~3/2 = 701.747&lt;br /&gt;
POTE generator: ~3/2 = 701.747&lt;br /&gt;
Mapping generator: ~3&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 15 25 51 56|, &amp;lt;0 1 -8 -14 -30 -33|]&lt;br /&gt;
Map: [&amp;lt;1 0 15 25 51 56|, &amp;lt;0 1 -8 -14 -30 -33|]&lt;br /&gt;
Line 552: Line 596:
Commas: 121/120, 225/224, 3125/3087&lt;br /&gt;
Commas: 121/120, 225/224, 3125/3087&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~220/189 = 248.918&lt;br /&gt;
POTE generator: ~63/55 = 248.918&lt;br /&gt;
Mapping generator: ~110/63&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 15 25 9|, &amp;lt;0 2 -16 -28 -7|]&lt;br /&gt;
Map: [&amp;lt;1 0 15 25 9|, &amp;lt;0 2 -16 -28 -7|]&lt;br /&gt;
Line 561: Line 606:
Commas: 121/120, 169/168, 225/224, 275/273&lt;br /&gt;
Commas: 121/120, 169/168, 225/224, 275/273&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~52/45 = 248.918&lt;br /&gt;
POTE generator: ~15/13 = 248.918&lt;br /&gt;
Mapping generator: ~26/15&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 15 25 9 14|, &amp;lt;0 2 -16 -28 -7 -13|]&lt;br /&gt;
Map: [&amp;lt;1 0 15 25 9 14|, &amp;lt;0 2 -16 -28 -7 -13|]&lt;br /&gt;
Line 575: Line 621:
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 5/4&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 5/4&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 233.930&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~8/7 = 233.930&lt;br /&gt;
Mapping generator: ~8/7&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 7 3|, &amp;lt;0 3 -24 -1|]&lt;br /&gt;
Map: [&amp;lt;1 1 7 3|, &amp;lt;0 3 -24 -1|]&lt;br /&gt;
Line 591: Line 638:
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 5/4&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 5/4&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 233.931&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~8/7 = 233.931&lt;br /&gt;
Mapping generator: ~8/7&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 7 3 -2|, &amp;lt;0 3 -24 -1 28|]&lt;br /&gt;
Map: [&amp;lt;1 1 7 3 -2|, &amp;lt;0 3 -24 -1 28|]&lt;br /&gt;
Line 601: Line 649:
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~8/7 = 233.890&lt;br /&gt;
POTE generator: ~8/7 = 233.890&lt;br /&gt;
Mapping generator: ~8/7&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 7 3 -2 0|, &amp;lt;0 3 -24 -1 28 19|]&lt;br /&gt;
Map: [&amp;lt;1 1 7 3 -2 0|, &amp;lt;0 3 -24 -1 28 19|]&lt;br /&gt;
Line 610: Line 659:
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~9/7 = 433.901&lt;br /&gt;
POTE generator: ~9/7 = 433.901&lt;br /&gt;
Mapping generator: ~9/7&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 1 22 2|, &amp;lt;0 3 -24 5|]&lt;br /&gt;
Map: [&amp;lt;2 1 22 2|, &amp;lt;0 3 -24 5|]&lt;br /&gt;
Line 619: Line 669:
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~9/7 = 433.911&lt;br /&gt;
POTE generator: ~9/7 = 433.911&lt;br /&gt;
Mapping generator: ~9/7&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 1 22 2 25|, &amp;lt;0 3 -24 5 -25|]&lt;br /&gt;
Map: [&amp;lt;2 1 22 2 25|, &amp;lt;0 3 -24 5 -25|]&lt;br /&gt;
Line 628: Line 679:
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~3/2 = 701.556&lt;br /&gt;
POTE generator: ~3/2 = 701.556&lt;br /&gt;
Mapping generator: ~3&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 15 6|, &amp;lt;0 1 -8 -2|]&lt;br /&gt;
Map: [&amp;lt;1 0 15 6|, &amp;lt;0 1 -8 -2|]&lt;br /&gt;
Line 638: Line 690:
&lt;br /&gt;
&lt;br /&gt;
POTE generator ~3/2 = 702.136&lt;br /&gt;
POTE generator ~3/2 = 702.136&lt;br /&gt;
Mapping generator: ~3&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 15 6 13|, &amp;lt;0 1 -8 -2 -6|]&lt;br /&gt;
