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Wikispaces>genewardsmith **Imported revision 216552748 - Original comment: ** |
Wikispaces>Osmiorisbendi **Imported revision 222452698 - 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:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2011-04-23 19:18:31 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>222452698</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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<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">=<span style="color: #007a22; display: block; font-size: 118%;">39 tone equal temperament</span>= | <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">=<span style="color: #007a22; display: block; font-size: 118%;">39 tone equal temperament</span>= | ||
If we take 22\39 as a fifth, can be used in Mavila Temperament, and from that point of view seems to have attracted the attention of the Armodue school, an Italian group interested in 16EDO, **Hornbostel Temperament** and allied systems (like a 23 and 25 EDOs [1/3-tones]; 39 and 41 EDOs [1/5-tones]; 55 and 57 EDOs [1/7-tones]; 69 and 73 EDOs [1/9-tones] & 85 and 89 EDOs [1/11-tones]). However, its 23\39 fifth, five and three-quarters cents sharp, is in much better tune than the Mavila fifth which like all Mavila fifths is very, very flat, in this case, 25 cents flat. Together with its best third which is the familiar 400 cents of 12 equal, we get a system which tempers out the diesis, 128/125, and the amity comma, 1600000/1594323. We have two choices for a map for 7, but the sharp one works better with the 3 and 5, which adds 64/63 and 126/125 to the list. Tempering out both 128/125 and 64/63 makes 39EDO in some ways allied to | If we take 22\39 as a fifth, can be used in Mavila Temperament, and from that point of view seems to have attracted the attention of the Armodue school, an Italian group interested in 16EDO, **Hornbostel Temperament** and allied systems (like a 23 and 25 EDOs [1/3-tones]; 39 and 41 EDOs [1/5-tones]; 55 and 57 EDOs [1/7-tones]; 69 and 73 EDOs [1/9-tones] & 85 and 89 EDOs [1/11-tones]). However, its 23\39 fifth, five and three-quarters cents sharp, is in much better tune than the Mavila fifth which like all Mavila fifths is very, very flat, in this case, 25 cents flat. Together with its best third which is the familiar 400 cents of 12 equal, we get a system which tempers out the diesis, 128/125, and the amity comma, 1600000/1594323. We have two choices for a map for 7, but the sharp one works better with the 3 and 5, which adds 64/63 and 126/125 to the list. Tempering out both 128/125 and 64/63 makes 39EDO in some few ways allied to 12-ET in supporting augene temperament, and is in fact an excellent choice for an augene tuning, but one difference is that 39 has a fine 11, and adding it to consideration we find that 39-EDO tempers out 99/98 and 121/120 also. This better choice for 39et is <39 62 91 110 135|. | ||
[[image:Teclado_Tricésimononafónico.PNG width="676" height="393"]] | |||
//A prototype of Armodue 1/5-tone Keyboard. Armodue-Hornbostel Family Temperaments//. | |||
**39-EDO Intervals:** | **39-EDO Intervals:** | ||
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10 10 10 9 - [[MOSScales|MOS]] of type [[3L 1s]] | 10 10 10 9 - [[MOSScales|MOS]] of type [[3L 1s]] | ||
11 3 11 11 3 - [[MOSScales|MOS]] of type [[3L 2s]] | 11 3 11 11 3 - [[MOSScales|MOS]] of type [[3L 2s]] | ||
11 3 11 3 11 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of type <span style="color: #660000; cursor: pointer;">[[3L 2s]]</span> | |||
9 6 9 9 6 - [[MOSScales|MOS]] of type [[3L 2s]] | 9 6 9 9 6 - [[MOSScales|MOS]] of type [[3L 2s]] | ||
