Diaschismic family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 191030138 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 191866586 - 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:genewardsmith|genewardsmith]] and made on <tt>2011-01- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-01-08 17:21:33 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>191866586</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> | ||
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The second comma of the [[Normal lists|normal comma list]] defines which 7-limit family member we are looking at. Pajara derives from 64/63 and is a popular and well-known choice. Diaschismic adds 2097152/2066715 to obtain 7-limit harmony by more complex methods, but with greater accuracy. Keen adds 2240/2187, echidna 1728/1715 and shrutar 245/243, the sensamagic comma. The pajara, diaschismic and keen keep the same 1/2 octave period and fifth generator, but shrutar has a generator of a quarter-tone (which can be taken as [[36_35|36/35]], the septimal quarter-tone) and echidna has a generator of 9/7. | The second comma of the [[Normal lists|normal comma list]] defines which 7-limit family member we are looking at. Pajara derives from 64/63 and is a popular and well-known choice. Diaschismic adds 2097152/2066715 to obtain 7-limit harmony by more complex methods, but with greater accuracy. Keen adds 2240/2187, echidna 1728/1715 and shrutar 245/243, the sensamagic comma. The pajara, diaschismic and keen keep the same 1/2 octave period and fifth generator, but shrutar has a generator of a quarter-tone (which can be taken as [[36_35|36/35]], the septimal quarter-tone) and echidna has a generator of 9/7. | ||
==Pajara== | |||
Pajara, with wedgie <<2 -4 -4 -11 -12 2|| is closely associated with 22et (not to mention [[Paul Erlich]]) but other tunings are possible. The 1/2 octave period serves as both a [[10_7|10/7]] and a [[7_5|7/5]]. Aside from 22et, 34 with the val <34 54 79 96| and 56 with the val <56 89 130 158| are are interesting alternatives, with more accpetable fifths, and a tetrad which is more clearly a dominant seventh. As such, they are closer to the tuning of 12et and of common practice Western music in general, while retaining the distictiveness of a sharp fifth. | Pajara, with wedgie <<2 -4 -4 -11 -12 2|| is closely associated with 22et (not to mention [[Paul Erlich]]) but other tunings are possible. The 1/2 octave period serves as both a [[10_7|10/7]] and a [[7_5|7/5]]. Aside from 22et, 34 with the val <34 54 79 96| and 56 with the val <56 89 130 158| are are interesting alternatives, with more accpetable fifths, and a tetrad which is more clearly a dominant seventh. As such, they are closer to the tuning of 12et and of common practice Western music in general, while retaining the distictiveness of a sharp fifth. | ||
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EDOs: 22, 34, 56 | EDOs: 22, 34, 56 | ||
===11-limit=== | |||
Commas: 50/49, 64/63, 99/98 | Commas: 50/49, 64/63, 99/98 | ||
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EDOs: 22, 34, 56, 146 | EDOs: 22, 34, 56, 146 | ||
==Diaschismic== | |||
A simpler characterization than the one given by the normal comma list is that diaschismic adds 126/125 or 5120/5103 to the set of commas, and it can also be called 46&58. However described, diaschismic has wedgie <<2 -4 -16 -11 -31 -26||, with a 1/2 period and a sharp fifth generator like pajara, but not so sharp, giving a more accurate but more complex temperament. [[58edo|58et]] provides an excellent tuning, but an alternative is to make [[7_4|7/4]] just by making the fifth 703.897 cents, as opposed to 703.448 cents for 58et. | A simpler characterization than the one given by the normal comma list is that diaschismic adds 126/125 or 5120/5103 to the set of commas, and it can also be called 46&58. However described, diaschismic has wedgie <<2 -4 -16 -11 -31 -26||, with a 1/2 period and a sharp fifth generator like pajara, but not so sharp, giving a more accurate but more complex temperament. [[58edo|58et]] provides an excellent tuning, but an alternative is to make [[7_4|7/4]] just by making the fifth 703.897 cents, as opposed to 703.448 cents for 58et. | ||
