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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Todo|inline=1| intro }} |
| 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>2011-06-21 16:44:17 UTC</tt>.<br>
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| : The original revision id was <tt>238036939</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| 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>
| |
| <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|flat]]
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|
| =Marveltwin and Marvel= | | == Marveltwin and marvel == |
| The //marveltwin comma//, 325/324, bears a curiously close analogy to the marvel comma, 225/224. 325/324 can be added to the [[11-limit]] version of marvel, which tempers out 225/224 and 385/384, to get [[13-limit]] marvel, aka hecate. But it's also interesting to leave 11 out of it. From 225/224 we get that a 5-limit approximation for 7 is 225/224 * 7 = 225/32. Similarly from 325/324 we get a 5-limit approximation of 13 from 324/325 * 13 = 324/25. If we define the major/minor transformation of the 5-limit as the result of fixing 2 and 3 and replacing 5 by 24/5, then major/minor applied to 225/32 is 162/25, which is (324/25)/2. Similarly, major/minor applied to 324/25 is 225/16 = 2 * (225/32). 225/224 tells us that two 16/15 in a row are an approximate 8/7, and 325/324 tells us two 10/9 in a row are an approximate 16/13. Needless to say, major/minor applied to 16/15 is 10/9, and applied to 10/9 is 16/15. | | The marveltwin comma, [[325/324]], bears a curiously close analogy to the marvel comma, [[225/224]]. 325/324 can be added to the [[11-limit]] version of marvel, which tempers out 225/224 and 385/384, to get [[13-limit]] marvel, aka hecate. But it's also interesting to leave 11 out of it. From 225/224 we get that a 5-limit approximation for 7 is 225/224 * 7 = 225/32. Similarly from 325/324 we get a 5-limit approximation of 13 from 324/325 * 13 = 324/25. If we define the major/minor transformation of the 5-limit as the result of fixing 2 and 3 and replacing 5 by 24/5, then major/minor applied to 225/32 is 162/25, which is (324/25)/2. Similarly, major/minor applied to 324/25 is 225/16 = 2 * (225/32). 225/224 tells us that two 16/15 in a row are an approximate 8/7, and 325/324 tells us two 10/9 in a row are an approximate 16/13. Needless to say, major/minor applied to 16/15 is 10/9, and applied to 10/9 is 16/15. |
|
| |
|
| =Rank five= | | == Rank-5 temperaments == |
| Comma: 325/324
| | [[Subgroup]]: 2.3.5.7.11.13 |
|
| |
|
| 13 and 15 limit minimax tuning
| | [[Comma list]]: 325/324 |
| || [1 0 0 0 0 0> ||
| |
| || [0 1 0 0 0 0> ||
| |
| || [2/3 4/3 1/3 0 0 -1/3> ||
| |
| || [2/3 4/3 -2/3 1 0 -1/3> ||
| |
| || [2/3 4/3 -2/3 0 1 -1/3> ||
| |
| || [2/3 4/3 -2/3 0 0 2/3> ||
| |
|
| |
|
| Fifths are pure; 5, 7, 11 and 13 are all flat by (325/324)^(1/3), which is 1.778 cents.
