Schismatic family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 344219888 - Original comment: ** |
Wikispaces>guest **Imported revision 380545928 - Original comment: ** |
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<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: | : This revision was by author [[User:guest|guest]] and made on <tt>2012-11-08 13:36:29 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>380545928</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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">[[toc]] | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">[[toc]] | ||
=Five limit= | |||
=Five limit= | The 5-limit parent comma for the schismatic family is the [[schisma]] of 32805/32768, which is the amount by which the Pythagorean comma exceeds the [[Didymus comma]] ([[81_80|81/80]]), or alternatively put, the difference between a just major third and a Pythagorean diminished fourth. Its [[monzo]] is |-15 8 1>, and flipping that yields <<1 -8 -15|| for the [[Wedgies and Multivals|wedgie]]. This tells us the generator is a fifth and that we will need eight fourths in succession to reach the pitch class of a major third. In fact, 10 = (4/3)^8 * 32805/32768. | ||
The 5-limit parent comma for the schismatic family is the [[schisma]] of 32805/32768, which is the amount by which the Pythagorean comma exceeds the [[Didymus comma]] ([[81_80|81/80]]), or alternatively put, the difference between a just major third and a | |||
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. | ||
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EDOs: [[12edo|12]], [[29edo|29]], [[41edo|41]], [[53edo|53]], [[118edo|118]], [[171edo|171]], [[289edo|289]], 460, 749, 3456bc, 4205bc, 4954bc, 5703bc | EDOs: [[12edo|12]], [[29edo|29]], [[41edo|41]], [[53edo|53]], [[118edo|118]], [[171edo|171]], [[289edo|289]], 460, 749, 3456bc, 4205bc, 4954bc, 5703bc | ||
=Seven limit children= | =Seven limit children= | ||
The second comma of the [[Normal lists|normal comma list]] defines which 7-limit family member we are looking at. Adding |25 -14 0 -1> gives garibaldi, |-44 26 0 1> grackle, |6 -2 0 -1> schism and |-59 39 0 -1> pontiac; these all have a fifth as generator. Bischismic adds |-69 40 0 2> and has a fifth generator with a half-octave period. Guiron adds 1029/1024 = |-10 1 0 3>, with an 8/7 generator, three of which give the fifth, and term adds |-94 54 0 3> with a 1/3 octave period. Sesquiquartififths adds |-35 15 0 4> and slices the fifth in four. | The second comma of the [[Normal lists|normal comma list]] defines which 7-limit family member we are looking at. Adding |25 -14 0 -1> gives garibaldi, |-44 26 0 1> grackle, |6 -2 0 -1> schism and |-59 39 0 -1> pontiac; these all have a fifth as generator. Bischismic adds |-69 40 0 2> and has a fifth generator with a half-octave period. Guiron adds 1029/1024 = |-10 1 0 3>, with an 8/7 generator, three of which give the fifth, and term adds |-94 54 0 3> with a 1/3 octave period. Sesquiquartififths adds |-35 15 0 4> and slices the fifth in four. | ||
=Garibaldi= | =Garibaldi= | ||
Commas: 225/224, 3125/3087 | Commas: 225/224, 3125/3087 | ||
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[[Eigenmonzo]]s: 2, 7/6 | [[Eigenmonzo]]s: 2, 7/6 | ||
9-limit: [|1 0 0 0>, |25/16 1/8 0 -1/16>, | 9-limit: [|1 0 0 0>, |25/16 1/8 0 -1/16>, | ||
|5/2 -1 0 1/2>, |25/8 -7/4 0 7/8>] | |5/2 -1 0 1/2>, |25/8 -7/4 0 7/8>] | ||
Eigenmonzos: 2, 9/7 | Eigenmonzos: 2, 9/7 | ||
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Badness: 0.0216 | Badness: 0.0216 | ||
==11-limit== | ==11-limit== | ||
Commas: 225/224, 385/384, 2200/2187 | Commas: 225/224, 385/384, 2200/2187 | ||
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Badness: 0.0274 | Badness: 0.0274 | ||
===13-limit=== | ===13-limit=== | ||
Commas: 225/224, 275/273, 325/324, 385/384 | Commas: 225/224, 275/273, 325/324, 385/384 | ||
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Badness: 0.0207 | Badness: 0.0207 | ||
==Cassandra== | ==Cassandra== | ||
Commas: 100/99, 225/224, 245/242 | Commas: 100/99, 225/224, 245/242 | ||
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Badness: 0.0236 | Badness: 0.0236 | ||
===13-limit Cassandra=== | ===13-limit Cassandra=== | ||
Commas: 100/99, 105/104, 196/195, 245/242 | Commas: 100/99, 105/104, 196/195, 245/242 | ||
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Badness: 0.0207 | Badness: 0.0207 | ||
==Helenus== | ==Helenus== | ||
Commas: 99/98 176/175 3125/3087 | Commas: 99/98 176/175 3125/3087 | ||
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Badness: 0.0356 | Badness: 0.0356 | ||
