26edo: Difference between revisions
Wikispaces>vaisvil **Imported revision 602800226 - Original comment: ** |
Wikispaces>xenwolf **Imported revision 602835062 - 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:xenwolf|xenwolf]] and made on <tt>2016-12-27 08:38:18 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>602835062</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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//26edo// divides the [[octave]] into 26 equal parts of 46.154 [[cent]]s each. It tempers out 81/80 in the [[5-limit]], making it a meantone tuning with a very flat fifth. In the [[7-limit]], it tempers out 50/49, 525/512 and 875/864, and supports [[Meantone family|injera]], [[Meantone family|flattone]], [[Jubilismic clan#Lemba|lemba]] and [[Jubilismic clan#Doublewide|doublewide]] temperaments. It really comes into its own as a higher-limit temperament, being the smallest equal division which represents the [[13-limit|13 odd limit]] [[consistent|consistently]]. 26edo has a very good approximation of the harmonic seventh ([[7_4|7/4]]). | //26edo// divides the [[octave]] into 26 equal parts of 46.154 [[cent]]s each. It tempers out 81/80 in the [[5-limit]], making it a meantone tuning with a very flat fifth. In the [[7-limit]], it tempers out 50/49, 525/512 and 875/864, and supports [[Meantone family|injera]], [[Meantone family|flattone]], [[Jubilismic clan#Lemba|lemba]] and [[Jubilismic clan#Doublewide|doublewide]] temperaments. It really comes into its own as a higher-limit temperament, being the smallest equal division which represents the [[13-limit|13 odd limit]] [[consistent|consistently]]. 26edo has a very good approximation of the harmonic seventh ([[7_4|7/4]]). | ||
= | == Structure == | ||
The structure of 26edo is an interesting beast, with various approaches relating it to various rank two temperaments. | The structure of 26edo is an interesting beast, with various approaches relating it to various rank two temperaments. | ||
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5. It also has a pretty good 17th harmonic and tempers out the comma 459:448, thus three fifths gives a 17:14 and four gives a 21:17; "mushtone". Mushtone is high in badness, but 26edo does it pretty well (and [[33edo]] even better). Because 26edo also tempers out 85:84, the septendecimal major and minor thirds are equivalent to their pental counterparts, making mushtone the same as flattone. | 5. It also has a pretty good 17th harmonic and tempers out the comma 459:448, thus three fifths gives a 17:14 and four gives a 21:17; "mushtone". Mushtone is high in badness, but 26edo does it pretty well (and [[33edo]] even better). Because 26edo also tempers out 85:84, the septendecimal major and minor thirds are equivalent to their pental counterparts, making mushtone the same as flattone. | ||
= | == Intervals == | ||
|| | ||~ Degrees ||~ Size in | ||
[[cent|cents]] ||~ Approximate Ratios* ||~ Solfege || | |||
Ratios* || Solfege || | ||= 0 ||> 0<span style="color: #fff;">.00</span> ||= 1/1 || do || | ||
|| 0 || 0 ||= 1/1 || do || | ||= 1 ||> 46.15 ||= [[33_32|33/32]], [[49_48|49/48]], [[36_35|36/35]], [[25_24|25/24]] || di || | ||
|| 1 || 46. | ||= 2 ||> 92.31 ||= [[21_20|21/20]], [[22_21|22/21]], [[26_25|26/25]] || rih || | ||
||= 3 ||> 138.46 ||= [[12_11|12/11]], [[13_12|13/12]], [[14_13|14/13]], [[16_15|16/15]] || ru || | |||
|| 2 || 92. | ||= 4 ||> 184.62 ||= [[9_8|9/8]], [[10_9|10/9]], [[11_10|11/10]] || re || | ||
||= 5 ||> 230.77 ||= [[8_7|8/7]], 15/13 || ri || | |||
|| 3 || 138.46 | ||= 6 ||> 276.92 ||= [[7_6|7/6]], [[13_11|13/11]], [[33_28|33/28]] || ma || | ||
||= 7 ||> 323.08 ||= [[6_5|6/5]] || me || | |||
|| 4 || 184. | ||= 8 ||> 369.23 ||= [[5_4|5/4]], [[11_9|11/9]], [[16_13|16/13]] || muh/mi || | ||