| Line 52: | Line 52: | ||
EDOs: 46, 58, 162 | EDOs: 46, 58, 162 | ||
===11-limit=== | |||
Commas: 126/125, 176/175, 896/891 | Commas: 126/125, 176/175, 896/891 | ||
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EDOs: 46, 58, 104, 162 | EDOs: 46, 58, 104, 162 | ||
===13-limit=== | |||
Commas: 126/125, 196/195, 364/363, 2048/2025 | Commas: 126/125, 196/195, 364/363, 2048/2025 | ||
| Line 70: | Line 70: | ||
EDOs: [[46edo]], [[58edo]], [[162edo]] | EDOs: [[46edo]], [[58edo]], [[162edo]] | ||
===17-limit=== | |||
Commas: 126/125, 136/135, 176/175, 196/195, 256/255 | Commas: 126/125, 136/135, 176/175, 196/195, 256/255 | ||
| Line 79: | Line 79: | ||
EDOs: 46, 58, 104 | EDOs: 46, 58, 104 | ||
==Keen== | |||
Keen adds 875/864 as well as 2240/2187 to the set of commas, and has wedgie <<2 -4 18 -11 23 53||. It may also be described as the 22&56 temperament. [[78edo|78et]] is a good tuning choice, and remains a good one in the 11-limit, where keen, <<2 -4 18 -12 ...||, is really more interesting, adding 100/99 and 385/384 to the commas. | Keen adds 875/864 as well as 2240/2187 to the set of commas, and has wedgie <<2 -4 18 -11 23 53||. It may also be described as the 22&56 temperament. [[78edo|78et]] is a good tuning choice, and remains a good one in the 11-limit, where keen, <<2 -4 18 -12 ...||, is really more interesting, adding 100/99 and 385/384 to the commas. | ||
| Line 90: | Line 90: | ||
EDOs: 22, 56, 78 | EDOs: 22, 56, 78 | ||
===11-limit=== | |||
Commas: 100/99, 385/384, 1232/1215 | Commas: 100/99, 385/384, 1232/1215 | ||
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EDOs: 22, 56, 78 | EDOs: 22, 56, 78 | ||
==Echidna== | |||
Echidna adds 1728/1715 to the commas and takes 9/7 as a generator. It has a wedgie <<6 -12 10 -33 -1 57|| and may be called the 22&58 temperament. [[58edo|58et]] or [[80edo|80et]] make for good tunings, or their vals can be add to <138 219 321 388|. | Echidna adds 1728/1715 to the commas and takes 9/7 as a generator. It has a wedgie <<6 -12 10 -33 -1 57|| and may be called the 22&58 temperament. [[58edo|58et]] or [[80edo|80et]] make for good tunings, or their vals can be add to <138 219 321 388|. | ||
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Map: [<2 1 9 2|, <0 3 -6 5|] | Map: [<2 1 9 2|, <0 3 -6 5|] | ||
EDOs: 22, 58, 80, 138, 218 | EDOs: 22, 58, 80, 138, 218 | ||
Badness: 0.0580 | |||
===11-limit=== | |||
Commas: 176/175, 896/891, 540/539 | Commas: 176/175, 896/891, 540/539 | ||
| Line 126: | Line 126: | ||
EDOs: 22, 58, 80, 138, 218 | EDOs: 22, 58, 80, 138, 218 | ||
Badness: 0.0260 | |||
===13-limit=== | |||
Commas: 176/175, 351/350, 364/363, 540/539 | Commas: 176/175, 351/350, 364/363, 540/539 | ||
| Line 134: | Line 135: | ||
Map: [<2 1 9 2 12 19|, <0 3 -6 5 -7 -16|] | Map: [<2 1 9 2 12 19|, <0 3 -6 5 -7 -16|] | ||
EDOs: 22, 58, 80, 138 | EDOs: 22, 58, 80, 138 | ||
Badness: 0.0237 | |||
===17-limit=== | |||
Commas: 136/135, 176/175, 221/220, 256/255, 540/539 | Commas: 136/135, 176/175, 221/220, 256/255, 540/539 | ||
| Line 142: | Line 144: | ||
Map: [<2 1 9 2 12 19 6|, <0 3 -6 5 -7 -16 3|] | Map: [<2 1 9 2 12 19 6|, <0 3 -6 5 -7 -16 3|] | ||
EDOs: 22, 58, 80, 138, 494 | EDOs: 22, 58, 80, 138, 494 | ||
Badness: 0.0203 | |||
==Echidnic== | |||