Map: [&amp;lt;1 0 15 6 13|, &amp;lt;0 1 -8 -2 -6|]&lt;br /&gt;
Line 657: Line 710:
&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 701.757&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 701.757&lt;br /&gt;
Mapping generator: ~3&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 15 -59|, &amp;lt;0 1 -8 39|]&lt;br /&gt;
Map: [&amp;lt;1 0 15 -59|, &amp;lt;0 1 -8 39|]&lt;br /&gt;
Line 673: Line 727:
&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 701.239&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 701.239&lt;br /&gt;
Mapping generator: ~3&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 15 -44|, &amp;lt;0 1 -8 -26|]&lt;br /&gt;
Map: [&amp;lt;1 0 15 -44|, &amp;lt;0 1 -8 -26|]&lt;br /&gt;
Line 689: Line 744:
&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 701.592&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 701.592&lt;br /&gt;
Mapping generator: ~3&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 0 30 69|, &amp;lt;0 1 -8 -20|]&lt;br /&gt;
Map: [&amp;lt;2 0 30 69|, &amp;lt;0 1 -8 -20|]&lt;br /&gt;
Line 699: Line 755:
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~3/2 = 701.612&lt;br /&gt;
POTE generator: ~3/2 = 701.612&lt;br /&gt;
Mapping generator: ~3&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 0 30 69 102|, &amp;lt;0 1 -8 -20 -30|]&lt;br /&gt;
Map: [&amp;lt;2 0 30 69 102|, &amp;lt;0 1 -8 -20 -30|]&lt;br /&gt;
Line 708: Line 765:
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~3/2 = 701.590&lt;br /&gt;
POTE generator: ~3/2 = 701.590&lt;br /&gt;
Mapping generator: ~3&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 0 30 69 102 -75|, &amp;lt;0 1 -8 -20 -30 26|]&lt;br /&gt;
Map: [&amp;lt;2 0 30 69 102 -75|, &amp;lt;0 1 -8 -20 -30 26|]&lt;br /&gt;
Line 717: Line 775:
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~36/35 = 50.920&lt;br /&gt;
POTE generator: ~36/35 = 50.920&lt;br /&gt;
Mapping generator: ~35/24&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 1 22 -15|, &amp;lt;0 2 -16 19|]&lt;br /&gt;
Map: [&amp;lt;2 1 22 -15|, &amp;lt;0 2 -16 19|]&lt;br /&gt;
Line 727: Line 786:
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~36/35 = 50.918&lt;br /&gt;
POTE generator: ~36/35 = 50.918&lt;br /&gt;
Mapping generator: ~16/11&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 1 22 -15 8|, &amp;lt;0 2 -16 19 -1|]&lt;br /&gt;
Map: [&amp;lt;2 1 22 -15 8|, &amp;lt;0 2 -16 19 -1|]&lt;br /&gt;
Line 736: Line 796:
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~36/35 = 50.938&lt;br /&gt;
POTE generator: ~36/35 = 50.938&lt;br /&gt;
Mapping generator: ~16/11&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 1 22 -15 8 15|, &amp;lt;0 2 -16 19 -1 -7|]&lt;br /&gt;
Map: [&amp;lt;2 1 22 -15 8 15|, &amp;lt;0 2 -16 19 -1 -7|]&lt;br /&gt;
Line 750: Line 811:
Eigenmonzos: 2, 9/7&lt;br /&gt;
Eigenmonzos: 2, 9/7&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 701.742&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~3/2 = 701.742&lt;br /&gt;
Mapping generator: ~3&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;3 0 45 94|, &amp;lt;0 1 -8 -18|]&lt;br /&gt;
Map: [&amp;lt;3 0 45 94|, &amp;lt;0 1 -8 -18|]&lt;br /&gt;
Line 766: Line 828:
Eigenmonzos: 2, 9/7&lt;br /&gt;
Eigenmonzos: 2, 9/7&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 175.434&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~448/405 = 175.434&lt;br /&gt;
Mapping generator: ~448/405&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 7 5|, &amp;lt;0 4 -32 -15|]&lt;br /&gt;
Map: [&amp;lt;1 1 7 5|, &amp;lt;0 4 -32 -15|]&lt;br /&gt;