| | [[Mapping]]: |
| Eigenmonzo subgroup: 2.3.7/5.11/5.13/5
| | {| class="right-all" |
| | |- |
| | | {{lbrack}}⟨ || 1 || 0 || 0 || 0 || 0 || 2 || {{rbrack}}, |
| | |- |
| | | ⟨ || 0 || 1 || 0 || 0 || 0 || 4 || {{rbrack}}, |
| | |- |
| | | ⟨ || 0 || 0 || 1 || 0 || 0 || -2 || {{rbrack}}, |
| | |- |
| | | ⟨ || 0 || 0 || 0 || 1 || 0 || 0 || {{rbrack}}, |
| | |- |
| | | ⟨ || 0 || 0 || 0 || 0 || 1 || 0 || {{rbrack}}{{rbrack}} |
| | |} |
|
| |
|
| Map:
| | [[Minimax tuning]]s: |
| || <1 0 0 0 0 2] || | | * 13- and 15-odd-limit |
| || <0 1 0 0 0 4] || | | : {| class="right-all" |
| || <0 0 1 0 0 -2] || | | |- |
| || <0 0 0 1 0 0] || | | | {{lbrack}}{{lbrack}} || 1 || 0 || 0 || 0 || 0 || 0 || ⟩ |
| || <0 0 0 0 1 0] || | | |- |
| | | {{lbrack}} || 0 || 1 || 0 || 0 || 0 || 0 || ⟩ |
| | |- |
| | | {{lbrack}} || 2/3 || 4/3 || 1/3 || 0 || 0 || -1/3 || ⟩ |
| | |- |
| | | {{lbrack}} || 2/3 || 4/3 || -2/3 || 1 || 0 || -1/3 || ⟩ |
| | |- |
| | | {{lbrack}} || 2/3 || 4/3 || -2/3 || 0 || 1 || -1/3 || ⟩ |
| | |- |
| | | {{lbrack}} || 2/3 || 4/3 || -2/3 || 0 || 0 || 2/3 || ⟩{{rbrack}} |
| | |} |
| | : 3 pure; 5, 7, 11 and 13 all flat by (325/324)<sup>1/3</sup>, which is 1.778 cents. |
| | : [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3.7/5.11/5.13/5 |
|
| |
|
| Edos: 7, 12, 15, 19, 26, 34, 41, 46, 53, 72, 87, 121, 140, 159, 193, 212, 299, 333
| | {{Optimal ET sequence|legend=1| 7, 12, 15, 19, 26, 34, 41, 46, 53, 72, 87, 121, 140, 159, 193, 212, 299, 333 }} |
|
| |
|
| =Rank four= | | == Rank-4 temperaments == |
| | === 225/224 === |
| | [[Subgroup]]: 2.3.5.7.11.13 |
|
| |
|
| ==225/224==
| | [[Comma list]]: 225/224, 325/324 |
|
| |
|
| 13-limit eigenmonzo subgroup: 2.7.11/5.13/5
| | {{Mapping|legend=1| 1 0 0 -5 0 2 | 0 1 0 2 0 4 | 0 0 1 2 0 -2 | 0 0 0 0 1 0 }} |
| 15-limit eigenmonzo subgroup: 2.7.15/11.15/13
| |
|
| |
|
| Map:
| | [[Minimax tuning]]s: |
| || <1 0 0 -5 0 2] ||
| | * 13-limit unchanged-interval (eigenmonzo) basis: 2.7.11/5.13/5 |
| || <0 1 0 2 0 4] ||
| | * 15-limit unchanged-interval (eigenmonzo) basis: 2.7.15/11.15/13 |
| || <0 0 1 2 0 -2] ||
| |
| || <0 0 0 0 1 0]] ||
| |
| Edos: 12, 19, 41, 53, 72, 166
| |
|
| |
|
| ==385/384== | | {{Optimal ET sequence|legend=1| 12, 19, 41, 53, 72, 166 }} |
|
| |
|
| ==364/363==
| | [[Badness]]: 3.668 × 10<sup>-6</sup> |
|
| |
|
| ==441/440== | | === 385/384 === |
| | See [[Keenanismic family #Martwin]]. |
|
| |
|
| ==169/168== | | === 364/363 === |
| | [[Subgroup]]: 2.3.5.7.11.13 |
|
| |
|
| ==540/539==
| | [[Comma list]]: 325/324, 364/363 |
|
| |
|
| ==352/351== | | {{Optimal ET sequence|legend=1| 15, 26, 41, 46, 72, 87, 121, 159, 193, 239, 280 }} |
|
| |
|
| ==625/624==
| | [[Badness]]: 3.011 × 10<sup>-6</sup> |
|
| |
|
| =Rank three= | | === 441/440 === |
| | [[Subgroup]]: 2.3.5.7.11.13 |
|
| |
|
| ==Portending==
| | [[Comma list]]: 325/324, 441/440 |
| Commas: 325/324, 364/363, 441/440
| |
|
| |
|
| ==Marvel (Hecate)== | | {{Optimal ET sequence|legend=1| 12, 15, 26, 41, 46, 72, 87, 159 }} |
| Commas: 225/224, 325/324, 385/384
| |
|
| |
|
| ==Sumatra==
| | [[Badness]]: 3.037 × 10<sup>-6</sup> |
| Commas: 325/324, 385/384, 625/624
| |
|
| |
|
| EDOs: 15, 19, 34, 53, 72, 87, 140, 159, 212, 299
| | === 169/168 === |
| Optimal patent val: [[299edo]]
| | [[Subgroup]]: 2.3.5.7.11.13 |
| Badness: 0.000680
| |
|
| |
|
| </pre></div>
| | [[Comma list]]: 169/168, 325/324 |
| <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>Marveltwin</title></head><body><!-- ws:start:WikiTextTocRule:30:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --><a href="#Marveltwin and Marvel">Marveltwin and Marvel</a><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --> | <a href="#Rank five">Rank five</a><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --> | <a href="#Rank four">Rank four</a><!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --><!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --><!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --><!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --><!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --><!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --><!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --> | <a href="#Rank three">Rank three</a><!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --><!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --><!-- ws:end:WikiTextTocRule:44 --><!-- ws:start:WikiTextTocRule:45: --><!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: -->