Commas: 686/675, 1029/1024 | |||
[[POTE tuning|POTE generator]]: 234.492 | |||
Map: [<2 2 7 6|, <0 3 -6 1|] | |||
EDOs: 10, 36, 46, 286, 332 | |||
Badness: 0.0722 | |||
===11-limit=== | |||
Commas: 385/384, 441/444, 686/675 | |||
[[POTE tuning|POTE generator]]: 235.096 | |||
Map: [<2 2 7 6 3|, <0 3 -6 1 10|] | |||
EDOs: 10, 46, 102, 148, 342 | |||
Badness: 0.0451 | |||
===13-limit=== | |||
Commas: 91/90, 169/168, 385/384, 441/440 | |||
[[POTE tuning|POTE generator]]: 235.088 | |||
Map: [<2 2 7 6 3 7|, <0 3 -6 1 10 1|] | |||
EDOs: 10, 46, 102, 148, 194, 342 | |||
Badness: 0.0289 | |||
==Shrutar== | |||
Shrutar adds 245/243 to the commas, and also tempers out 6144/6125. With wedgie <<4 -8 14 -22 11 55||, it can also be described as 22&46. Its generator can be taken as either 36/35 or 35/24; the latter is interesting since along with 15/14 and 21/20, it connects opposite sides of a hexany. [[68edo]] makes for a good tuning, but another and excellent choice is a generator of 14^(1/7), making 7s just. | Shrutar adds 245/243 to the commas, and also tempers out 6144/6125. With wedgie <<4 -8 14 -22 11 55||, it can also be described as 22&46. Its generator can be taken as either 36/35 or 35/24; the latter is interesting since along with 15/14 and 21/20, it connects opposite sides of a hexany. [[68edo]] makes for a good tuning, but another and excellent choice is a generator of 14^(1/7), making 7s just. | ||
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EDOs: 22, 46, 68, 250 | EDOs: 22, 46, 68, 250 | ||
===11-limit=== | |||
Commas: 2048/2025, 245/243, 121/120 | Commas: 2048/2025, 245/243, 121/120 | ||
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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. Pajara derives from 64/63 and is a popular and well-known choice. Diaschismic adds 2097152/2066715 to obtain 7-limit harmony by more complex methods, but with greater accuracy. Keen adds 2240/2187, echidna 1728/1715 and shrutar 245/243, the sensamagic comma. The pajara, diaschismic and keen keep the same 1/2 octave period and fifth generator, but shrutar has a generator of a quarter-tone (which can be taken as <a class="wiki_link" href="/36_35">36/35</a>, the septimal quarter-tone) and echidna has a generator of 9/7.<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. Pajara derives from 64/63 and is a popular and well-known choice. Diaschismic adds 2097152/2066715 to obtain 7-limit harmony by more complex methods, but with greater accuracy. Keen adds 2240/2187, echidna 1728/1715 and shrutar 245/243, the sensamagic comma. The pajara, diaschismic and keen keep the same 1/2 octave period and fifth generator, but shrutar has a generator of a quarter-tone (which can be taken as <a class="wiki_link" href="/36_35">36/35</a>, the septimal quarter-tone) and echidna has a generator of 9/7.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt; | <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-Pajara"></a><!-- ws:end:WikiTextHeadingRule:2 -->Pajara</h2> | ||
Pajara, with wedgie &lt;&lt;2 -4 -4 -11 -12 2|| is closely associated with 22et (not to mention <a class="wiki_link" href="/Paul%20Erlich">Paul Erlich</a>) but other tunings are possible. The 1/2 octave period serves as both a <a class="wiki_link" href="/10_7">10/7</a> and a <a class="wiki_link" href="/7_5">7/5</a>. Aside from 22et, 34 with the val &lt;34 54 79 96| and 56 with the val &lt;56 89 130 158| are are interesting alternatives, with more accpetable fifths, and a tetrad which is more clearly a dominant seventh. As such, they are closer to the tuning of 12et and of common practice Western music in general, while retaining the distictiveness of a sharp fifth.