9 6 9 6 9 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of type <span style="color: #660000; cursor: pointer;">[[3L 2s]]</span> | |||
9 9 9 9 3 - [[MOSScales|MOS]] of type [[4L 1s|4L 1s (bug)]] | 9 9 9 9 3 - [[MOSScales|MOS]] of type [[4L 1s|4L 1s (bug)]] | ||
9 3 9 9 9 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of type <span style="color: #660000; cursor: pointer;">[[4L 1s|4L 1s (bug)]]</span> | |||
8 8 8 8 7 - [[MOSScales|MOS]] of type [[4L 1s|4L 1s (bug)]] | 8 8 8 8 7 - [[MOSScales|MOS]] of type [[4L 1s|4L 1s (bug)]] | ||
10 3 10 3 10 3 - [[MOSScales|MOS]] of type [[3L 3s]] | 10 3 10 3 10 3 - [[MOSScales|MOS]] of type [[3L 3s]] | ||
| Line 75: | Line 80: | ||
8 5 8 5 8 5 - [[MOSScales|MOS]] of type [[3L 3s]] | 8 5 8 5 8 5 - [[MOSScales|MOS]] of type [[3L 3s]] | ||
7 7 7 7 7 4 - [[MOSScales|MOS]] of type [[5L 1s|5L 1s (Grumpy hexatonic)]] | 7 7 7 7 7 4 - [[MOSScales|MOS]] of type [[5L 1s|5L 1s (Grumpy hexatonic)]] | ||
7 4 7 7 7 7 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of type <span style="cursor: pointer;">[[5L 1s|5L 1s (Grumpy hexatonic)]]</span> | |||
3 9 3 9 3 9 3 - [[MOSScales|MOS]] of type [[3L 4s]] | 3 9 3 9 3 9 3 - [[MOSScales|MOS]] of type [[3L 4s]] | ||
5 5 7 5 5 5 7 - [[MOSScales|MOS]] of type [[2L 5s|2L 5s (mavila)]] | 5 5 7 5 5 5 7 - [[MOSScales|MOS]] of type [[2L 5s|2L 5s (mavila)]] | ||
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4 4 4 4 4 4 4 4 4 3 - [[MOSScales|MOS]] of type [[9L 1s|9L 1s (Grumpy decatonic)]] | 4 4 4 4 4 4 4 4 4 3 - [[MOSScales|MOS]] of type [[9L 1s|9L 1s (Grumpy decatonic)]] | ||
4 4 3 4 4 4 4 4 4 4 - [[MOSScales|MOS]] of type [[9L 1s|9L 1s (Grumpy decatonic)]] | 4 4 3 4 4 4 4 4 4 4 - [[MOSScales|MOS]] of type [[9L 1s|9L 1s (Grumpy decatonic)]] | ||
3 3 5 3 3 3 5 3 3 3 5 - [[MOSScales|MOS]] of type [[3L 8s]] | **3 3 5 3 3 3 5 3 3 3 5** - [[MOSScales|MOS]] of type [[3L 8s]] | ||
3 3 3 3 3 3 3 3 3 3 3 3 3 = [[13edo]] | 3 3 3 3 3 3 3 3 3 3 3 3 3 = [[13edo]] | ||
**3 3 3 2 3 3 3 3 2 3 3 3 3 2** - [[MOSScales|MOS]] of type [[11L 3s]] | **3 3 3 2 3 3 3 3 2 3 3 3 3 2** - [[MOSScales|MOS]] of type [[11L 3s]] | ||
3 2 3 3 2 3 2 3 3 2 3 2 3 3 2 - [[MOSScales|MOS]] of type [[9L 6s]] | 3 2 3 3 2 3 2 3 3 2 3 2 3 3 2 - [[MOSScales|MOS]] of type [[9L 6s]] | ||
3 2 3 2 3 2 2 3 2 3 2 3 2 3 2 2 - [[MOSScales|MOS]] of type [[7L 9s]] | 3 2 3 2 3 2 2 3 2 3 2 3 2 3 2 2 - [[MOSScales|MOS]] of type [[7L 9s]] | ||
2 2 3 2 2 2 3 2 2 3 2 2 3 2 2 2 3 - [[MOSScales|MOS]] of type [[5L 12s]] | **2 2 3 2 2 2 3 2 2 3 2 2 3 2 2 2 3** - [[MOSScales|MOS]] of type [[5L 12s]] | ||
2 2 2 2 2 3 2 2 2 2 2 3 2 2 2 2 2 3 - [[MOSScales|MOS]] of type [[3L 15s]] | 2 2 2 2 2 3 2 2 2 2 2 3 2 2 2 2 2 3 - [[MOSScales|MOS]] of type [[3L 15s]] | ||
**3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3** - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of type [[10L 9s]] | |||
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 - [[MOSScales|MOS]] of type [[19L 1s]] | 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 - [[MOSScales|MOS]] of type [[19L 1s]] | ||
2 2 2 1 2 2 2 1 2 2 2 1 2 2 2 2 1 2 2 2 2 1 - [[MOSScales|MOS]] of type [[17L 5s]] | 2 2 2 1 2 2 2 1 2 2 2 1 2 2 2 2 1 2 2 2 2 1 - [[MOSScales|MOS]] of type [[17L 5s]] | ||
2 2 1 2 2 1 2 2 1 2 2 1 2 2 1 2 2 2 1 2 2 2 1 - [[MOSScales|MOS]] of type [[16L 7s]] | **2 2 1 2 2 1 2 2 1 2 2 1 2 2 1 2 2 2 1 2 2 2 1** - [[MOSScales|MOS]] of type [[16L 7s]] | ||
2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 - [[MOSScales|MOS]] of type [[13L 13s]] | 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 - [[MOSScales|MOS]] of type [[13L 13s]] | ||
2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 - [[MOSScales|MOS]] of type [[10L 19s]] | **2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1** - [[MOSScales|MOS]] of type [[10L 19s]] | ||
