29edo: Difference between revisions
Wikispaces>genewardsmith **Imported revision 243134003 - Original comment: ** |
Wikispaces>keenanpepper **Imported revision 260686550 - 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:keenanpepper|keenanpepper]] and made on <tt>2011-10-02 17:00:01 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>260686550</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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Moreover, it represents the 2.3.11/5.13/5 subgroup to very high accuracy, and 2.3.7/5.11/5.13/5 to a lesser but still good accuracy, and so can be used with this subgroup, which is liberally supplied with chords such as the 1-11/7-13/7 (7:11:13) chord, the [[The Archipelago|barbados triad]] 1-13/10-3/2 (10:13:15), the minor barbados triad 1-15/13-3/2, the 1-14/11-3/2 (22:28:33) triad, the 1-13/11-3/2 triad (22:26:33), and the [[petrmic triad]], a 13-limit [[Dyadic chord|essentially tempered dyadic chord]]. 29 tempers out 352/351, 676/675 and 4000/3993 from the 2.3.11/5.13/5 subgroup, and in addition 196/195 and 364/363 from the 2.3.7/5.11/5.13/5 subgroup, so we have various relationships from the tempering, such as the fact that the 1-13/11-3/2 chord and the 1-14/11-3/2 chord are inverses of each other, a major-minor pairing. A larger subgroup containing both of these subgroups is the [[k*N subgroups|3*29 subgroup]] 2.3.125.175.275.325; on this subgroup 29 tunes the same as 87, and the commas of 29 on this subgroup are the same as the 13-limit commas of 87. Still another subgroup of interest is the [[k*N subgroups|2*29 subgroup]] 2.3.25.35.55.65.85; on this subgroup 29 tunes the same as 58 and has the same 17-limit commas. | Moreover, it represents the 2.3.11/5.13/5 subgroup to very high accuracy, and 2.3.7/5.11/5.13/5 to a lesser but still good accuracy, and so can be used with this subgroup, which is liberally supplied with chords such as the 1-11/7-13/7 (7:11:13) chord, the [[The Archipelago|barbados triad]] 1-13/10-3/2 (10:13:15), the minor barbados triad 1-15/13-3/2, the 1-14/11-3/2 (22:28:33) triad, the 1-13/11-3/2 triad (22:26:33), and the [[petrmic triad]], a 13-limit [[Dyadic chord|essentially tempered dyadic chord]]. 29 tempers out 352/351, 676/675 and 4000/3993 from the 2.3.11/5.13/5 subgroup, and in addition 196/195 and 364/363 from the 2.3.7/5.11/5.13/5 subgroup, so we have various relationships from the tempering, such as the fact that the 1-13/11-3/2 chord and the 1-14/11-3/2 chord are inverses of each other, a major-minor pairing. A larger subgroup containing both of these subgroups is the [[k*N subgroups|3*29 subgroup]] 2.3.125.175.275.325; on this subgroup 29 tunes the same as 87, and the commas of 29 on this subgroup are the same as the 13-limit commas of 87. Still another subgroup of interest is the [[k*N subgroups|2*29 subgroup]] 2.3.25.35.55.65.85; on this subgroup 29 tunes the same as 58 and has the same 17-limit commas. | ||
=Intervals= | =Intervals and linear temperaments= | ||
|| Degrees of 29-EDO || Cents value || | ||~ Degrees of 29-EDO ||~ Cents value ||~ Generator for temperaments || | ||
|| 0 || 0 || | || 0 || 0 || || | ||
|| 1 || 41.379 || | || 1 || 41.379 || || | ||
|| 2 || 82.759 || | || 2 || 82.759 || [[Nautilus]] || | ||
|| 3 || 124.138 || | || 3 || 124.138 || [[Negri]]/[[Negril]] || | ||
|| 4 || 165.517 || | || 4 || 165.517 || [[Porcupine]]/[[Porky]]/[[Coendou]] || | ||
|| 5 || 206.897 || | || 5 || 206.897 || || | ||
|| 6 || 248.276 || | || 6 || 248.276 || [[Immunity]] || | ||
|| 7· || 289.655 || | || 7· || 289.655 || || | ||
|| 8 || 331.034 || | || 8 || 331.034 || || | ||
|| 9 || 372.414 || | || 9 || 372.414 || || | ||