| |
| <!-- ws:end:WikiTextTocRule:46 --><br />
| |
| <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Marveltwin and Marvel"></a><!-- ws:end:WikiTextHeadingRule:0 -->Marveltwin and Marvel</h1>
| |
| The <em>marveltwin comma</em>, 325/324, bears a curiously close analogy to the marvel comma, 225/224. 325/324 can be added to the <a class="wiki_link" href="/11-limit">11-limit</a> version of marvel, which tempers out 225/224 and 385/384, to get <a class="wiki_link" href="/13-limit">13-limit</a> marvel, aka hecate. But it's also interesting to leave 11 out of it. From 225/224 we get that a 5-limit approximation for 7 is 225/224 * 7 = 225/32. Similarly from 325/324 we get a 5-limit approximation of 13 from 324/325 * 13 = 324/25. If we define the major/minor transformation of the 5-limit as the result of fixing 2 and 3 and replacing 5 by 24/5, then major/minor applied to 225/32 is 162/25, which is (324/25)/2. Similarly, major/minor applied to 324/25 is 225/16 = 2 * (225/32). 225/224 tells us that two 16/15 in a row are an approximate 8/7, and 325/324 tells us two 10/9 in a row are an approximate 16/13. Needless to say, major/minor applied to 16/15 is 10/9, and applied to 10/9 is 16/15.<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Rank five"></a><!-- ws:end:WikiTextHeadingRule:2 -->Rank five</h1>
| |
| Comma: 325/324<br />
| |
| <br />
| |
| 13 and 15 limit minimax tuning<br />
| |
|
| |
|
| | {{Optimal ET sequence|legend=1| 7, 19, 26, 46, 53, 72, 152 }} |
|
| |
|
| <table class="wiki_table">
| | [[Badness]]: 2.975 × 10<sup>-6</sup> |
| <tr>
| |
| <td>[1 0 0 0 0 0&gt;<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>[0 1 0 0 0 0&gt;<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>[2/3 4/3 1/3 0 0 -1/3&gt;<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>[2/3 4/3 -2/3 1 0 -1/3&gt;<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>[2/3 4/3 -2/3 0 1 -1/3&gt;<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>[2/3 4/3 -2/3 0 0 2/3&gt;<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <br />
| | === 540/539 === |
| Fifths are pure; 5, 7, 11 and 13 are all flat by (325/324)^(1/3), which is 1.778 cents. <br />
| | [[Subgroup]]: 2.3.5.7.11.13 |
| Eigenmonzo subgroup: 2.3.7/5.11/5.13/5<br />
| |
| <br />
| |
| Map: <br />
| |
|
| |
|
| | [[Comma list]]: 325/324, 540/539 |
|
| |
|
| <table class="wiki_table">
| | {{Optimal ET sequence|legend=1| 19, 41, 53, 72, 121, 166, 193 }} |
| <tr>
| |
| <td>&lt;1 0 0 0 0 2]<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>&lt;0 1 0 0 0 4]<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>&lt;0 0 1 0 0 -2]<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>&lt;0 0 0 1 0 0]<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>&lt;0 0 0 0 1 0]<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <br />
| | [[Badness]]: 3.281 × 10<sup>-6</sup> |
| Edos: 7, 12, 15, 19, 26, 34, 41, 46, 53, 72, 87, 121, 140, 159, 193, 212, 299, 333<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Rank four"></a><!-- ws:end:WikiTextHeadingRule:4 -->Rank four</h1>
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Rank four-225/224"></a><!-- ws:end:WikiTextHeadingRule:6 -->225/224</h2>
| |
| <br />
| |
| 13-limit eigenmonzo subgroup: 2.7.11/5.13/5<br />
| |
| 15-limit eigenmonzo subgroup: 2.7.15/11.15/13<br />
| |
| <br />
| |
| Map:<br />
| |
|
| |
|
| | === 352/351 === |
| | [[Subgroup]]: 2.3.5.7.11.13 |
|
| |
|
| <table class="wiki_table">
| | [[Comma list]]: 325/324, 352/351 |
| <tr>
| |