2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 - [[MOSScales|MOS]] of type [[8L 23s]] | 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 - [[MOSScales|MOS]] of type [[8L 23s]] | ||
2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 - [[MOSScales|MOS]] of type [[6L 27s]]</pre></div> | 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 - [[MOSScales|MOS]] of type [[6L 27s]]</pre></div> | ||
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<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>39edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x39 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #007a22; display: block; font-size: 118%;">39 tone equal temperament</span></h1> | <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>39edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x39 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #007a22; display: block; font-size: 118%;">39 tone equal temperament</span></h1> | ||
<br /> | <br /> | ||
If we take 22\39 as a fifth, can be used in Mavila Temperament, and from that point of view seems to have attracted the attention of the Armodue school, an Italian group interested in 16EDO, <strong>Hornbostel Temperament</strong> and allied systems (like a 23 and 25 EDOs [1/3-tones]; 39 and 41 EDOs [1/5-tones]; 55 and 57 EDOs [1/7-tones]; 69 and 73 EDOs [1/9-tones] &amp; 85 and 89 EDOs [1/11-tones]). However, its 23\39 fifth, five and three-quarters cents sharp, is in much better tune than the Mavila fifth which like all Mavila fifths is very, very flat, in this case, 25 cents flat. Together with its best third which is the familiar 400 cents of 12 equal, we get a system which tempers out the diesis, 128/125, and the amity comma, 1600000/1594323. We have two choices for a map for 7, but the sharp one works better with the 3 and 5, which adds 64/63 and 126/125 to the list. Tempering out both 128/125 and 64/63 makes 39EDO in some ways allied to | If we take 22\39 as a fifth, can be used in Mavila Temperament, and from that point of view seems to have attracted the attention of the Armodue school, an Italian group interested in 16EDO, <strong>Hornbostel Temperament</strong> and allied systems (like a 23 and 25 EDOs [1/3-tones]; 39 and 41 EDOs [1/5-tones]; 55 and 57 EDOs [1/7-tones]; 69 and 73 EDOs [1/9-tones] &amp; 85 and 89 EDOs [1/11-tones]). However, its 23\39 fifth, five and three-quarters cents sharp, is in much better tune than the Mavila fifth which like all Mavila fifths is very, very flat, in this case, 25 cents flat. Together with its best third which is the familiar 400 cents of 12 equal, we get a system which tempers out the diesis, 128/125, and the amity comma, 1600000/1594323. We have two choices for a map for 7, but the sharp one works better with the 3 and 5, which adds 64/63 and 126/125 to the list. Tempering out both 128/125 and 64/63 makes 39EDO in some few ways allied to 12-ET in supporting augene temperament, and is in fact an excellent choice for an augene tuning, but one difference is that 39 has a fine 11, and adding it to consideration we find that 39-EDO tempers out 99/98 and 121/120 also. This better choice for 39et is &lt;39 62 91 110 135|.<br /> | ||
<br /> | |||
<!-- ws:start:WikiTextLocalImageRule:588:&lt;img src=&quot;/file/view/Teclado_Tric%C3%A9simononaf%C3%B3nico.PNG/156058129/676x393/Teclado_Tric%C3%A9simononaf%C3%B3nico.PNG&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 393px; width: 676px;&quot; /&gt; --><img src="/file/view/Teclado_Tric%C3%A9simononaf%C3%B3nico.PNG/156058129/676x393/Teclado_Tric%C3%A9simononaf%C3%B3nico.PNG" alt="Teclado_Tricésimononafónico.PNG" title="Teclado_Tricésimononafónico.PNG" style="height: 393px; width: 676px;" /><!-- ws:end:WikiTextLocalImageRule:588 --><br /> | |||