||= 9 ||> 415.38 ||= [[9_7|9/7]], [[14_11|14/11]], [[33_26|33/26]] || maa || | |||
|| 5 || 230.77 | ||= 10 ||> 461.54 ||= [[21_16|21/16]], [[13_10|13/10]] || fe || | ||
||= 11 ||> 507.69 ||= [[4_3|4/3]] || fa || | |||
|| 6 || 276.92 | ||= 12 ||> 553.85 ||= [[11_8|11/8]], [[18_13|18/13]] || fu || | ||
||= 13 ||> 600<span style="color: #fff;">.00</span> ||= [[7_5|7/5]], [[10_7|10/7]] || fi/se || | |||
|| 7 || 323.08 | ||= 14 ||> 646.15 ||= [[16_11|16/11]], [[13_9|13/9]] || su || | ||
||= 15 ||> 692.31 ||= [[3_2|3/2]] || sol || | |||
|| 8 || 369.23 | ||= 16 ||> 738.46 ||= [[32_21|32/21]], [[20_13|20/13]] || si || | ||
||= 17 ||> 784.62 ||= [[11_7|11/7]], [[14_9|14/9]] || leh || | |||
|| 9 || 415. | ||= 18 ||> 830.77 ||= [[13_8|13/8]], [[8_5|8/5]] || le/lu || | ||
||= 19 ||> 876.92 ||= [[5_3|5/3]] || la || | |||
|| 10 || 461.54 | ||= 20 ||> 923.08 ||= [[12_7|12/7]], [[22_13|22/13]] || li || | ||
||= 21 ||> 969.23 ||= [[7_4|7/4]] || ta || | |||
|| 11 || 507.69 | ||= 22 ||> 1015.38 ||= [[9_5|9/5]], [[16_9|16/9]], [[20_11|20/11]] || te || | ||
||= 23 ||> 1061.54 ||= [[11_6|11/6]], [[13_7|13/7]], [[15_8|15/8]], [[24_13|24/13]] || tu/ti || | |||
|| 12 || 553.85 | ||= 24 ||> 1107.69 ||= [[21_11|21/11]], [[25_13|25/13]], [[40_21|40/21]] || to || | ||
||= 25 ||> 1153.85 ||= [[64_33|64/33]], [[96_49|96/49]], [[35_18|35/18]], [[48_25|48/25]] || da || | |||
|| 13 || 600.00 | ||= 26 ||> 1200<span style="color: #fff;">.00</span> ||= 2/1 || do || | ||
|| 14 || 646.15 | |||
|| 15 || 692.31 | |||
|| 16 || 738.46 | |||
|| 17 || 784. | |||
|| 18 || 830.77 | |||
|| 19 || 876.92 | |||
|| 20 || 923.08 | |||
|| 21 || 969.23 | |||
|| 22 || 1015. | |||
|| 23 || 1061. | |||
|| 24 || 1107. | |||
|| 25 || 1153.85 | |||
|| 26 || 1200 | |||
*based on treating 26-EDO as a 13-limit temperament; other approaches are possible. | *based on treating 26-EDO as a 13-limit temperament; other approaches are possible. | ||
==Selected just intervals by error== | ==Selected just intervals by error== | ||
The following table shows how [[Just-24|some prominent just intervals]] are represented in 26edo (ordered by absolute error). | The following table shows how [[Just-24|some prominent just intervals]] are represented in 26edo (ordered by absolute error). | ||
|| | ||~ Interval, complement ||~ Error (abs., in [[cent|cents]]) || | ||
||= [[13_12|13/12]], [[24_13|24/13]] ||= 0.111 || | ||= [[13_12|13/12]], [[24_13|24/13]] ||= 0.111 || | ||
||= [[8_7|8/7]], [[7_4|7/4]] ||= 0.405 || | ||= [[8_7|8/7]], [[7_4|7/4]] ||= 0.405 || | ||
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[[http://micro.soonlabel.com/26edo/20161224_26edo_wing.mp3|Morpheous Wing in 26 edo]] by [[Chris Vaisvil]]</pre></div> | [[http://micro.soonlabel.com/26edo/20161224_26edo_wing.mp3|Morpheous Wing in 26 edo]] by [[Chris Vaisvil]]</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>26edo</title></head><body><!-- ws:start:WikiTextTocRule:21:&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:21 --><!-- ws:start:WikiTextTocRule:22: --><div style="margin-left: | <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>26edo</title></head><body><!-- ws:start:WikiTextTocRule:21:&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:21 --><!-- ws:start:WikiTextTocRule:22: --><div style="margin-left: 2em;"><a href="#x-Structure"> Structure </a></div> | ||
<!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --><div style="margin-left: | <!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --><div style="margin-left: 2em;"><a href="#x-Intervals"> Intervals </a></div> | ||
<!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --><div style="margin-left: 2em;"><a href="# | <!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --><div style="margin-left: 2em;"><a href="#x-Selected just intervals by error">Selected just intervals by error</a></div> | ||