| <td>&lt;1 0 0 -5 0 2]<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>&lt;0 1 0 2 0 4]<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>&lt;0 0 1 2 0 -2]<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>&lt;0 0 0 0 1 0]]<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| Edos: 12, 19, 41, 53, 72, 166<br />
| | {{Optimal ET sequence|legend=1| 7, 34, 41, 46, 53, 80, 87, 121, 140, 261, 358, 401 }} |
| <br />
| | |
| <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Rank four-385/384"></a><!-- ws:end:WikiTextHeadingRule:8 -->385/384</h2>
| | [[Badness]]: 3.434 × 10<sup>-6</sup> |
| <br />
| | |
| <!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="Rank four-364/363"></a><!-- ws:end:WikiTextHeadingRule:10 -->364/363</h2>
| | === 625/624 === |
| <br />
| | [[Subgroup]]: 2.3.5.7.11.13 |
| <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Rank four-441/440"></a><!-- ws:end:WikiTextHeadingRule:12 -->441/440</h2>
| | |
| <br />
| | [[Comma list]]: 325/324, 625/624 |
| <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="Rank four-169/168"></a><!-- ws:end:WikiTextHeadingRule:14 -->169/168</h2>
| | |
| <br />
| | {{Optimal ET sequence|legend=1| 15, 19, 34, 53, 72, 87, 121, 140, 159, 193, 212, 299, 333 }} |
| <!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="Rank four-540/539"></a><!-- ws:end:WikiTextHeadingRule:16 -->540/539</h2>
| | |
| <br />
| | [[Badness]]: 3.563 × 10<sup>-6</sup> |
| <!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Rank four-352/351"></a><!-- ws:end:WikiTextHeadingRule:18 -->352/351</h2>
| | |
| <br />
| | == Rank-3 temperaments == |
| <!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="Rank four-625/624"></a><!-- ws:end:WikiTextHeadingRule:20 -->625/624</h2>
| | Notable rank-3 temperaments of marveltwin include: |
| <br />
| | |
| <!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc11"><a name="Rank three"></a><!-- ws:end:WikiTextHeadingRule:22 -->Rank three</h1>
| | * [[Portent|Portending]] → [[Gamelismic family #Portending|Gamelismic family]] |
| <br />
| | : +385/384, 441/440 |
| <!-- ws:start:WikiTextHeadingRule:24:&lt;h2&gt; --><h2 id="toc12"><a name="Rank three-Portending"></a><!-- ws:end:WikiTextHeadingRule:24 -->Portending</h2>
| | * [[Marvel|Marvel (hecate)]] → [[Marvel family #Hecate|Marvel family]] |
| Commas: 325/324, 364/363, 441/440<br />
| | : +225/224, 385/384 |
| <br />
| | * [[Enlil|Enlil a.k.a. sumatra]] → [[Kleismic rank-3 family #Enlil|Kleismic rank-3 family]] |
| <!-- ws:start:WikiTextHeadingRule:26:&lt;h2&gt; --><h2 id="toc13"><a name="Rank three-Marvel (Hecate)"></a><!-- ws:end:WikiTextHeadingRule:26 -->Marvel (Hecate)</h2>
| | : +385/384, 625/624 |
| Commas: 225/224, 325/324, 385/384<br />
| | |
| <br />
| | [[Category:Regular temperament theory]] |
| <!-- ws:start:WikiTextHeadingRule:28:&lt;h2&gt; --><h2 id="toc14"><a name="Rank three-Sumatra"></a><!-- ws:end:WikiTextHeadingRule:28 -->Sumatra</h2>
| | [[Category:Commatic realms]] |
| Commas: 325/324, 385/384, 625/624<br />
| | [[Category:Marveltwin]] |
| <br />
| |
| EDOs: 15, 19, 34, 53, 72, 87, 140, 159, 212, 299<br />
| |
| Optimal patent val: <a class="wiki_link" href="/299edo">299edo</a><br />
| |
| Badness: 0.000680</body></html></pre></div>
| |
|
Todo: intro
|
Marveltwin and marvel
The marveltwin comma, 325/324, bears a curiously close analogy to the marvel comma, 225/224. 325/324 can be added to the 11-limit version of marvel, which tempers out 225/224 and 385/384, to get 13-limit marvel, aka hecate. But it's also interesting to leave 11 out of it. From 225/224 we get that a 5-limit approximation for 7 is 225/224 * 7 = 225/32. Similarly from 325/324 we get a 5-limit approximation of 13 from 324/325 * 13 = 324/25. If we define the major/minor transformation of the 5-limit as the result of fixing 2 and 3 and replacing 5 by 24/5, then major/minor applied to 225/32 is 162/25, which is (324/25)/2. Similarly, major/minor applied to 324/25 is 225/16 = 2 * (225/32). 225/224 tells us that two 16/15 in a row are an approximate 8/7, and 325/324 tells us two 10/9 in a row are an approximate 16/13. Needless to say, major/minor applied to 16/15 is 10/9, and applied to 10/9 is 16/15.