<em>A prototype of Armodue 1/5-tone Keyboard. Armodue-Hornbostel Family Temperaments</em>.<br /> | |||
<br /> | <br /> | ||
<br /> | <br /> | ||
<strong>39-EDO Intervals:</strong><br /> | <strong>39-EDO Intervals:</strong><br /> | ||
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10 10 10 9 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%201s">3L 1s</a><br /> | 10 10 10 9 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%201s">3L 1s</a><br /> | ||
11 3 11 11 3 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%202s">3L 2s</a><br /> | 11 3 11 11 3 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%202s">3L 2s</a><br /> | ||
11 3 11 3 11 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of type <span style="color: #660000; cursor: pointer;"><a class="wiki_link" href="/3L%202s">3L 2s</a></span><br /> | |||
9 6 9 9 6 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%202s">3L 2s</a><br /> | 9 6 9 9 6 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%202s">3L 2s</a><br /> | ||
9 6 9 6 9 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of type <span style="color: #660000; cursor: pointer;"><a class="wiki_link" href="/3L%202s">3L 2s</a></span><br /> | |||
9 9 9 9 3 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/4L%201s">4L 1s (bug)</a><br /> | 9 9 9 9 3 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/4L%201s">4L 1s (bug)</a><br /> | ||
9 3 9 9 9 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of type <span style="color: #660000; cursor: pointer;"><a class="wiki_link" href="/4L%201s">4L 1s (bug)</a></span><br /> | |||
8 8 8 8 7 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/4L%201s">4L 1s (bug)</a><br /> | 8 8 8 8 7 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/4L%201s">4L 1s (bug)</a><br /> | ||
10 3 10 3 10 3 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%203s">3L 3s</a><br /> | 10 3 10 3 10 3 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%203s">3L 3s</a><br /> | ||
| Line 722: | Line 733: | ||
8 5 8 5 8 5 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%203s">3L 3s</a><br /> | 8 5 8 5 8 5 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%203s">3L 3s</a><br /> | ||
7 7 7 7 7 4 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/5L%201s">5L 1s (Grumpy hexatonic)</a><br /> | 7 7 7 7 7 4 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/5L%201s">5L 1s (Grumpy hexatonic)</a><br /> | ||
7 4 7 7 7 7 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of type <span style="cursor: pointer;"><a class="wiki_link" href="/5L%201s">5L 1s (Grumpy hexatonic)</a></span><br /> | |||
3 9 3 9 3 9 3 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%204s">3L 4s</a><br /> | 3 9 3 9 3 9 3 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%204s">3L 4s</a><br /> | ||
5 5 7 5 5 5 7 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/2L%205s">2L 5s (mavila)</a><br /> | 5 5 7 5 5 5 7 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/2L%205s">2L 5s (mavila)</a><br /> | ||
| Line 735: | Line 747: | ||
4 4 4 4 4 4 4 4 4 3 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/9L%201s">9L 1s (Grumpy decatonic)</a><br /> | 4 4 4 4 4 4 4 4 4 3 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/9L%201s">9L 1s (Grumpy decatonic)</a><br /> | ||
4 4 3 4 4 4 4 4 4 4 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/9L%201s">9L 1s (Grumpy decatonic)</a><br /> | 4 4 3 4 4 4 4 4 4 4 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/9L%201s">9L 1s (Grumpy decatonic)</a><br /> | ||
3 3 5 3 3 3 5 3 3 3 5 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%208s">3L 8s</a><br /> | <strong>3 3 5 3 3 3 5 3 3 3 5</strong> - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%208s">3L 8s</a><br /> | ||