<!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --><div style="margin-left: 1em;"><a href="#Rank two temperaments">Rank two temperaments</a></div> | <!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --><div style="margin-left: 1em;"><a href="#Rank two temperaments">Rank two temperaments</a></div> | ||
<!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --><div style="margin-left: 2em;"><a href="#Rank two temperaments-Hendec in 26et">Hendec in 26et</a></div> | <!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --><div style="margin-left: 2em;"><a href="#Rank two temperaments-Hendec in 26et">Hendec in 26et</a></div> | ||
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<!-- ws:end:WikiTextTocRule:32 --><em>26edo</em> divides the <a class="wiki_link" href="/octave">octave</a> into 26 equal parts of 46.154 <a class="wiki_link" href="/cent">cent</a>s each. It tempers out 81/80 in the <a class="wiki_link" href="/5-limit">5-limit</a>, making it a meantone tuning with a very flat fifth. In the <a class="wiki_link" href="/7-limit">7-limit</a>, it tempers out 50/49, 525/512 and 875/864, and supports <a class="wiki_link" href="/Meantone%20family">injera</a>, <a class="wiki_link" href="/Meantone%20family">flattone</a>, <a class="wiki_link" href="/Jubilismic%20clan#Lemba">lemba</a> and <a class="wiki_link" href="/Jubilismic%20clan#Doublewide">doublewide</a> temperaments. It really comes into its own as a higher-limit temperament, being the smallest equal division which represents the <a class="wiki_link" href="/13-limit">13 odd limit</a> <a class="wiki_link" href="/consistent">consistently</a>. 26edo has a very good approximation of the harmonic seventh (<a class="wiki_link" href="/7_4">7/4</a>).<br /> | <!-- ws:end:WikiTextTocRule:32 --><em>26edo</em> divides the <a class="wiki_link" href="/octave">octave</a> into 26 equal parts of 46.154 <a class="wiki_link" href="/cent">cent</a>s each. It tempers out 81/80 in the <a class="wiki_link" href="/5-limit">5-limit</a>, making it a meantone tuning with a very flat fifth. In the <a class="wiki_link" href="/7-limit">7-limit</a>, it tempers out 50/49, 525/512 and 875/864, and supports <a class="wiki_link" href="/Meantone%20family">injera</a>, <a class="wiki_link" href="/Meantone%20family">flattone</a>, <a class="wiki_link" href="/Jubilismic%20clan#Lemba">lemba</a> and <a class="wiki_link" href="/Jubilismic%20clan#Doublewide">doublewide</a> temperaments. It really comes into its own as a higher-limit temperament, being the smallest equal division which represents the <a class="wiki_link" href="/13-limit">13 odd limit</a> <a class="wiki_link" href="/consistent">consistently</a>. 26edo has a very good approximation of the harmonic seventh (<a class="wiki_link" href="/7_4">7/4</a>).<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:1:&lt; | <!-- ws:start:WikiTextHeadingRule:1:&lt;h2&gt; --><h2 id="toc0"><a name="x-Structure"></a><!-- ws:end:WikiTextHeadingRule:1 --> Structure </h2> | ||
<br /> | <br /> | ||
The structure of 26edo is an interesting beast, with various approaches relating it to various rank two temperaments.<br /> | The structure of 26edo is an interesting beast, with various approaches relating it to various rank two temperaments.<br /> | ||
| Line 234: | Line 207: | ||