===13-limit Helenus=== | ===13-limit Helenus=== | ||
Commas: 99/98, 176/175, 275/273, 847/845 | Commas: 99/98, 176/175, 275/273, 847/845 | ||
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Badness: 0.0263 | Badness: 0.0263 | ||
=Hemigari= | =Hemigari= | ||
Commas: 121/120, 225/224, 3125/3087 | Commas: 121/120, 225/224, 3125/3087 | ||
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Badness: 0.0507 | Badness: 0.0507 | ||
==13-limit== | ==13-limit== | ||
Commas: 121/120, 169/168, 225/224, 275/273 | Commas: 121/120, 169/168, 225/224, 275/273 | ||
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Badness: 27.464 | Badness: 27.464 | ||
=Guiron= | =Guiron= | ||
[[Comma|Commas]]: 1029/1024, 10976/10935 | [[Comma|Commas]]: 1029/1024, 10976/10935 | ||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
7+9 limit: [|1 0 0 0>, |15/8 0 -1/8 0>, | 7+9 limit: [|1 0 0 0>, |15/8 0 -1/8 0>, | ||
|0 0 1 0>, |65/24 0 1/24 0>] | |0 0 1 0>, |65/24 0 1/24 0>] | ||
[[Eigenmonzo|Eigenmonzos]]: 2, 5/4 | [[Eigenmonzo|Eigenmonzos]]: 2, 5/4 | ||
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Badness: 0.0475 | Badness: 0.0475 | ||
==11-limit== | ==11-limit== | ||
[[Comma|Commas]]: 385/384, 441/440, 10976/10935 | [[Comma|Commas]]: 385/384, 441/440, 10976/10935 | ||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
[|1 0 0 0 0>, |15/8 0 -1/8 0 0>, | [|1 0 0 0 0>, |15/8 0 -1/8 0 0>, | ||
|0 0 1 0 0>, |65/24 0 1/24 0 0>, | |0 0 1 0 0>, |65/24 0 1/24 0 0>, | ||
|37/6 0 -7/6 0 0>] | |37/6 0 -7/6 0 0>] | ||
[[Eigenmonzo|Eigenmonzos]]: 2, 5/4 | [[Eigenmonzo|Eigenmonzos]]: 2, 5/4 | ||
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Badness: 0.0266 | Badness: 0.0266 | ||
==13-limit== | ==13-limit== | ||
Commas: 196/195, 352/351, 385/384, 729/728 | Commas: 196/195, 352/351, 385/384, 729/728 | ||
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Badness: 0.0284 | Badness: 0.0284 | ||
=Pogo= | =Pogo= | ||
Commas: 32805/32768, 118098/117649 | Commas: 32805/32768, 118098/117649 | ||
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Badness: 0.0796 | Badness: 0.0796 | ||
==11-limit== | ==11-limit== | ||
Commas: 540/539, 4000/3993, 32805/32768 | Commas: 540/539, 4000/3993, 32805/32768 | ||
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Badness: 0.0319 | Badness: 0.0319 | ||
=Schism= | =Schism= | ||
Commas: 64/63, 360/343 | Commas: 64/63, 360/343 | ||
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Badness: 0.0566 | Badness: 0.0566 | ||
==11-limit== | ==11-limit== | ||
Commas: 45/44, 64/63, 99/98 | Commas: 45/44, 64/63, 99/98 | ||
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Badness: 0.0375 | Badness: 0.0375 | ||
=Pontiac= | =Pontiac= | ||
Commas: 32805/32768, 4375/4374 | Commas: 32805/32768, 4375/4374 | ||
7-limit minimax: | 7-limit minimax: | ||
[|1 0 0 0>, |74/47 0 -1/47 1/47>, |113/47 0 8/47 -8/47>, | [|1 0 0 0>, |74/47 0 -1/47 1/47>, |113/47 0 8/47 -8/47>, | ||
|113/47 0 -39/47 39/47>] | |113/47 0 -39/47 39/47>] | ||
Eigenmonzos: 2, 7/5 | Eigenmonzos: 2, 7/5 | ||
9-limit minimax: | 9-limit minimax: | ||
[|1 0 0 0>, |3/2 1/5 -1/10 0>, | [|1 0 0 0>, |3/2 1/5 -1/10 0>, | ||
|3 -8/5 4/5 0>, |-1/2 39/5 -39/10 0>] | |3 -8/5 4/5 0>, |-1/2 39/5 -39/10 0>] | ||
Eigenmonzos: 2, 10/9 | Eigenmonzos: 2, 10/9 | ||
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Badness: 0.0141 | Badness: 0.0141 | ||
=Grackle= | =Grackle= | ||
Commas: 126/125, 32805/32768 | Commas: 126/125, 32805/32768 | ||
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Badness: 0.070 | Badness: 0.070 | ||
=Bischismic= | =Bischismic= | ||
Commas: 3136/3125, 32805/32768 | Commas: 3136/3125, 32805/32768 | ||
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Badness: 0.0547 | Badness: 0.0547 | ||
==11-limit== | ==11-limit== | ||
Commas: 441/440, 3136/3125, 8019/8000 | Commas: 441/440, 3136/3125, 8019/8000 | ||
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Badness: 0.0282 | Badness: 0.0282 | ||
==13-limit== | ==13-limit== | ||
Commas: 441/440, 729/728, 1001/1000, 3136/3125 | Commas: 441/440, 729/728, 1001/1000, 3136/3125 | ||
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Badness: 0.0287 | Badness: 0.0287 | ||
=Kleischismic= | =Kleischismic= | ||
Commas: 32805/32768, 1500625/1492992 | Commas: 32805/32768, 1500625/1492992 | ||
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Badness: 0.1106 | Badness: 0.1106 | ||
==11-limit== | ==11-limit== | ||
Commas: 385/384, 9801/9800, 14641/14580 | Commas: 385/384, 9801/9800, 14641/14580 | ||
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Badness: 0.0367 | Badness: 0.0367 | ||
==13-limit== | ==13-limit== | ||