3 3 3 3 3 3 3 3 3 3 3 3 3 = <a class="wiki_link" href="/13edo">13edo</a><br /> | 3 3 3 3 3 3 3 3 3 3 3 3 3 = <a class="wiki_link" href="/13edo">13edo</a><br /> | ||
<strong>3 3 3 2 3 3 3 3 2 3 3 3 3 2</strong> - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/11L%203s">11L 3s</a><br /> | <strong>3 3 3 2 3 3 3 3 2 3 3 3 3 2</strong> - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/11L%203s">11L 3s</a><br /> | ||
3 2 3 3 2 3 2 3 3 2 3 2 3 3 2 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/9L%206s">9L 6s</a><br /> | 3 2 3 3 2 3 2 3 3 2 3 2 3 3 2 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/9L%206s">9L 6s</a><br /> | ||
3 2 3 2 3 2 2 3 2 3 2 3 2 3 2 2 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/7L%209s">7L 9s</a><br /> | 3 2 3 2 3 2 2 3 2 3 2 3 2 3 2 2 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/7L%209s">7L 9s</a><br /> | ||
2 2 3 2 2 2 3 2 2 3 2 2 3 2 2 2 3 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/5L%2012s">5L 12s</a><br /> | <strong>2 2 3 2 2 2 3 2 2 3 2 2 3 2 2 2 3</strong> - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/5L%2012s">5L 12s</a><br /> | ||
2 2 2 2 2 3 2 2 2 2 2 3 2 2 2 2 2 3 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%2015s">3L 15s</a><br /> | 2 2 2 2 2 3 2 2 2 2 2 3 2 2 2 2 2 3 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%2015s">3L 15s</a><br /> | ||
<strong>3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3</strong> - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of type <a class="wiki_link" href="/10L%209s">10L 9s</a><br /> | |||
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/19L%201s">19L 1s</a><br /> | 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/19L%201s">19L 1s</a><br /> | ||
2 2 2 1 2 2 2 1 2 2 2 1 2 2 2 2 1 2 2 2 2 1 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/17L%205s">17L 5s</a><br /> | 2 2 2 1 2 2 2 1 2 2 2 1 2 2 2 2 1 2 2 2 2 1 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/17L%205s">17L 5s</a><br /> | ||
2 2 1 2 2 1 2 2 1 2 2 1 2 2 1 2 2 2 1 2 2 2 1 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/16L%207s">16L 7s</a><br /> | <strong>2 2 1 2 2 1 2 2 1 2 2 1 2 2 1 2 2 2 1 2 2 2 1</strong> - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/16L%207s">16L 7s</a><br /> | ||
2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/13L%2013s">13L 13s</a><br /> | 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/13L%2013s">13L 13s</a><br /> | ||
2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/10L%2019s">10L 19s</a><br /> | <strong>2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1</strong> - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/10L%2019s">10L 19s</a><br /> | ||
2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/8L%2023s">8L 23s</a><br /> | 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/8L%2023s">8L 23s</a><br /> | ||
2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/6L%2027s">6L 27s</a></body></html></pre></div> | 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/6L%2027s">6L 27s</a></body></html></pre></div> | ||
Revision as of 19:18, 23 April 2011