<br /> | Pajara, with wedgie &lt;&lt;2 -4 -4 -11 -12 2|| is closely associated with 22et (not to mention <a class="wiki_link" href="/Paul%20Erlich">Paul Erlich</a>) but other tunings are possible. The 1/2 octave period serves as both a <a class="wiki_link" href="/10_7">10/7</a> and a <a class="wiki_link" href="/7_5">7/5</a>. Aside from 22et, 34 with the val &lt;34 54 79 96| and 56 with the val &lt;56 89 130 158| are are interesting alternatives, with more accpetable fifths, and a tetrad which is more clearly a dominant seventh. As such, they are closer to the tuning of 12et and of common practice Western music in general, while retaining the distictiveness of a sharp fifth.<br /> | ||
<br /> | <br /> | ||
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EDOs: 22, 34, 56<br /> | EDOs: 22, 34, 56<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt; | <!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x-Pajara-11-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->11-limit</h3> | ||
Commas: 50/49, 64/63, 99/98<br /> | Commas: 50/49, 64/63, 99/98<br /> | ||
<br /> | <br /> | ||
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EDOs: 22, 34, 56, 146<br /> | EDOs: 22, 34, 56, 146<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:6:&lt; | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x-Diaschismic"></a><!-- ws:end:WikiTextHeadingRule:6 -->Diaschismic</h2> | ||
A simpler characterization than the one given by the normal comma list is that diaschismic adds 126/125 or 5120/5103 to the set of commas, and it can also be called 46&amp;58. However described, diaschismic has wedgie &lt;&lt;2 -4 -16 -11 -31 -26||, with a 1/2 period and a sharp fifth generator like pajara, but not so sharp, giving a more accurate but more complex temperament. <a class="wiki_link" href="/58edo">58et</a> provides an excellent tuning, but an alternative is to make <a class="wiki_link" href="/7_4">7/4</a> just by making the fifth 703.897 cents, as opposed to 703.448 cents for 58et.<br /> | A simpler characterization than the one given by the normal comma list is that diaschismic adds 126/125 or 5120/5103 to the set of commas, and it can also be called 46&amp;58. However described, diaschismic has wedgie &lt;&lt;2 -4 -16 -11 -31 -26||, with a 1/2 period and a sharp fifth generator like pajara, but not so sharp, giving a more accurate but more complex temperament. <a class="wiki_link" href="/58edo">58et</a> provides an excellent tuning, but an alternative is to make <a class="wiki_link" href="/7_4">7/4</a> just by making the fifth 703.897 cents, as opposed to 703.448 cents for 58et.<br /> | ||
<br /> | <br /> | ||
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EDOs: 46, 58, 162<br /> | EDOs: 46, 58, 162<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:8:&lt; | <!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><a name="x-Diaschismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:8 -->11-limit</h3> | ||
Commas: 126/125, 176/175, 896/891<br /> | Commas: 126/125, 176/175, 896/891<br /> | ||
<br /> | <br /> | ||
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EDOs: 46, 58, 104, 162<br /> | EDOs: 46, 58, 104, 162<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:10:&lt; | <!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="x-Diaschismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:10 -->13-limit</h3> | ||
Commas: 126/125, 196/195, 364/363, 2048/2025<br /> | Commas: 126/125, 196/195, 364/363, 2048/2025<br /> | ||
<br /> | <br /> | ||
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EDOs: <a class="wiki_link" href="/46edo">46edo</a>, <a class="wiki_link" href="/58edo">58edo</a>, <a class="wiki_link" href="/162edo">162edo</a><br /> | EDOs: <a class="wiki_link" href="/46edo">46edo</a>, <a class="wiki_link" href="/58edo">58edo</a>, <a class="wiki_link" href="/162edo">162edo</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:12:&lt; | <!-- ws:start:WikiTextHeadingRule:12:&lt;h3&gt; --><h3 id="toc6"><a name="x-Diaschismic-17-limit"></a><!-- ws:end:WikiTextHeadingRule:12 -->17-limit</h3> | ||