Commas: 352/351, 385/384, 729/728, 1575/1573 | Commas: 352/351, 385/384, 729/728, 1575/1573 | ||
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Badness: 0.0376 | Badness: 0.0376 | ||
=Term= | =Term= | ||
Commas: 32805/32768, 250047/250000 | Commas: 32805/32768, 250047/250000 | ||
| Line 333: | Line 332: | ||
Badness: 0.0200 | Badness: 0.0200 | ||
=Sesquiquartififths= | =Sesquiquartififths= | ||
Commas: 2401/2400, 32805/32768 | Commas: 2401/2400, 32805/32768 | ||
| Line 350: | Line 349: | ||
Badness: 0.0112 | Badness: 0.0112 | ||
==Sesquart== | ==Sesquart== | ||
Commas: 243/242, 441/440, 16384/16335 | Commas: 243/242, 441/440, 16384/16335 | ||
| Line 360: | Line 359: | ||
Badness: 0.0293 | Badness: 0.0293 | ||
=Sextilififths= | =Sextilififths= | ||
Commas: 32768/32805, 235298/234375 | Commas: 32768/32805, 235298/234375 | ||
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Badness: 0.1088 | Badness: 0.1088 | ||
==11-limit== | ==11-limit== | ||
Commas: 441/440, 4000/3993, 235298/234375 | Commas: 441/440, 4000/3993, 235298/234375 | ||
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Badness: 0.0455 | Badness: 0.0455 | ||
==13-limit== | ==13-limit== | ||
Commas: 363/363, 441/440, 676/675, 10985/10976 | Commas: 363/363, 441/440, 676/675, 10985/10976 | ||
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Badness: 0.0253 | Badness: 0.0253 | ||
=Tsaharuk= | =Tsaharuk= | ||
Commas: 32805/32768, 420175/419904 | Commas: 32805/32768, 420175/419904 | ||
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Badness: 0.0307 | Badness: 0.0307 | ||
=Quanharuk= | =Quanharuk= | ||
Commas: 16875/16807, 32805/32768 | Commas: 16875/16807, 32805/32768 | ||
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Badness: 0.0720 | Badness: 0.0720 | ||
==11-limit== | ==11-limit== | ||
Commas: 540/539, 1375/1372, 32805/32768 | Commas: 540/539, 1375/1372, 32805/32768 | ||
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Badness: 0.0315 | Badness: 0.0315 | ||
=Octant= | =Octant= | ||
Commas: 32805/32768, 2259436291848/2251875390625 | Commas: 32805/32768, 2259436291848/2251875390625 | ||
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Badness: 0.1572 | Badness: 0.1572 | ||
==11-limit== | ==11-limit== | ||
Commas: 9801/9800, 32805/32768, 46656/46585 | Commas: 9801/9800, 32805/32768, 46656/46585 | ||
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Badness: 0.0448 | Badness: 0.0448 | ||
==13-limit== | ==13-limit== | ||
Commas: 729/728, 1575/1573, 2200/2197, 6656/6655 | Commas: 729/728, 1575/1573, 2200/2197, 6656/6655 | ||
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Map: [<8 0 120 -117 15 93|, <0 1 -8 11 1 -5|] | Map: [<8 0 120 -117 15 93|, <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> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Schismatic family</title></head><body><!-- ws:start:WikiTextTocRule:76:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:76 --><!-- ws:start:WikiTextTocRule:77: --><div style="margin-left: 1em;"><a href="#Five limit">Five limit</a></div> | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Schismatic family</title></head><body><!-- ws:start:WikiTextTocRule:76:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:76 --><!-- ws:start:WikiTextTocRule:77: --><div style="margin-left: 1em;"><a href="#Five limit">Five limit</a></div> | ||
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<!-- ws:end:WikiTextTocRule:113 --><!-- ws:start:WikiTextTocRule:114: --><div style="margin-left: 2em;"><a href="#Octant-13-limit">13-limit</a></div> | <!-- ws:end:WikiTextTocRule:113 --><!-- ws:start:WikiTextTocRule:114: --><div style="margin-left: 2em;"><a href="#Octant-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule:114 --><!-- ws:start:WikiTextTocRule:115: --></div> | <!-- ws:end:WikiTextTocRule:114 --><!-- ws:start:WikiTextTocRule:115: --></div> | ||
<!-- ws:end:WikiTextTocRule:115 --> | <!-- ws:end:WikiTextTocRule:115 --><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Five limit"></a><!-- ws:end:WikiTextHeadingRule:0 -->Five limit</h1> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Five limit"></a><!-- ws:end:WikiTextHeadingRule:0 -->Five limit</h1> | The 5-limit parent comma for the schismatic family is the <a class="wiki_link" href="/schisma">schisma</a> of 32805/32768, which is the amount by which the Pythagorean comma exceeds the <a class="wiki_link" href="/Didymus%20comma">Didymus comma</a> (<a class="wiki_link" href="/81_80">81/80</a>), or alternatively put, the difference between a just major third and a Pythagorean diminished fourth. Its <a class="wiki_link" href="/monzo">monzo</a> is |-15 8 1&gt;, and flipping that yields &lt;&lt;1 -8 -15|| for the <a class="wiki_link" href="/Wedgies%20and%20Multivals">wedgie</a>. This tells us the generator is a fifth and that we will need eight fourths in succession to reach the pitch class of a major third. In fact, 10 = (4/3)^8 * 32805/32768.<br /> | ||