Line 777: Line 840:
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~256/231 = 175.406&lt;br /&gt;
POTE generator: ~256/231 = 175.406&lt;br /&gt;
Mapping generator: ~256/231&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 7 5 2|, &amp;lt;0 4 -32 -15 10|]&lt;br /&gt;
Map: [&amp;lt;1 1 7 5 2|, &amp;lt;0 4 -32 -15 10|]&lt;br /&gt;
Line 786: Line 850:
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~21/20 = 83.053&lt;br /&gt;
POTE generator: ~21/20 = 83.053&lt;br /&gt;
Mapping generator: ~21/20&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 -1 -1|, &amp;lt;0 -6 48 55|]&lt;br /&gt;
Map: [&amp;lt;1 2 -1 -1|, &amp;lt;0 -6 48 55|]&lt;br /&gt;
Line 795: Line 860:
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~21/20 = 83.049&lt;br /&gt;
POTE generator: ~21/20 = 83.049&lt;br /&gt;
Mapping generator: ~21/20&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 -1 -1 0|, &amp;lt;0 -6 48 55 50|]&lt;br /&gt;
Map: [&amp;lt;1 2 -1 -1 0|, &amp;lt;0 -6 48 55 50|]&lt;br /&gt;
Line 804: Line 870:
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~21/20 = 83.049&lt;br /&gt;
POTE generator: ~21/20 = 83.049&lt;br /&gt;
Mapping generator: ~21/20&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 -1 -1 0 1|, &amp;lt;0 -6 48 55 50 39|]&lt;br /&gt;
Map: [&amp;lt;1 2 -1 -1 0 1|, &amp;lt;0 -6 48 55 50 39|]&lt;br /&gt;
Line 813: Line 880:
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~243/224 = 140.350&lt;br /&gt;
POTE generator: ~243/224 = 140.350&lt;br /&gt;
Mapping generator: ~243/224&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 7 0|, &amp;lt;0 5 -40 24|]&lt;br /&gt;
Map: [&amp;lt;1 1 7 0|, &amp;lt;0 5 -40 24|]&lt;br /&gt;
Line 823: Line 891:
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~56/45 = 380.355&lt;br /&gt;
POTE generator: ~56/45 = 380.355&lt;br /&gt;
Mapping generator: ~56/45&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 15 12|, &amp;lt;0 5 -40 -29|]&lt;br /&gt;
Map: [&amp;lt;1 0 15 12|, &amp;lt;0 5 -40 -29|]&lt;br /&gt;
Line 833: Line 902:
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~56/45 = 380.352&lt;br /&gt;
POTE generator: ~56/45 = 380.352&lt;br /&gt;
Mapping generator: ~56/45&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 15 12 -7|, &amp;lt;0 5 -40 -29 33|]&lt;br /&gt;
Map: [&amp;lt;1 0 15 12 -7|, &amp;lt;0 5 -40 -29 33|]&lt;br /&gt;
Line 842: Line 912:
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~3/2 = 701.713&lt;br /&gt;
POTE generator: ~3/2 = 701.713&lt;br /&gt;
Mapping generator: ~3&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;8 0 120 -117|, &amp;lt;0 1 -8 11|]&lt;br /&gt;
Map: [&amp;lt;8 0 120 -117|, &amp;lt;0 1 -8 11|]&lt;br /&gt;
Line 852: Line 923:
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~3/2 = 701.713&lt;br /&gt;
POTE generator: ~3/2 = 701.713&lt;br /&gt;
Mapping generator: ~3&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;8 0 120 -117 15|, &amp;lt;0 1 -8 11 1|]&lt;br /&gt;
Map: [&amp;lt;8 0 120 -117 15|, &amp;lt;0 1 -8 11 1|]&lt;br /&gt;
Line 861: Line 933:
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~3/2 = 701.725&lt;br /&gt;
POTE generator: ~3/2 = 701.725&lt;br /&gt;
Mapping generator: ~3&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;8 0 120 -117 15 93|, &amp;lt;0 1 -8 11 1 -5|]&lt;br /&gt;
Map: [&amp;lt;8 0 120 -117 15 93|, &amp;lt;0 1 -8 11 1 -5|]&lt;br /&gt;
EDOs: 24, 224, 472, 696&lt;br /&gt;
EDOs: 24, 224, 472, 696&lt;br /&gt;
Badness: 0.0304&lt;/body&gt;&lt;/html&gt;</pre></div>
Badness: 0.0304&lt;/body&gt;&lt;/html&gt;</pre></div>
Retrieved from "https://en.xen.wiki/w/Schismatic_family"