Commas: 126/125, 136/135, 176/175, 196/195, 256/255<br /> | Commas: 126/125, 136/135, 176/175, 196/195, 256/255<br /> | ||
<br /> | <br /> | ||
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EDOs: 46, 58, 104<br /> | EDOs: 46, 58, 104<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:14:&lt; | <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="x-Keen"></a><!-- ws:end:WikiTextHeadingRule:14 -->Keen</h2> | ||
Keen adds 875/864 as well as 2240/2187 to the set of commas, and has wedgie &lt;&lt;2 -4 18 -11 23 53||. It may also be described as the 22&amp;56 temperament. <a class="wiki_link" href="/78edo">78et</a> is a good tuning choice, and remains a good one in the 11-limit, where keen, &lt;&lt;2 -4 18 -12 ...||, is really more interesting, adding 100/99 and 385/384 to the commas.<br /> | Keen adds 875/864 as well as 2240/2187 to the set of commas, and has wedgie &lt;&lt;2 -4 18 -11 23 53||. It may also be described as the 22&amp;56 temperament. <a class="wiki_link" href="/78edo">78et</a> is a good tuning choice, and remains a good one in the 11-limit, where keen, &lt;&lt;2 -4 18 -12 ...||, is really more interesting, adding 100/99 and 385/384 to the commas.<br /> | ||
<br /> | <br /> | ||
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EDOs: 22, 56, 78<br /> | EDOs: 22, 56, 78<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:16:&lt; | <!-- ws:start:WikiTextHeadingRule:16:&lt;h3&gt; --><h3 id="toc8"><a name="x-Keen-11-limit"></a><!-- ws:end:WikiTextHeadingRule:16 -->11-limit</h3> | ||
Commas: 100/99, 385/384, 1232/1215<br /> | Commas: 100/99, 385/384, 1232/1215<br /> | ||
<br /> | <br /> | ||
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EDOs: 22, 56, 78<br /> | EDOs: 22, 56, 78<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:18:&lt; | <!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="x-Echidna"></a><!-- ws:end:WikiTextHeadingRule:18 -->Echidna</h2> | ||
Echidna adds 1728/1715 to the commas and takes 9/7 as a generator. It has a wedgie &lt;&lt;6 -12 10 -33 -1 57|| and may be called the 22&amp;58 temperament. <a class="wiki_link" href="/58edo">58et</a> or <a class="wiki_link" href="/80edo">80et</a> make for good tunings, or their vals can be add to &lt;138 219 321 388|.<br /> | Echidna adds 1728/1715 to the commas and takes 9/7 as a generator. It has a wedgie &lt;&lt;6 -12 10 -33 -1 57|| and may be called the 22&amp;58 temperament. <a class="wiki_link" href="/58edo">58et</a> or <a class="wiki_link" href="/80edo">80et</a> make for good tunings, or their vals can be add to &lt;138 219 321 388|.<br /> | ||
<br /> | <br /> | ||
| Line 268: | Line 298: | ||
<br /> | <br /> | ||
Map: [&lt;2 1 9 2|, &lt;0 3 -6 5|]<br /> | Map: [&lt;2 1 9 2|, &lt;0 3 -6 5|]<br /> | ||
EDOs: 22, 58, 80, 138, 218<br /> | EDOs: 22, 58, 80, 138, 218<br /> | ||
Badness: 0.0580<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:20:&lt; | <!-- ws:start:WikiTextHeadingRule:20:&lt;h3&gt; --><h3 id="toc10"><a name="x-Echidna-11-limit"></a><!-- ws:end:WikiTextHeadingRule:20 -->11-limit</h3> | ||
Commas: 176/175, 896/891, 540/539<br /> | Commas: 176/175, 896/891, 540/539<br /> | ||
<br /> | <br /> | ||
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<br /> | <br /> | ||
EDOs: 22, 58, 80, 138, 218<br /> | EDOs: 22, 58, 80, 138, 218<br /> | ||
Badness: 0.0260<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:22:&lt; | <!-- ws:start:WikiTextHeadingRule:22:&lt;h3&gt; --><h3 id="toc11"><a name="x-Echidna-13-limit"></a><!-- ws:end:WikiTextHeadingRule:22 -->13-limit</h3> | ||