The 5-limit parent comma for the schismatic family is the <a class="wiki_link" href="/schisma">schisma</a> of 32805/32768, which is the amount by which the Pythagorean comma exceeds the <a class="wiki_link" href="/Didymus%20comma">Didymus comma</a> (<a class="wiki_link" href="/81_80">81/80</a>), or alternatively put, the difference between a just major third and a | |||
<br /> | <br /> | ||
The 5-limit version of the temperament is a <a class="wiki_link" href="/Microtempering">microtemperament</a>, sometimes called <strong>Helmholtz</strong> 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. <a class="wiki_link" href="/53edo">53edo</a> is a possible tuning for schismatic, but you need <a class="wiki_link" href="/118edo">118edo</a> 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.<br /> | The 5-limit version of the temperament is a <a class="wiki_link" href="/Microtempering">microtemperament</a>, sometimes called <strong>Helmholtz</strong> 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. <a class="wiki_link" href="/53edo">53edo</a> is a possible tuning for schismatic, but you need <a class="wiki_link" href="/118edo">118edo</a> 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.<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Seven limit children"></a><!-- ws:end:WikiTextHeadingRule:2 -->Seven limit children</h1> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Seven limit children"></a><!-- ws:end:WikiTextHeadingRule:2 -->Seven limit children</h1> | ||
The second comma of the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> defines which 7-limit family member we are looking at. Adding |25 -14 0 -1&gt; gives garibaldi, |-44 26 0 1&gt; grackle, |6 -2 0 -1&gt; schism and |-59 39 0 -1&gt; pontiac; these all have a fifth as generator. Bischismic adds |-69 40 0 2&gt; and has a fifth generator with a half-octave period. Guiron adds 1029/1024 = |-10 1 0 3&gt;, with an 8/7 generator, three of which give the fifth, and term adds |-94 54 0 3&gt; with a 1/3 octave period. Sesquiquartififths adds |-35 15 0 4&gt; and slices the fifth in four.<br /> | The second comma of the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> defines which 7-limit family member we are looking at. Adding |25 -14 0 -1&gt; gives garibaldi, |-44 26 0 1&gt; grackle, |6 -2 0 -1&gt; schism and |-59 39 0 -1&gt; pontiac; these all have a fifth as generator. Bischismic adds |-69 40 0 2&gt; and has a fifth generator with a half-octave period. Guiron adds 1029/1024 = |-10 1 0 3&gt;, with an 8/7 generator, three of which give the fifth, and term adds |-94 54 0 3&gt; with a 1/3 octave period. Sesquiquartififths adds |-35 15 0 4&gt; and slices the fifth in four.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Garibaldi"></a><!-- ws:end:WikiTextHeadingRule:4 -->Garibaldi</h1> | <!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Garibaldi"></a><!-- ws:end:WikiTextHeadingRule:4 -->Garibaldi</h1> | ||
Commas: 225/224, 3125/3087<br /> | Commas: 225/224, 3125/3087<br /> | ||
<br /> | <br /> | ||
7-limit minimax tuning:<br /> | 7-limit minimax tuning:<br /> | ||
| Line 516: | Line 513: | ||
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzo</a>s: 2, 7/6<br /> | <a class="wiki_link" href="/Eigenmonzo">Eigenmonzo</a>s: 2, 7/6<br /> | ||
<br /> | <br /> | ||
9-limit: [|1 0 0 0&gt;, |25/16 1/8 0 -1/16&gt;, <br /> | 9-limit: [|1 0 0 0&gt;, |25/16 1/8 0 -1/16&gt;,<br /> | ||
|5/2 -1 0 1/2&gt;, |25/8 -7/4 0 7/8&gt;]<br /> | |5/2 -1 0 1/2&gt;, |25/8 -7/4 0 7/8&gt;]<br /> | ||
Eigenmonzos: 2, 9/7<br /> | Eigenmonzos: 2, 9/7<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Garibaldi-11-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->11-limit</h2> | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Garibaldi-11-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->11-limit</h2> | ||
Commas: 225/224, 385/384, 2200/2187<br /> | Commas: 225/224, 385/384, 2200/2187<br /> | ||
<br /> | <br /> | ||
Minimax tuning:<br /> | Minimax tuning:<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><a name="Garibaldi-11-limit-13-limit"></a><!-- ws:end:WikiTextHeadingRule:8 -->13-limit</h3> | <!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><a name="Garibaldi-11-limit-13-limit"></a><!-- ws:end:WikiTextHeadingRule:8 -->13-limit</h3> | ||