|| 10 || 413.793 || | || 10 || 413.793 || [[Roman]] || | ||
|| 11 || 455.172 || | || 11 || 455.172 || [[Ammonite]] || | ||
|| 12· || 496.552 || | || 12· || 496.552 || [[Helmholtz]]/[[Garibaldi]]/[[Cassandra]]/[[Leapday]] || | ||
|| 13 || 537.931 || | || 13 || 537.931 || || | ||
|| 14 || 579.310 || | || 14 || 579.310 || [[Tritonic]] || | ||
|| 15 || 620.690 || | || 15 || 620.690 || || | ||
|| 16 || 662.069 || | || 16 || 662.069 || || | ||
|| 17· || 703.448 || | || 17· || 703.448 || || | ||
|| 18 || 744.828 || | || 18 || 744.828 || || | ||
|| 19 || 786.207 || | || 19 || 786.207 || || | ||
|| 20 || 827.586 || | || 20 || 827.586 || || | ||
|| 21 || 868.966 || | || 21 || 868.966 || || | ||
|| 22· || 910.345 || | || 22· || 910.345 || || | ||
|| 23 || 951.724 || | || 23 || 951.724 || || | ||
|| 24 || 993.103 || | || 24 || 993.103 || || | ||
|| 25 || 1034.483 || | || 25 || 1034.483 || || | ||
|| 26 || 1075.862 || | || 26 || 1075.862 || || | ||
|| 27 || 1117.241 || | || 27 || 1117.241 || || | ||
|| 28 || 1158.621 || | || 28 || 1158.621 || || | ||
=Commas= | =Commas= | ||
| Line 84: | Line 84: | ||
[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/Paint%20in%20the%20Water%2029.mp3|Paint in the Water 29]] by [[Igliashon Jones]]</pre></div> | [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/Paint%20in%20the%20Water%2029.mp3|Paint in the Water 29]] by [[Igliashon Jones]]</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>29edo</title></head><body><!-- ws:start:WikiTextTocRule:10:&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:10 --><!-- ws:start:WikiTextTocRule:11: --><a href="#x29 tone equal temperament">29 tone equal temperament</a><!-- ws:end:WikiTextTocRule:11 --><!-- ws:start:WikiTextTocRule:12: --> | <a href="#Intervals">Intervals</a><!-- ws:end:WikiTextTocRule:12 --><!-- ws:start:WikiTextTocRule:13: --> | <a href="#Commas">Commas</a><!-- ws:end:WikiTextTocRule:13 --><!-- ws:start:WikiTextTocRule:14: --> | <a href="#Scales">Scales</a><!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --> | <a href="#Music">Music</a><!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --> | <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>29edo</title></head><body><!-- ws:start:WikiTextTocRule:10:&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:10 --><!-- ws:start:WikiTextTocRule:11: --><a href="#x29 tone equal temperament">29 tone equal temperament</a><!-- ws:end:WikiTextTocRule:11 --><!-- ws:start:WikiTextTocRule:12: --> | <a href="#Intervals and linear temperaments">Intervals and linear temperaments</a><!-- ws:end:WikiTextTocRule:12 --><!-- ws:start:WikiTextTocRule:13: --> | <a href="#Commas">Commas</a><!-- ws:end:WikiTextTocRule:13 --><!-- ws:start:WikiTextTocRule:14: --> | <a href="#Scales">Scales</a><!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --> | <a href="#Music">Music</a><!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --> | ||
<!-- ws:end:WikiTextTocRule:16 --><hr /> | <!-- ws:end:WikiTextTocRule:16 --><hr /> | ||
<br /> | <br /> | ||
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Moreover, it represents the 2.3.11/5.13/5 subgroup to very high accuracy, and 2.3.7/5.11/5.13/5 to a lesser but still good accuracy, and so can be used with this subgroup, which is liberally supplied with chords such as the 1-11/7-13/7 (7:11:13) chord, the <a class="wiki_link" href="/The%20Archipelago">barbados triad</a> 1-13/10-3/2 (10:13:15), the minor barbados triad 1-15/13-3/2, the 1-14/11-3/2 (22:28:33) triad, the 1-13/11-3/2 triad (22:26:33), and the <a class="wiki_link" href="/petrmic%20triad">petrmic triad</a>, a 13-limit <a class="wiki_link" href="/Dyadic%20chord">essentially tempered dyadic chord</a>. 