Rank-5 temperaments
Subgroup: 2.3.5.7.11.13
Comma list: 325/324
Mapping:
| [⟨ |
1 |
0 |
0 |
0 |
0 |
2 |
],
|
| ⟨ |
0 |
1 |
0 |
0 |
0 |
4 |
],
|
| ⟨ |
0 |
0 |
1 |
0 |
0 |
-2 |
],
|
| ⟨ |
0 |
0 |
0 |
1 |
0 |
0 |
],
|
| ⟨ |
0 |
0 |
0 |
0 |
1 |
0 |
]]
|
Minimax tunings:
| [[ |
1 |
0 |
0 |
0 |
0 |
0 |
⟩
|
| [ |
0 |
1 |
0 |
0 |
0 |
0 |
⟩
|
| [ |
2/3 |
4/3 |
1/3 |
0 |
0 |
-1/3 |
⟩
|
| [ |
2/3 |
4/3 |
-2/3 |
1 |
0 |
-1/3 |
⟩
|
| [ |
2/3 |
4/3 |
-2/3 |
0 |
1 |
-1/3 |
⟩
|
| [ |
2/3 |
4/3 |
-2/3 |
0 |
0 |
2/3 |
⟩]
|
- 3 pure; 5, 7, 11 and 13 all flat by (325/324)1/3, which is 1.778 cents.
- unchanged-interval (eigenmonzo) basis: 2.3.7/5.11/5.13/5
Optimal ET sequence: 7, 12, 15, 19, 26, 34, 41, 46, 53, 72, 87, 121, 140, 159, 193, 212, 299, 333
Rank-4 temperaments
225/224
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 325/324
Mapping: [⟨1 0 0 -5 0 2], ⟨0 1 0 2 0 4], ⟨0 0 1 2 0 -2], ⟨0 0 0 0 1 0]]
Minimax tunings:
- 13-limit unchanged-interval (eigenmonzo) basis: 2.7.11/5.13/5
- 15-limit unchanged-interval (eigenmonzo) basis: 2.7.15/11.15/13
Optimal ET sequence: 12, 19, 41, 53, 72, 166
Badness: 3.668 × 10-6
385/384
See Keenanismic family #Martwin.
364/363
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 364/363
Optimal ET sequence: 15, 26, 41, 46, 72, 87, 121, 159, 193, 239, 280
Badness: 3.011 × 10-6
441/440
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 441/440
Optimal ET sequence: 12, 15, 26, 41, 46, 72, 87, 159
Badness: 3.037 × 10-6
169/168
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 325/324
Optimal ET sequence: 7, 19, 26, 46, 53, 72, 152
Badness: 2.975 × 10-6
540/539
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 540/539
Optimal ET sequence: 19, 41, 53, 72, 121, 166, 193
Badness: 3.281 × 10-6
352/351
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 352/351
Optimal ET sequence: 7, 34, 41, 46, 53, 80, 87, 121, 140, 261, 358, 401
Badness: 3.434 × 10-6
625/624
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 625/624
Optimal ET sequence: 15, 19, 34, 53, 72, 87, 121, 140, 159, 193, 212, 299, 333
Badness: 3.563 × 10-6
Rank-3 temperaments
Notable rank-3 temperaments of marveltwin include:
- +385/384, 441/440
- +225/224, 385/384
- +385/384, 625/624