Commas: 225/224, 275/273, 325/324, 385/384<br /> | Commas: 225/224, 275/273, 325/324, 385/384<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~3/2 = 702.113<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~3/2 = 702.113<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="Garibaldi-Cassandra"></a><!-- ws:end:WikiTextHeadingRule:10 -->Cassandra</h2> | <!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="Garibaldi-Cassandra"></a><!-- ws:end:WikiTextHeadingRule:10 -->Cassandra</h2> | ||
Commas: 100/99, 225/224, 245/242<br /> | Commas: 100/99, 225/224, 245/242<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~3/2 = 702.321<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~3/2 = 702.321<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:12:&lt;h3&gt; --><h3 id="toc6"><a name="Garibaldi-Cassandra-13-limit Cassandra"></a><!-- ws:end:WikiTextHeadingRule:12 -->13-limit Cassandra</h3> | <!-- ws:start:WikiTextHeadingRule:12:&lt;h3&gt; --><h3 id="toc6"><a name="Garibaldi-Cassandra-13-limit Cassandra"></a><!-- ws:end:WikiTextHeadingRule:12 -->13-limit Cassandra</h3> | ||
Commas: 100/99, 105/104, 196/195, 245/242<br /> | Commas: 100/99, 105/104, 196/195, 245/242<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~3/2 = 702.559<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~3/2 = 702.559<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="Garibaldi-Helenus"></a><!-- ws:end:WikiTextHeadingRule:14 -->Helenus</h2> | <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="Garibaldi-Helenus"></a><!-- ws:end:WikiTextHeadingRule:14 -->Helenus</h2> | ||
Commas: 99/98 176/175 3125/3087<br /> | Commas: 99/98 176/175 3125/3087<br /> | ||
<br /> | <br /> | ||
POTE generator: ~3/2 = 701.725<br /> | POTE generator: ~3/2 = 701.725<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:16:&lt;h3&gt; --><h3 id="toc8"><a name="Garibaldi-Helenus-13-limit Helenus"></a><!-- ws:end:WikiTextHeadingRule:16 -->13-limit Helenus</h3> | <!-- ws:start:WikiTextHeadingRule:16:&lt;h3&gt; --><h3 id="toc8"><a name="Garibaldi-Helenus-13-limit Helenus"></a><!-- ws:end:WikiTextHeadingRule:16 -->13-limit Helenus</h3> | ||
Commas: 99/98, 176/175, 275/273, 847/845<br /> | Commas: 99/98, 176/175, 275/273, 847/845<br /> | ||
<br /> | <br /> | ||
POTE generator: ~3/2 = 701.747<br /> | POTE generator: ~3/2 = 701.747<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc9"><a name="Hemigari"></a><!-- ws:end:WikiTextHeadingRule:18 -->Hemigari</h1> | <!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc9"><a name="Hemigari"></a><!-- ws:end:WikiTextHeadingRule:18 -->Hemigari</h1> | ||
Commas: 121/120, 225/224, 3125/3087<br /> | Commas: 121/120, 225/224, 3125/3087<br /> | ||
<br /> | <br /> | ||
POTE generator: ~63/55 = 248.918<br /> | POTE generator: ~63/55 = 248.918<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="Hemigari-13-limit"></a><!-- ws:end:WikiTextHeadingRule:20 -->13-limit</h2> | <!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="Hemigari-13-limit"></a><!-- ws:end:WikiTextHeadingRule:20 -->13-limit</h2> | ||
Commas: 121/120, 169/168, 225/224, 275/273<br /> | Commas: 121/120, 169/168, 225/224, 275/273<br /> | ||
<br /> | <br /> | ||
POTE generator: ~15/13 = 248.918<br /> | POTE generator: ~15/13 = 248.918<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc11"><a name="Guiron"></a><!-- ws:end:WikiTextHeadingRule:22 -->Guiron</h1> | <!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc11"><a name="Guiron"></a><!-- ws:end:WikiTextHeadingRule:22 -->Guiron</h1> | ||
<a class="wiki_link" href="/Comma">Commas</a>: 1029/1024, 10976/10935<br /> | <a class="wiki_link" href="/Comma">Commas</a>: 1029/1024, 10976/10935<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>:<br /> | <a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>:<br /> | ||
7+9 limit: [|1 0 0 0&gt;, |15/8 0 -1/8 0&gt;, <br /> | 7+9 limit: [|1 0 0 0&gt;, |15/8 0 -1/8 0&gt;,<br /> | ||
|0 0 1 0&gt;, |65/24 0 1/24 0&gt;]<br /> | |0 0 1 0&gt;, |65/24 0 1/24 0&gt;]<br /> | ||
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 5/4<br /> | <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 5/4<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:24:&lt;h2&gt; --><h2 id="toc12"><a name="Guiron-11-limit"></a><!-- ws:end:WikiTextHeadingRule:24 -->11-limit</h2> | <!-- ws:start:WikiTextHeadingRule:24:&lt;h2&gt; --><h2 id="toc12"><a name="Guiron-11-limit"></a><!-- ws:end:WikiTextHeadingRule:24 -->11-limit</h2> | ||
<a class="wiki_link" href="/Comma">Commas</a>: 385/384, 441/440, 10976/10935<br /> | <a class="wiki_link" href="/Comma">Commas</a>: 385/384, 441/440, 10976/10935<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>:<br /> | <a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>:<br /> | ||