5. It also has a pretty good 17th harmonic and tempers out the comma 459:448, thus three fifths gives a 17:14 and four gives a 21:17; &quot;mushtone&quot;. Mushtone is high in badness, but 26edo does it pretty well (and <a class="wiki_link" href="/33edo">33edo</a> even better). Because 26edo also tempers out 85:84, the septendecimal major and minor thirds are equivalent to their pental counterparts, making mushtone the same as flattone.<br /> | 5. It also has a pretty good 17th harmonic and tempers out the comma 459:448, thus three fifths gives a 17:14 and four gives a 21:17; &quot;mushtone&quot;. Mushtone is high in badness, but 26edo does it pretty well (and <a class="wiki_link" href="/33edo">33edo</a> even better). Because 26edo also tempers out 85:84, the septendecimal major and minor thirds are equivalent to their pental counterparts, making mushtone the same as flattone.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:3:&lt; | <!-- ws:start:WikiTextHeadingRule:3:&lt;h2&gt; --><h2 id="toc1"><a name="x-Intervals"></a><!-- ws:end:WikiTextHeadingRule:3 --> Intervals </h2> | ||
<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
< | <th>Degrees<br /> | ||
</ | </th> | ||
< | <th>Size in <br /> | ||
<a class="wiki_link" href="/cent">cents</a><br /> | |||
</th> | |||
< | <th>Approximate Ratios*<br /> | ||
Ratios*<br /> | </th> | ||
</ | <th>Solfege<br /> | ||
< | </th> | ||
</ | |||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>0<br /> | <td style="text-align: center;">0<br /> | ||
</td> | </td> | ||
<td>0<br /> | <td style="text-align: right;">0<span style="color: #fff;">.00</span><br /> | ||
</td> | </td> | ||
<td style="text-align: center;">1/1<br /> | <td style="text-align: center;">1/1<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>1<br /> | <td style="text-align: center;">1<br /> | ||
</td> | </td> | ||
<td>46. | <td style="text-align: right;">46.15<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><a class="wiki_link" href="/33_32">33/32</a>, <a class="wiki_link" href="/49_48">49/48</a>, <a class="wiki_link" href="/36_35">36/35</a>, <a class="wiki_link" href="/25_24">25/24</a><br /> | <td style="text-align: center;"><a class="wiki_link" href="/33_32">33/32</a>, <a class="wiki_link" href="/49_48">49/48</a>, <a class="wiki_link" href="/36_35">36/35</a>, <a class="wiki_link" href="/25_24">25/24</a><br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>2<br /> | <td style="text-align: center;">2<br /> | ||
</td> | </td> | ||
<td>92. | <td style="text-align: right;">92.31<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><a class="wiki_link" href="/21_20">21/20</a>, <a class="wiki_link" href="/22_21">22/21</a>, <a class="wiki_link" href="/26_25">26/25</a><br /> | <td style="text-align: center;"><a class="wiki_link" href="/21_20">21/20</a>, <a class="wiki_link" href="/22_21">22/21</a>, <a class="wiki_link" href="/26_25">26/25</a><br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>3<br /> | <td style="text-align: center;">3<br /> | ||
</td> | </td> | ||
<td>138.46 | <td style="text-align: right;">138.46<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><a class="wiki_link" href="/12_11">12/11</a>, <a class="wiki_link" href="/13_12">13/12</a>, <a class="wiki_link" href="/14_13">14/13</a>, <a class="wiki_link" href="/16_15">16/15</a><br /> | <td style="text-align: center;"><a class="wiki_link" href="/12_11">12/11</a>, <a class="wiki_link" href="/13_12">13/12</a>, <a class="wiki_link" href="/14_13">14/13</a>, <a class="wiki_link" href="/16_15">16/15</a><br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>4<br /> | <td style="text-align: center;">4<br /> | ||
</td> | </td> | ||
<td>184. | <td style="text-align: right;">184.62<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><a class="wiki_link" href="/9_8">9/8</a>, <a class="wiki_link" href="/10_9">10/9</a>, <a class="wiki_link" href="/11_10">11/10</a><br /> | <td style="text-align: center;"><a class="wiki_link" href="/9_8">9/8</a>, <a class="wiki_link" href="/10_9">10/9</a>, <a class="wiki_link" href="/11_10">11/10</a><br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>5<br /> | <td style="text-align: center;">5<br /> | ||
</td> | </td> | ||