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=<span style="color: #007a22; display: block; font-size: 118%;">39 tone equal temperament</span>= If we take 22\39 as a fifth, can be used in Mavila Temperament, and from that point of view seems to have attracted the attention of the Armodue school, an Italian group interested in 16EDO, **Hornbostel Temperament** and allied systems (like a 23 and 25 EDOs [1/3-tones]; 39 and 41 EDOs [1/5-tones]; 55 and 57 EDOs [1/7-tones]; 69 and 73 EDOs [1/9-tones] & 85 and 89 EDOs [1/11-tones]). However, its 23\39 fifth, five and three-quarters cents sharp, is in much better tune than the Mavila fifth which like all Mavila fifths is very, very flat, in this case, 25 cents flat. Together with its best third which is the familiar 400 cents of 12 equal, we get a system which tempers out the diesis, 128/125, and the amity comma, 1600000/1594323. We have two choices for a map for 7, but the sharp one works better with the 3 and 5, which adds 64/63 and 126/125 to the list. Tempering out both 128/125 and 64/63 makes 39EDO in some few ways allied to 12-ET in supporting augene temperament, and is in fact an excellent choice for an augene tuning, but one difference is that 39 has a fine 11, and adding it to consideration we find that 39-EDO tempers out 99/98 and 121/120 also. This better choice for 39et is <39 62 91 110 135|. [[image:Teclado_Tricésimononafónico.PNG width="676" height="393"]] //A prototype of Armodue 1/5-tone Keyboard. Armodue-Hornbostel Family Temperaments//. **39-EDO Intervals:** || **NOMENCLATURE** || || **|** = Semisharp **t** = Semiflat || || **DEGREE** || **NOTE** || **CENTS** || **[[Nearest just interval|Nearest Just I]]nterval** || **Cents** || **Error** || || 0 || **1** || 0 || **1/1** || 0 || **None** || || 1 || 1| || 30.7692 || 57/56 || 30.6421 || +0.1271 || || 2 || 1# || 61.5385 || 29/28 || 60.7513 || +0.7872 || || 3 || 2b || 92.3077 || 39/37 || 91.1386 || +1.1691 || || 4 || 2t || 123.0769 || 44/41 || 122.2555 || +0.8214 || || 5 || 2 || 153.8462 || 35/32 || 155.1396 || -1.2934 || || 6 || 2| || 184.6154 || 10/9 || 182.4037 || +2.2117 || || **7·** || **2#** || **215.3846** || **17/15** || **216.6867** || **-1.3021** || || 8 || 3b || 246.1538 || 15/13 || 247.7411 || -1.5873 || || 9 || 3t || 276.9231 || 27/23 || 277.5907 || -0.6676 || || 10 || 3 || 307.6923 || 43/36 || 307.6077 || +0.0846 || || 11 || 3| || 338.4615 || 17/14 || 336.1295 || +2.332 || || **12·** || **3#** || **369.2308** || **26/21** || **369.7468** || **-0.516** || || 13 || 4b || 400 || 34/27 || 399.0904 || +0.9096 || || 14 || 4t || 430.7692 || 41/32 || 429.0624 || +1.7068 || || 15 || 4 || 461.5385 || 30/23 || 459.9944 || +1.5441 || || 16 || 4| (5t) || 492.3077 || 85/64 || 491.2691 || +1.0386 || || **17·** || **5** || **523.0769** || **23/17** || **523.3189** || **-0.242** || || 18 || 5| || 553.8462 || 11/8 || 551.3179 || +2.5283 || || 19 || 5# || 584.6154 || 7/5 || 582.5122 || +2.1032 || || 20 || 6b || 615.3846 || 10/7 || 617.4878 || -2.1032 || || 21 || 6t || 646.1538 || 16/11 || 648.6821 || -2.5283 || || **22·** || **6** || **676.9231** || **34/23** || **676.6811** || **+0.242** || || 23 || 6| || 707.6923 || 128/85 || 708.7309 || -1.0386 || || 24 || 6# || 738.4615 || 23/15 || 740.0056 || -1.5441 || || 25 || 7b || 769.2308 || 64/41 || 770.9376 || -1.7068 || || 26 || 7t || 800 || 27/17 || 800.9096 || -0.9096 || || **27·** || **7** || **830.7692** || **21/13** || **830.2532** || **+0.516** || || 28 || 7| || 861.5385 || 28/17 || 863.8705 || -2.332 || || 29 || 7# (A) || 892.3077 || 72/43 || 892.3923 || -0.0846 || || 30 || 8b || 923.0769 || 46/27 || 922.4093 || +0.6676 || || 31 || 8t || 953.8462 || 26/15 || 952.2589 || +1.5873 || || **32·** || **8** || **984.6154** || **30/17** || **983.3133** || **+1.3021** || || 33 || 8| || 1015.3846 || 9/5 || 1017.5963 || -2.2117 || || 34 || 8# || 1046.1538 || 64/35 || 1044.8604 || +1.2934 || || 35 || 9b || 1076.9231 || 41/22 || 1077.7445 || -0.8214 || || 36 || 9t || 1107.6923 || 74/39 || 1108.8614 || -1.1691 || || 37 || 9 || 1138.4615 || 56/29 || 1139.2487 || -0.7872 || || 38 || 9| (1t) || 1169.2308 || 112/57 || 1169.3579 || -0.1271 || || **39··(or 0)** || **1** || **1200** || **2/1** || **1200** || **None** || **39 tone equal [[modes]]:** 15 15 9 - [[MOSScales|MOS]] of