[|1 0 0 0 0&gt;, |15/8 0 -1/8 0 0&gt;, <br /> | [|1 0 0 0 0&gt;, |15/8 0 -1/8 0 0&gt;,<br /> | ||
|0 0 1 0 0&gt;, |65/24 0 1/24 0 0&gt;, <br /> | |0 0 1 0 0&gt;, |65/24 0 1/24 0 0&gt;,<br /> | ||
|37/6 0 -7/6 0 0&gt;]<br /> | |37/6 0 -7/6 0 0&gt;]<br /> | ||
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 5/4<br /> | <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 5/4<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:26:&lt;h2&gt; --><h2 id="toc13"><a name="Guiron-13-limit"></a><!-- ws:end:WikiTextHeadingRule:26 -->13-limit</h2> | <!-- ws:start:WikiTextHeadingRule:26:&lt;h2&gt; --><h2 id="toc13"><a name="Guiron-13-limit"></a><!-- ws:end:WikiTextHeadingRule:26 -->13-limit</h2> | ||
Commas: 196/195, 352/351, 385/384, 729/728<br /> | Commas: 196/195, 352/351, 385/384, 729/728<br /> | ||
<br /> | <br /> | ||
POTE generator: ~8/7 = 233.890<br /> | POTE generator: ~8/7 = 233.890<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:28:&lt;h1&gt; --><h1 id="toc14"><a name="Pogo"></a><!-- ws:end:WikiTextHeadingRule:28 -->Pogo</h1> | <!-- ws:start:WikiTextHeadingRule:28:&lt;h1&gt; --><h1 id="toc14"><a name="Pogo"></a><!-- ws:end:WikiTextHeadingRule:28 -->Pogo</h1> | ||
Commas: 32805/32768, 118098/117649<br /> | Commas: 32805/32768, 118098/117649<br /> | ||
<br /> | <br /> | ||
POTE generator: ~9/7 = 433.901<br /> | POTE generator: ~9/7 = 433.901<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:30:&lt;h2&gt; --><h2 id="toc15"><a name="Pogo-11-limit"></a><!-- ws:end:WikiTextHeadingRule:30 -->11-limit</h2> | <!-- ws:start:WikiTextHeadingRule:30:&lt;h2&gt; --><h2 id="toc15"><a name="Pogo-11-limit"></a><!-- ws:end:WikiTextHeadingRule:30 -->11-limit</h2> | ||
Commas: 540/539, 4000/3993, 32805/32768<br /> | Commas: 540/539, 4000/3993, 32805/32768<br /> | ||
<br /> | <br /> | ||
POTE generator: ~9/7 = 433.911<br /> | POTE generator: ~9/7 = 433.911<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:32:&lt;h1&gt; --><h1 id="toc16"><a name="Schism"></a><!-- ws:end:WikiTextHeadingRule:32 -->Schism</h1> | <!-- ws:start:WikiTextHeadingRule:32:&lt;h1&gt; --><h1 id="toc16"><a name="Schism"></a><!-- ws:end:WikiTextHeadingRule:32 -->Schism</h1> | ||
Commas: 64/63, 360/343<br /> | Commas: 64/63, 360/343<br /> | ||
<br /> | <br /> | ||
POTE generator: ~3/2 = 701.556<br /> | POTE generator: ~3/2 = 701.556<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:34:&lt;h2&gt; --><h2 id="toc17"><a name="Schism-11-limit"></a><!-- ws:end:WikiTextHeadingRule:34 -->11-limit</h2> | <!-- ws:start:WikiTextHeadingRule:34:&lt;h2&gt; --><h2 id="toc17"><a name="Schism-11-limit"></a><!-- ws:end:WikiTextHeadingRule:34 -->11-limit</h2> | ||
Commas: 45/44, 64/63, 99/98<br /> | Commas: 45/44, 64/63, 99/98<br /> | ||
<br /> | <br /> | ||
POTE generator ~3/2 = 702.136<br /> | POTE generator ~3/2 = 702.136<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:36:&lt;h1&gt; --><h1 id="toc18"><a name="Pontiac"></a><!-- ws:end:WikiTextHeadingRule:36 -->Pontiac</h1> | <!-- ws:start:WikiTextHeadingRule:36:&lt;h1&gt; --><h1 id="toc18"><a name="Pontiac"></a><!-- ws:end:WikiTextHeadingRule:36 -->Pontiac</h1> | ||
Commas: 32805/32768, 4375/4374<br /> | Commas: 32805/32768, 4375/4374<br /> | ||
<br /> | <br /> | ||
7-limit minimax:<br /> | 7-limit minimax:<br /> | ||
[|1 0 0 0&gt;, |74/47 0 -1/47 1/47&gt;, |113/47 0 8/47 -8/47&gt;, <br /> | [|1 0 0 0&gt;, |74/47 0 -1/47 1/47&gt;, |113/47 0 8/47 -8/47&gt;,<br /> | ||
|113/47 0 -39/47 39/47&gt;]<br /> | |113/47 0 -39/47 39/47&gt;]<br /> | ||
Eigenmonzos: 2, 7/5<br /> | Eigenmonzos: 2, 7/5<br /> | ||
<br /> | <br /> | ||
9-limit minimax:<br /> | 9-limit minimax:<br /> | ||
[|1 0 0 0&gt;, |3/2 1/5 -1/10 0&gt;, <br /> | [|1 0 0 0&gt;, |3/2 1/5 -1/10 0&gt;,<br /> | ||
|3 -8/5 4/5 0&gt;, |-1/2 39/5 -39/10 0&gt;]<br /> | |3 -8/5 4/5 0&gt;, |-1/2 39/5 -39/10 0&gt;]<br /> | ||
Eigenmonzos: 2, 10/9<br /> | Eigenmonzos: 2, 10/9<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:38:&lt;h1&gt; --><h1 id="toc19"><a name="Grackle"></a><!-- ws:end:WikiTextHeadingRule:38 -->Grackle</h1> | <!-- ws:start:WikiTextHeadingRule:38:&lt;h1&gt; --><h1 id="toc19"><a name="Grackle"></a><!-- ws:end:WikiTextHeadingRule:38 -->Grackle</h1> | ||
Commas: 126/125, 32805/32768<br /> | Commas: 126/125, 32805/32768<br /> | ||
<br /> | <br /> | ||
7-limit minimax<br /> | 7-limit minimax<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:40:&lt;h1&gt; --><h1 id="toc20"><a name="Bischismic"></a><!-- ws:end:WikiTextHeadingRule:40 -->Bischismic</h1> | <!-- ws:start:WikiTextHeadingRule:40:&lt;h1&gt; --><h1 id="toc20"><a name="Bischismic"></a><!-- ws:end:WikiTextHeadingRule:40 -->Bischismic</h1> | ||