<td>230.77 | <td style="text-align: right;">230.77<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><a class="wiki_link" href="/8_7">8/7</a>, 15/13<br /> | <td style="text-align: center;"><a class="wiki_link" href="/8_7">8/7</a>, 15/13<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>6<br /> | <td style="text-align: center;">6<br /> | ||
</td> | </td> | ||
<td>276.92 | <td style="text-align: right;">276.92<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><a class="wiki_link" href="/7_6">7/6</a>, <a class="wiki_link" href="/13_11">13/11</a>, <a class="wiki_link" href="/33_28">33/28</a><br /> | <td style="text-align: center;"><a class="wiki_link" href="/7_6">7/6</a>, <a class="wiki_link" href="/13_11">13/11</a>, <a class="wiki_link" href="/33_28">33/28</a><br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>7<br /> | <td style="text-align: center;">7<br /> | ||
</td> | </td> | ||
<td>323.08 | <td style="text-align: right;">323.08<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><a class="wiki_link" href="/6_5">6/5</a><br /> | <td style="text-align: center;"><a class="wiki_link" href="/6_5">6/5</a><br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>8<br /> | <td style="text-align: center;">8<br /> | ||
</td> | </td> | ||
<td>369.23 | <td style="text-align: right;">369.23<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><a class="wiki_link" href="/5_4">5/4</a>, <a class="wiki_link" href="/11_9">11/9</a>, <a class="wiki_link" href="/16_13">16/13</a><br /> | <td style="text-align: center;"><a class="wiki_link" href="/5_4">5/4</a>, <a class="wiki_link" href="/11_9">11/9</a>, <a class="wiki_link" href="/16_13">16/13</a><br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>9<br /> | <td style="text-align: center;">9<br /> | ||
</td> | </td> | ||
<td>415. | <td style="text-align: right;">415.38<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><a class="wiki_link" href="/9_7">9/7</a>, <a class="wiki_link" href="/14_11">14/11</a>, <a class="wiki_link" href="/33_26">33/26</a><br /> | <td style="text-align: center;"><a class="wiki_link" href="/9_7">9/7</a>, <a class="wiki_link" href="/14_11">14/11</a>, <a class="wiki_link" href="/33_26">33/26</a><br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>10<br /> | <td style="text-align: center;">10<br /> | ||
</td> | </td> | ||
<td>461.54 | <td style="text-align: right;">461.54<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><a class="wiki_link" href="/21_16">21/16</a>, <a class="wiki_link" href="/13_10">13/10</a><br /> | <td style="text-align: center;"><a class="wiki_link" href="/21_16">21/16</a>, <a class="wiki_link" href="/13_10">13/10</a><br /> | ||
| Line 371: | Line 333: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>11<br /> | <td style="text-align: center;">11<br /> | ||
</td> | </td> | ||
<td>507.69 | <td style="text-align: right;">507.69<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><a class="wiki_link" href="/4_3">4/3</a><br /> | <td style="text-align: center;"><a class="wiki_link" href="/4_3">4/3</a><br /> | ||
| Line 382: | Line 343: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>12<br /> | <td style="text-align: center;">12<br /> | ||
</td> | </td> | ||
<td>553.85 | <td style="text-align: right;">553.85<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><a class="wiki_link" href="/11_8">11/8</a>, <a class="wiki_link" href="/18_13">18/13</a><br /> | <td style="text-align: center;"><a class="wiki_link" href="/11_8">11/8</a>, <a class="wiki_link" href="/18_13">18/13</a><br /> | ||
| Line 393: | Line 353: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>13<br /> | <td style="text-align: center;">13<br /> | ||
</td> | </td> | ||
<td>600.00 | <td style="text-align: right;">600<span style="color: #fff;">.00</span><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><a class="wiki_link" href="/7_5">7/5</a>, <a class="wiki_link" href="/10_7">10/7</a><br /> | <td style="text-align: center;"><a class="wiki_link" href="/7_5">7/5</a>, <a class="wiki_link" href="/10_7">10/7</a><br /> | ||