type [[2L 1s]] 14 14 11 - [[MOSScales|MOS]] of type [[2L 1s]] 13 13 13 = [[3edo]] 11 11 11 6 - [[MOSScales|MOS]] of type [[3L 1s]] 10 10 10 9 - [[MOSScales|MOS]] of type [[3L 1s]] 11 3 11 11 3 - [[MOSScales|MOS]] of type [[3L 2s]] 11 3 11 3 11 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of type <span style="color: #660000; cursor: pointer;">[[3L 2s]]</span> 9 6 9 9 6 - [[MOSScales|MOS]] of type [[3L 2s]] 9 6 9 6 9 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of type <span style="color: #660000; cursor: pointer;">[[3L 2s]]</span> 9 9 9 9 3 - [[MOSScales|MOS]] of type [[4L 1s|4L 1s (bug)]] 9 3 9 9 9 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of type <span style="color: #660000; cursor: pointer;">[[4L 1s|4L 1s (bug)]]</span> 8 8 8 8 7 - [[MOSScales|MOS]] of type [[4L 1s|4L 1s (bug)]] 10 3 10 3 10 3 - [[MOSScales|MOS]] of type [[3L 3s]] 9 4 9 4 9 4 - [[MOSScales|MOS]] of type [[3L 3s]] 8 5 8 5 8 5 - [[MOSScales|MOS]] of type [[3L 3s]] 7 7 7 7 7 4 - [[MOSScales|MOS]] of type [[5L 1s|5L 1s (Grumpy hexatonic)]] 7 4 7 7 7 7 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of type <span style="cursor: pointer;">[[5L 1s|5L 1s (Grumpy hexatonic)]]</span> 3 9 3 9 3 9 3 - [[MOSScales|MOS]] of type [[3L 4s]] 5 5 7 5 5 5 7 - [[MOSScales|MOS]] of type [[2L 5s|2L 5s (mavila)]] 5 5 5 7 5 5 7 - [[MOSScales|MOS]] of type [[2L 5s|2L 5s (mavila)]] 5 7 5 5 7 5 5 - [[MOSScales|MOS]] of type [[2L 5s|2L 5s (mavila)]] 6 3 6 6 3 6 6 3 - [[MOSScales|MOS]] of type [[5L 3s]] 5 5 5 5 5 5 5 4 - [[MOSScales|MOS]] of type [[7L 1s|7L 1s (Grumpy octatonic)]] 5 4 5 5 5 5 5 5 - [[MOSScales|MOS]] of type [[7L 1s|7L 1s (Grumpy octatonic)]] **5 5 5 2 5 5 5 5 2** - [[MOSScales|MOS]] of type [[7L 2s|7L 2s (unfair mavila)]] 5 5 2 5 5 5 2 5 5 - [[MOSScales|MOS]] of type [[7L 2s|7L 2s (unfair mavila)]] 5 5 3 5 5 3 5 5 3 - [[MOSScales|MOS]] of type [[6L 3s|6L 3s (unfair augmented)]] 5 4 4 5 4 4 5 4 4 - [[MOSScales|MOS]] of type [[3L 6s|3L 6s (fair augmented)]] 4 4 4 4 4 4 4 4 4 3 - [[MOSScales|MOS]] of type [[9L 1s|9L 1s (Grumpy decatonic)]] 4 4 3 4 4 4 4 4 4 4 - [[MOSScales|MOS]] of type [[9L 1s|9L 1s (Grumpy decatonic)]] **3 3 5 3 3 3 5 3 3 3 5** - [[MOSScales|MOS]] of type [[3L 8s]] 3 3 3 3 3 3 3 3 3 3 3 3 3 = [[13edo]] **3 3 3 2 3 3 3 3 2 3 3 3 3 2** - [[MOSScales|MOS]] of type [[11L 3s]] 3 2 3 3 2 3 2 3 3 2 3 2 3 3 2 - [[MOSScales|MOS]] of type [[9L 6s]] 3 2 3 2 3 2 2 3 2 3 2 3 2 3 2 2 - [[MOSScales|MOS]] of type [[7L 9s]] **2 2 3 2 2 2 3 2 2 3 2 2 3 2 2 2 3** - [[MOSScales|MOS]] of type [[5L 12s]] 2 2 2 2 2 3 2 2 2 2 2 3 2 2 2 2 2 3 - [[MOSScales|MOS]] of type [[3L 15s]] **3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3** - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of type [[10L 9s]] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 - [[MOSScales|MOS]] of type [[19L 1s]] 2 2 2 1 2 2 2 1 2 2 2 1 2 2 2 2 1 2 2 2 2 1 - [[MOSScales|MOS]] of type [[17L 5s]] **2 2 1 2 2 1 2 2 1 2 2 1 2 2 1 2 2 2 1 2 2 2 1** - [[MOSScales|MOS]] of type [[16L 7s]] 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 - [[MOSScales|MOS]] of type [[13L 13s]] **2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1** - [[MOSScales|MOS]] of type [[10L 19s]] 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 - [[MOSScales|MOS]] of type [[8L 23s]] 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 - [[MOSScales|MOS]] of type [[6L 27s]]
Original HTML content:
<html><head><title>39edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="x39 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #007a22; display: block; font-size: 118%;">39 tone equal temperament</span></h1>
<br />