29 tempers out 352/351, 676/675 and 4000/3993 from the 2.3.11/5.13/5 subgroup, and in addition 196/195 and 364/363 from the 2.3.7/5.11/5.13/5 subgroup, so we have various relationships from the tempering, such as the fact that the 1-13/11-3/2 chord and the 1-14/11-3/2 chord are inverses of each other, a major-minor pairing. A larger subgroup containing both of these subgroups is the <a class="wiki_link" href="/k%2AN%20subgroups">3*29 subgroup</a> 2.3.125.175.275.325; on this subgroup 29 tunes the same as 87, and the commas of 29 on this subgroup are the same as the 13-limit commas of 87. Still another subgroup of interest is the <a class="wiki_link" href="/k%2AN%20subgroups">2*29 subgroup</a> 2.3.25.35.55.65.85; on this subgroup 29 tunes the same as 58 and has the same 17-limit commas.<br /> | Moreover, it represents the 2.3.11/5.13/5 subgroup to very high accuracy, and 2.3.7/5.11/5.13/5 to a lesser but still good accuracy, and so can be used with this subgroup, which is liberally supplied with chords such as the 1-11/7-13/7 (7:11:13) chord, the <a class="wiki_link" href="/The%20Archipelago">barbados triad</a> 1-13/10-3/2 (10:13:15), the minor barbados triad 1-15/13-3/2, the 1-14/11-3/2 (22:28:33) triad, the 1-13/11-3/2 triad (22:26:33), and the <a class="wiki_link" href="/petrmic%20triad">petrmic triad</a>, a 13-limit <a class="wiki_link" href="/Dyadic%20chord">essentially tempered dyadic chord</a>. 29 tempers out 352/351, 676/675 and 4000/3993 from the 2.3.11/5.13/5 subgroup, and in addition 196/195 and 364/363 from the 2.3.7/5.11/5.13/5 subgroup, so we have various relationships from the tempering, such as the fact that the 1-13/11-3/2 chord and the 1-14/11-3/2 chord are inverses of each other, a major-minor pairing. A larger subgroup containing both of these subgroups is the <a class="wiki_link" href="/k%2AN%20subgroups">3*29 subgroup</a> 2.3.125.175.275.325; on this subgroup 29 tunes the same as 87, and the commas of 29 on this subgroup are the same as the 13-limit commas of 87. Still another subgroup of interest is the <a class="wiki_link" href="/k%2AN%20subgroups">2*29 subgroup</a> 2.3.25.35.55.65.85; on this subgroup 29 tunes the same as 58 and has the same 17-limit commas.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 -->Intervals</h1> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Intervals and linear temperaments"></a><!-- ws:end:WikiTextHeadingRule:2 -->Intervals and linear temperaments</h1> | ||
<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
< | <th>Degrees of 29-EDO<br /> | ||
</ | </th> | ||
< | <th>Cents value<br /> | ||
</ | </th> | ||
<th>Generator for temperaments<br /> | |||
</th> | |||
</tr> | </tr> | ||
<tr> | <tr> | ||
| Line 113: | Line 115: | ||
</td> | </td> | ||
<td>0<br /> | <td>0<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 119: | Line 123: | ||
</td> | </td> | ||
<td>41.379<br /> | <td>41.379<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 125: | Line 131: | ||
</td> | </td> | ||
<td>82.759<br /> | <td>82.759<br /> | ||
</td> | |||
<td><a class="wiki_link" href="/Nautilus">Nautilus</a><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 131: | Line 139: | ||
</td> | </td> | ||
<td>124.138<br /> | <td>124.138<br /> | ||
</td> | |||
<td><a class="wiki_link" href="/Negri">Negri</a>/<a class="wiki_link" href="/Negril">Negril</a><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 137: | Line 147: | ||
</td> | </td> | ||
<td>165.517<br /> | <td>165.517<br /> | ||
</td> | |||
<td><a class="wiki_link" href="/Porcupine">Porcupine</a>/<a class="wiki_link" href="/Porky">Porky</a>/<a class="wiki_link" href="/Coendou">Coendou</a><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 143: | Line 155: | ||