| Line 404: | Line 363: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>14<br /> | <td style="text-align: center;">14<br /> | ||
</td> | </td> | ||
<td>646.15 | <td style="text-align: right;">646.15<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><a class="wiki_link" href="/16_11">16/11</a>, <a class="wiki_link" href="/13_9">13/9</a><br /> | <td style="text-align: center;"><a class="wiki_link" href="/16_11">16/11</a>, <a class="wiki_link" href="/13_9">13/9</a><br /> | ||
| Line 415: | Line 373: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>15<br /> | <td style="text-align: center;">15<br /> | ||
</td> | </td> | ||
<td>692.31 | <td style="text-align: right;">692.31<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><a class="wiki_link" href="/3_2">3/2</a><br /> | <td style="text-align: center;"><a class="wiki_link" href="/3_2">3/2</a><br /> | ||
| Line 426: | Line 383: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>16<br /> | <td style="text-align: center;">16<br /> | ||
</td> | </td> | ||
<td>738.46 | <td style="text-align: right;">738.46<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><a class="wiki_link" href="/32_21">32/21</a>, <a class="wiki_link" href="/20_13">20/13</a><br /> | <td style="text-align: center;"><a class="wiki_link" href="/32_21">32/21</a>, <a class="wiki_link" href="/20_13">20/13</a><br /> | ||
| Line 437: | Line 393: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>17<br /> | <td style="text-align: center;">17<br /> | ||
</td> | </td> | ||
<td>784. | <td style="text-align: right;">784.62<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><a class="wiki_link" href="/11_7">11/7</a>, <a class="wiki_link" href="/14_9">14/9</a><br /> | <td style="text-align: center;"><a class="wiki_link" href="/11_7">11/7</a>, <a class="wiki_link" href="/14_9">14/9</a><br /> | ||
| Line 448: | Line 403: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>18<br /> | <td style="text-align: center;">18<br /> | ||
</td> | </td> | ||
<td>830.77 | <td style="text-align: right;">830.77<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><a class="wiki_link" href="/13_8">13/8</a>, <a class="wiki_link" href="/8_5">8/5</a><br /> | <td style="text-align: center;"><a class="wiki_link" href="/13_8">13/8</a>, <a class="wiki_link" href="/8_5">8/5</a><br /> | ||
| Line 459: | Line 413: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>19<br /> | <td style="text-align: center;">19<br /> | ||
</td> | </td> | ||
<td>876.92 | <td style="text-align: right;">876.92<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><a class="wiki_link" href="/5_3">5/3</a><br /> | <td style="text-align: center;"><a class="wiki_link" href="/5_3">5/3</a><br /> | ||
| Line 470: | Line 423: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>20<br /> | <td style="text-align: center;">20<br /> | ||
</td> | </td> | ||
<td>923.08 | <td style="text-align: right;">923.08<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><a class="wiki_link" href="/12_7">12/7</a>, <a class="wiki_link" href="/22_13">22/13</a><br /> | <td style="text-align: center;"><a class="wiki_link" href="/12_7">12/7</a>, <a class="wiki_link" href="/22_13">22/13</a><br /> | ||
| Line 481: | Line 433: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>21<br /> | <td style="text-align: center;">21<br /> | ||
</td> | </td> | ||
<td>969.23 | <td style="text-align: right;">969.23<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><a class="wiki_link" href="/7_4">7/4</a><br /> | <td style="text-align: center;"><a class="wiki_link" href="/7_4">7/4</a><br /> | ||
| Line 492: | Line 443: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>22<br /> | <td style="text-align: center;">22<br /> | ||