Commas: 3136/3125, 32805/32768<br /> | Commas: 3136/3125, 32805/32768<br /> | ||
<br /> | <br /> | ||
7-limit minimax<br /> | 7-limit minimax<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:42:&lt;h2&gt; --><h2 id="toc21"><a name="Bischismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:42 -->11-limit</h2> | <!-- ws:start:WikiTextHeadingRule:42:&lt;h2&gt; --><h2 id="toc21"><a name="Bischismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:42 -->11-limit</h2> | ||
Commas: 441/440, 3136/3125, 8019/8000<br /> | Commas: 441/440, 3136/3125, 8019/8000<br /> | ||
<br /> | <br /> | ||
POTE generator: ~3/2 = 701.612<br /> | POTE generator: ~3/2 = 701.612<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:44:&lt;h2&gt; --><h2 id="toc22"><a name="Bischismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:44 -->13-limit</h2> | <!-- ws:start:WikiTextHeadingRule:44:&lt;h2&gt; --><h2 id="toc22"><a name="Bischismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:44 -->13-limit</h2> | ||
Commas: 441/440, 729/728, 1001/1000, 3136/3125<br /> | Commas: 441/440, 729/728, 1001/1000, 3136/3125<br /> | ||
<br /> | <br /> | ||
POTE generator: ~3/2 = 701.590<br /> | POTE generator: ~3/2 = 701.590<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:46:&lt;h1&gt; --><h1 id="toc23"><a name="Kleischismic"></a><!-- ws:end:WikiTextHeadingRule:46 -->Kleischismic</h1> | <!-- ws:start:WikiTextHeadingRule:46:&lt;h1&gt; --><h1 id="toc23"><a name="Kleischismic"></a><!-- ws:end:WikiTextHeadingRule:46 -->Kleischismic</h1> | ||
Commas: 32805/32768, 1500625/1492992<br /> | Commas: 32805/32768, 1500625/1492992<br /> | ||
<br /> | <br /> | ||
POTE generator: ~36/35 = 50.920<br /> | POTE generator: ~36/35 = 50.920<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:48:&lt;h2&gt; --><h2 id="toc24"><a name="Kleischismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:48 -->11-limit</h2> | <!-- ws:start:WikiTextHeadingRule:48:&lt;h2&gt; --><h2 id="toc24"><a name="Kleischismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:48 -->11-limit</h2> | ||
Commas: 385/384, 9801/9800, 14641/14580<br /> | Commas: 385/384, 9801/9800, 14641/14580<br /> | ||
<br /> | <br /> | ||
POTE generator: ~36/35 = 50.918<br /> | POTE generator: ~36/35 = 50.918<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:50:&lt;h2&gt; --><h2 id="toc25"><a name="Kleischismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:50 -->13-limit</h2> | <!-- ws:start:WikiTextHeadingRule:50:&lt;h2&gt; --><h2 id="toc25"><a name="Kleischismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:50 -->13-limit</h2> | ||
Commas: 352/351, 385/384, 729/728, 1575/1573<br /> | Commas: 352/351, 385/384, 729/728, 1575/1573<br /> | ||
<br /> | <br /> | ||
POTE generator: ~36/35 = 50.938<br /> | POTE generator: ~36/35 = 50.938<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:52:&lt;h1&gt; --><h1 id="toc26"><a name="Term"></a><!-- ws:end:WikiTextHeadingRule:52 -->Term</h1> | <!-- ws:start:WikiTextHeadingRule:52:&lt;h1&gt; --><h1 id="toc26"><a name="Term"></a><!-- ws:end:WikiTextHeadingRule:52 -->Term</h1> | ||
Commas: 32805/32768, 250047/250000<br /> | Commas: 32805/32768, 250047/250000<br /> | ||
<br /> | <br /> | ||
7-limit minimax<br /> | 7-limit minimax<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:54:&lt;h1&gt; --><h1 id="toc27"><a name="Sesquiquartififths"></a><!-- ws:end:WikiTextHeadingRule:54 -->Sesquiquartififths</h1> | <!-- ws:start:WikiTextHeadingRule:54:&lt;h1&gt; --><h1 id="toc27"><a name="Sesquiquartififths"></a><!-- ws:end:WikiTextHeadingRule:54 -->Sesquiquartififths</h1> | ||
Commas: 2401/2400, 32805/32768<br /> | Commas: 2401/2400, 32805/32768<br /> | ||
<br /> | <br /> | ||
7-limit minimax<br /> | 7-limit minimax<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:56:&lt;h2&gt; --><h2 id="toc28"><a name="Sesquiquartififths-Sesquart"></a><!-- ws:end:WikiTextHeadingRule:56 -->Sesquart</h2> | <!-- ws:start:WikiTextHeadingRule:56:&lt;h2&gt; --><h2 id="toc28"><a name="Sesquiquartififths-Sesquart"></a><!-- ws:end:WikiTextHeadingRule:56 -->Sesquart</h2> | ||
Commas: 243/242, 441/440, 16384/16335<br /> | Commas: 243/242, 441/440, 16384/16335<br /> | ||
<br /> | <br /> | ||
POTE generator: ~256/231 = 175.406<br /> | POTE generator: ~256/231 = 175.406<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:58:&lt;h1&gt; --><h1 id="toc29"><a name="Sextilififths"></a><!-- ws:end:WikiTextHeadingRule:58 -->Sextilififths</h1> | <!-- ws:start:WikiTextHeadingRule:58:&lt;h1&gt; --><h1 id="toc29"><a name="Sextilififths"></a><!-- ws:end:WikiTextHeadingRule:58 -->Sextilififths</h1> | ||