Commas: 176/175, 351/350, 364/363, 540/539<br /> | Commas: 176/175, 351/350, 364/363, 540/539<br /> | ||
<br /> | <br /> | ||
| Line 293: | Line 324: | ||
Map: [&lt;2 1 9 2 12 19|, &lt;0 3 -6 5 -7 -16|]<br /> | Map: [&lt;2 1 9 2 12 19|, &lt;0 3 -6 5 -7 -16|]<br /> | ||
EDOs: 22, 58, 80, 138<br /> | EDOs: 22, 58, 80, 138<br /> | ||
Badness: 0.0237<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:24:&lt; | <!-- ws:start:WikiTextHeadingRule:24:&lt;h3&gt; --><h3 id="toc12"><a name="x-Echidna-17-limit"></a><!-- ws:end:WikiTextHeadingRule:24 -->17-limit</h3> | ||
Commas: 136/135, 176/175, 221/220, 256/255, 540/539<br /> | Commas: 136/135, 176/175, 221/220, 256/255, 540/539<br /> | ||
<br /> | <br /> | ||
| Line 301: | Line 333: | ||
Map: [&lt;2 1 9 2 12 19 6|, &lt;0 3 -6 5 -7 -16 3|]<br /> | Map: [&lt;2 1 9 2 12 19 6|, &lt;0 3 -6 5 -7 -16 3|]<br /> | ||
EDOs: 22, 58, 80, 138, 494<br /> | EDOs: 22, 58, 80, 138, 494<br /> | ||
Badness: 0.0203<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:26:&lt;h2&gt; --><h2 id="toc13"><a name="x-Echidnic"></a><!-- ws:end:WikiTextHeadingRule:26 -->Echidnic</h2> | |||
Commas: 686/675, 1029/1024<br /> | |||
<br /> | |||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 234.492<br /> | |||
<br /> | |||
Map: [&lt;2 2 7 6|, &lt;0 3 -6 1|]<br /> | |||
EDOs: 10, 36, 46, 286, 332<br /> | |||
Badness: 0.0722<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:28:&lt;h3&gt; --><h3 id="toc14"><a name="x-Echidnic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:28 -->11-limit</h3> | |||
Commas: 385/384, 441/444, 686/675<br /> | |||
<br /> | |||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 235.096<br /> | |||
<br /> | |||
Map: [&lt;2 2 7 6 3|, &lt;0 3 -6 1 10|]<br /> | |||
EDOs: 10, 46, 102, 148, 342<br /> | |||
Badness: 0.0451<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:30:&lt;h3&gt; --><h3 id="toc15"><a name="x-Echidnic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:30 -->13-limit</h3> | |||
Commas: 91/90, 169/168, 385/384, 441/440<br /> | |||
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<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 235.088<br /> | |||
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Map: [&lt;2 2 7 6 3 7|, &lt;0 3 -6 1 10 1|]<br /> | |||
EDOs: 10, 46, 102, 148, 194, 342<br /> | |||
Badness: 0.0289<br /> | |||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="x-Shrutar"></a><!-- ws:end:WikiTextHeadingRule:32 -->Shrutar</h2> | ||
Shrutar adds 245/243 to the commas, and also tempers out 6144/6125. With wedgie &lt;&lt;4 -8 14 -22 11 55||, it can also be described as 22&amp;46. Its generator can be taken as either 36/35 or 35/24; the latter is interesting since along with 15/14 and 21/20, it connects opposite sides of a hexany. <a class="wiki_link" href="/68edo">68edo</a> makes for a good tuning, but another and excellent choice is a generator of 14^(1/7), making 7s just.<br /> | Shrutar adds 245/243 to the commas, and also tempers out 6144/6125. With wedgie &lt;&lt;4 -8 14 -22 11 55||, it can also be described as 22&amp;46. Its generator can be taken as either 36/35 or 35/24; the latter is interesting since along with 15/14 and 21/20, it connects opposite sides of a hexany. <a class="wiki_link" href="/68edo">68edo</a> makes for a good tuning, but another and excellent choice is a generator of 14^(1/7), making 7s just.<br /> | ||
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EDOs: 22, 46, 68, 250<br /> | EDOs: 22, 46, 68, 250<br /> | ||
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Commas: 2048/2025, 245/243, 121/120<br /> | Commas: 2048/2025, 245/243, 121/120<br /> | ||
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