</td> | </td> | ||
<td>206.897<br /> | <td>206.897<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 149: | Line 163: | ||
</td> | </td> | ||
<td>248.276<br /> | <td>248.276<br /> | ||
</td> | |||
<td><a class="wiki_link" href="/Immunity">Immunity</a><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 155: | Line 171: | ||
</td> | </td> | ||
<td>289.655<br /> | <td>289.655<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 161: | Line 179: | ||
</td> | </td> | ||
<td>331.034<br /> | <td>331.034<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 167: | Line 187: | ||
</td> | </td> | ||
<td>372.414<br /> | <td>372.414<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 173: | Line 195: | ||
</td> | </td> | ||
<td>413.793<br /> | <td>413.793<br /> | ||
</td> | |||
<td><a class="wiki_link" href="/Roman">Roman</a><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 179: | Line 203: | ||
</td> | </td> | ||
<td>455.172<br /> | <td>455.172<br /> | ||
</td> | |||
<td><a class="wiki_link" href="/Ammonite">Ammonite</a><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 185: | Line 211: | ||
</td> | </td> | ||
<td>496.552<br /> | <td>496.552<br /> | ||
</td> | |||
<td><a class="wiki_link" href="/Helmholtz">Helmholtz</a>/<a class="wiki_link" href="/Garibaldi">Garibaldi</a>/<a class="wiki_link" href="/Cassandra">Cassandra</a>/<a class="wiki_link" href="/Leapday">Leapday</a><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 191: | Line 219: | ||
</td> | </td> | ||
<td>537.931<br /> | <td>537.931<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 197: | Line 227: | ||
</td> | </td> | ||
<td>579.310<br /> | <td>579.310<br /> | ||
</td> | |||
<td><a class="wiki_link" href="/Tritonic">Tritonic</a><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 203: | Line 235: | ||
</td> | </td> | ||
<td>620.690<br /> | <td>620.690<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 209: | Line 243: | ||
</td> | </td> | ||
<td>662.069<br /> | <td>662.069<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 215: | Line 251: | ||
</td> | </td> | ||
<td>703.448<br /> | <td>703.448<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 221: | Line 259: | ||
</td> | </td> | ||
<td>744.828<br /> | <td>744.828<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 227: | Line 267: | ||
</td> | </td> | ||
<td>786.207<br /> | <td>786.207<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 233: | Line 275: | ||
</td> | </td> | ||
<td>827.586<br /> | <td>827.586<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 239: | Line 283: | ||
</td> | </td> | ||
<td>868.966<br /> | <td>868.966<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 245: | Line 291: | ||
</td> | </td> | ||
<td>910.345<br /> | <td>910.345<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 251: | Line 299: | ||
</td> | </td> | ||
<td>951.724<br /> | <td>951.724<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 257: | Line 307: | ||
</td> | </td> | ||
<td>993.103<br /> | <td>993.103<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 263: | Line 315: | ||
</td> | </td> | ||
<td>1034.483<br /> | <td>1034.483<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 269: | Line 323: | ||
</td> | </td> | ||
<td>1075.862<br /> | <td>1075.862<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 275: | Line 331: | ||
</td> | </td> | ||
<td>1117.241<br /> | <td>1117.241<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 281: | Line 339: | ||
</td> | </td> | ||
<td>1158.621<br /> | <td>1158.621<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||