Commas: 32768/32805, 235298/234375<br /> | Commas: 32768/32805, 235298/234375<br /> | ||
<br /> | <br /> | ||
POTE generator: ~21/20 = 83.053<br /> | POTE generator: ~21/20 = 83.053<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:60:&lt;h2&gt; --><h2 id="toc30"><a name="Sextilififths-11-limit"></a><!-- ws:end:WikiTextHeadingRule:60 -->11-limit</h2> | <!-- ws:start:WikiTextHeadingRule:60:&lt;h2&gt; --><h2 id="toc30"><a name="Sextilififths-11-limit"></a><!-- ws:end:WikiTextHeadingRule:60 -->11-limit</h2> | ||
Commas: 441/440, 4000/3993, 235298/234375<br /> | Commas: 441/440, 4000/3993, 235298/234375<br /> | ||
<br /> | <br /> | ||
POTE generator: ~21/20 = 83.049<br /> | POTE generator: ~21/20 = 83.049<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:62:&lt;h2&gt; --><h2 id="toc31"><a name="Sextilififths-13-limit"></a><!-- ws:end:WikiTextHeadingRule:62 -->13-limit</h2> | <!-- ws:start:WikiTextHeadingRule:62:&lt;h2&gt; --><h2 id="toc31"><a name="Sextilififths-13-limit"></a><!-- ws:end:WikiTextHeadingRule:62 -->13-limit</h2> | ||
Commas: 363/363, 441/440, 676/675, 10985/10976<br /> | Commas: 363/363, 441/440, 676/675, 10985/10976<br /> | ||
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POTE generator: ~21/20 = 83.049<br /> | POTE generator: ~21/20 = 83.049<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:64:&lt;h1&gt; --><h1 id="toc32"><a name="Tsaharuk"></a><!-- ws:end:WikiTextHeadingRule:64 -->Tsaharuk</h1> | <!-- ws:start:WikiTextHeadingRule:64:&lt;h1&gt; --><h1 id="toc32"><a name="Tsaharuk"></a><!-- ws:end:WikiTextHeadingRule:64 -->Tsaharuk</h1> | ||
Commas: 32805/32768, 420175/419904<br /> | Commas: 32805/32768, 420175/419904<br /> | ||
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POTE generator: ~243/224 = 140.350<br /> | POTE generator: ~243/224 = 140.350<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:66:&lt;h1&gt; --><h1 id="toc33"><a name="Quanharuk"></a><!-- ws:end:WikiTextHeadingRule:66 -->Quanharuk</h1> | <!-- ws:start:WikiTextHeadingRule:66:&lt;h1&gt; --><h1 id="toc33"><a name="Quanharuk"></a><!-- ws:end:WikiTextHeadingRule:66 -->Quanharuk</h1> | ||
Commas: 16875/16807, 32805/32768<br /> | Commas: 16875/16807, 32805/32768<br /> | ||
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POTE generator: ~56/45 = 380.355<br /> | POTE generator: ~56/45 = 380.355<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:68:&lt;h2&gt; --><h2 id="toc34"><a name="Quanharuk-11-limit"></a><!-- ws:end:WikiTextHeadingRule:68 -->11-limit</h2> | <!-- ws:start:WikiTextHeadingRule:68:&lt;h2&gt; --><h2 id="toc34"><a name="Quanharuk-11-limit"></a><!-- ws:end:WikiTextHeadingRule:68 -->11-limit</h2> | ||
Commas: 540/539, 1375/1372, 32805/32768<br /> | Commas: 540/539, 1375/1372, 32805/32768<br /> | ||
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POTE generator: ~56/45 = 380.352<br /> | POTE generator: ~56/45 = 380.352<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:70:&lt;h1&gt; --><h1 id="toc35"><a name="Octant"></a><!-- ws:end:WikiTextHeadingRule:70 -->Octant</h1> | <!-- ws:start:WikiTextHeadingRule:70:&lt;h1&gt; --><h1 id="toc35"><a name="Octant"></a><!-- ws:end:WikiTextHeadingRule:70 -->Octant</h1> | ||
Commas: 32805/32768, 2259436291848/2251875390625<br /> | Commas: 32805/32768, 2259436291848/2251875390625<br /> | ||
<br /> | <br /> | ||
POTE generator: ~3/2 = 701.713<br /> | POTE generator: ~3/2 = 701.713<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:72:&lt;h2&gt; --><h2 id="toc36"><a name="Octant-11-limit"></a><!-- ws:end:WikiTextHeadingRule:72 -->11-limit</h2> | <!-- ws:start:WikiTextHeadingRule:72:&lt;h2&gt; --><h2 id="toc36"><a name="Octant-11-limit"></a><!-- ws:end:WikiTextHeadingRule:72 -->11-limit</h2> | ||
Commas: 9801/9800, 32805/32768, 46656/46585<br /> | Commas: 9801/9800, 32805/32768, 46656/46585<br /> | ||
<br /> | <br /> | ||
POTE generator: ~3/2 = 701.713<br /> | POTE generator: ~3/2 = 701.713<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:74:&lt;h2&gt; --><h2 id="toc37"><a name="Octant-13-limit"></a><!-- ws:end:WikiTextHeadingRule:74 -->13-limit</h2> | <!-- ws:start:WikiTextHeadingRule:74:&lt;h2&gt; --><h2 id="toc37"><a name="Octant-13-limit"></a><!-- ws:end:WikiTextHeadingRule:74 -->13-limit</h2> | ||
Commas: 729/728, 1575/1573, 2200/2197, 6656/6655<br /> | Commas: 729/728, 1575/1573, 2200/2197, 6656/6655<br /> | ||
<br /> | <br /> | ||
POTE generator: ~3/2 = 701.725<br /> | POTE generator: ~3/2 = 701.725<br /> | ||