</td> | </td> | ||
<td>1015. | <td style="text-align: right;">1015.38<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><a class="wiki_link" href="/9_5">9/5</a>, <a class="wiki_link" href="/16_9">16/9</a>, <a class="wiki_link" href="/20_11">20/11</a><br /> | <td style="text-align: center;"><a class="wiki_link" href="/9_5">9/5</a>, <a class="wiki_link" href="/16_9">16/9</a>, <a class="wiki_link" href="/20_11">20/11</a><br /> | ||
| Line 503: | Line 453: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>23<br /> | <td style="text-align: center;">23<br /> | ||
</td> | </td> | ||
<td>1061. | <td style="text-align: right;">1061.54<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><a class="wiki_link" href="/11_6">11/6</a>, <a class="wiki_link" href="/13_7">13/7</a>, <a class="wiki_link" href="/15_8">15/8</a>, <a class="wiki_link" href="/24_13">24/13</a><br /> | <td style="text-align: center;"><a class="wiki_link" href="/11_6">11/6</a>, <a class="wiki_link" href="/13_7">13/7</a>, <a class="wiki_link" href="/15_8">15/8</a>, <a class="wiki_link" href="/24_13">24/13</a><br /> | ||
| Line 514: | Line 463: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>24<br /> | <td style="text-align: center;">24<br /> | ||
</td> | </td> | ||
<td>1107. | <td style="text-align: right;">1107.69<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><a class="wiki_link" href="/21_11">21/11</a>, <a class="wiki_link" href="/25_13">25/13</a>, <a class="wiki_link" href="/40_21">40/21</a><br /> | <td style="text-align: center;"><a class="wiki_link" href="/21_11">21/11</a>, <a class="wiki_link" href="/25_13">25/13</a>, <a class="wiki_link" href="/40_21">40/21</a><br /> | ||
| Line 525: | Line 473: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>25<br /> | <td style="text-align: center;">25<br /> | ||
</td> | </td> | ||
<td>1153.85 | <td style="text-align: right;">1153.85<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><a class="wiki_link" href="/64_33">64/33</a>, <a class="wiki_link" href="/96_49">96/49</a>, <a class="wiki_link" href="/35_18">35/18</a>, <a class="wiki_link" href="/48_25">48/25</a><br /> | <td style="text-align: center;"><a class="wiki_link" href="/64_33">64/33</a>, <a class="wiki_link" href="/96_49">96/49</a>, <a class="wiki_link" href="/35_18">35/18</a>, <a class="wiki_link" href="/48_25">48/25</a><br /> | ||
| Line 536: | Line 483: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>26<br /> | <td style="text-align: center;">26<br /> | ||
</td> | </td> | ||
<td>1200 | <td style="text-align: right;">1200<span style="color: #fff;">.00</span><br /> | ||
</td> | </td> | ||
<td style="text-align: center;">2/1<br /> | <td style="text-align: center;">2/1<br /> | ||
| Line 550: | Line 496: | ||
*based on treating 26-EDO as a 13-limit temperament; other approaches are possible.<br /> | *based on treating 26-EDO as a 13-limit temperament; other approaches are possible.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:5:&lt;h2&gt; --><h2 id="toc2"><a name=" | <!-- ws:start:WikiTextHeadingRule:5:&lt;h2&gt; --><h2 id="toc2"><a name="x-Selected just intervals by error"></a><!-- ws:end:WikiTextHeadingRule:5 -->Selected just intervals by error</h2> | ||
The following table shows how <a class="wiki_link" href="/Just-24">some prominent just intervals</a> are represented in 26edo (ordered by absolute error).<br /> | The following table shows how <a class="wiki_link" href="/Just-24">some prominent just intervals</a> are represented in 26edo (ordered by absolute error).<br /> | ||
| Line 556: | Line 502: | ||
<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
< | <th>Interval, complement<br /> | ||
</ | </th> | ||
< | <th>Error (abs., in <a class="wiki_link" href="/cent">cents</a>)<br /> | ||
</ | </th> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||