If we take 22\39 as a fifth, can be used in Mavila Temperament, and from that point of view seems to have attracted the attention of the Armodue school, an Italian group interested in 16EDO, <strong>Hornbostel Temperament</strong> and allied systems (like a 23 and 25 EDOs [1/3-tones]; 39 and 41 EDOs [1/5-tones]; 55 and 57 EDOs [1/7-tones]; 69 and 73 EDOs [1/9-tones] & 85 and 89 EDOs [1/11-tones]). However, its 23\39 fifth, five and three-quarters cents sharp, is in much better tune than the Mavila fifth which like all Mavila fifths is very, very flat, in this case, 25 cents flat. Together with its best third which is the familiar 400 cents of 12 equal, we get a system which tempers out the diesis, 128/125, and the amity comma, 1600000/1594323. We have two choices for a map for 7, but the sharp one works better with the 3 and 5, which adds 64/63 and 126/125 to the list. Tempering out both 128/125 and 64/63 makes 39EDO in some few ways allied to 12-ET in supporting augene temperament, and is in fact an excellent choice for an augene tuning, but one difference is that 39 has a fine 11, and adding it to consideration we find that 39-EDO tempers out 99/98 and 121/120 also. This better choice for 39et is <39 62 91 110 135|.<br />
<br />
<!-- ws:start:WikiTextLocalImageRule:588:<img src="/file/view/Teclado_Tric%C3%A9simononaf%C3%B3nico.PNG/156058129/676x393/Teclado_Tric%C3%A9simononaf%C3%B3nico.PNG" alt="" title="" style="height: 393px; width: 676px;" /> --><img src="/file/view/Teclado_Tric%C3%A9simononaf%C3%B3nico.PNG/156058129/676x393/Teclado_Tric%C3%A9simononaf%C3%B3nico.PNG" alt="Teclado_Tricésimononafónico.PNG" title="Teclado_Tricésimononafónico.PNG" style="height: 393px; width: 676px;" /><!-- ws:end:WikiTextLocalImageRule:588 --><br />
<em>A prototype of Armodue 1/5-tone Keyboard. Armodue-Hornbostel Family Temperaments</em>.<br />
<br />
<br />
<strong>39-EDO Intervals:</strong><br />
<table class="wiki_table">
<tr>
<td><strong>NOMENCLATURE</strong><br />
</td>
</tr>
<tr>
<td><strong>|</strong> = Semisharp<br />
<strong>t</strong> = Semiflat<br />
</td>
</tr>
</table>
<br />
<table class="wiki_table">
<tr>
<td><strong>DEGREE</strong><br />
</td>
<td><strong>NOTE</strong><br />
</td>
<td><strong>CENTS</strong><br />
</td>
<td><strong><a class="wiki_link" href="/Nearest%20just%20interval">Nearest Just I</a>nterval</strong><br />
</td>
<td><strong>Cents</strong><br />
</td>
<td><strong>Error</strong><br />
</td>
</tr>
<tr>
<td>0<br />
</td>
<td><strong>1</strong><br />
</td>
<td>0<br />
</td>
<td><strong>1/1</strong><br />
</td>
<td>0<br />
</td>
<td><strong>None</strong><br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>1|<br />
</td>
<td>30.7692<br />
</td>
<td>57/56<br />
</td>
<td>30.6421<br />
</td>
<td>+0.1271<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>1#<br />
</td>
<td>61.5385<br />
</td>
<td>29/28<br />
</td>
<td>60.7513<br />
</td>
<td>+0.7872<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>2b<br />
</td>
<td>92.3077<br />
</td>
<td>39/37<br />
</td>
<td>91.1386<br />
</td>
<td>+1.1691<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>2t<br />
</td>
<td>123.0769<br />
</td>
<td>44/41<br />
</td>
<td>122.2555<br />
</td>
<td>+0.8214<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>2<br />
</td>
<td>153.8462<br />
</td>
<td>35/32<br />
</td>
<td>155.1396<br />
</td>
<td>-1.2934<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>2|<br />
</td>
<td>184.6154<br />
</td>
<td>10/9<br />
</td>
<td>182.4037<br />
</td>
<td>+2.2117<br />
</td>
</tr>
<tr>
<td><strong>7·</strong><br />
</td>
<td><strong>2#</strong><br />
</td>
<td><strong>215.3846</strong><br />
</td>
<td><strong>17/15</strong><br />
</td>
<td><strong>216.6867</strong><br />
</td>
<td><strong>-1.3021</strong><br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>3b<br />
</td>
<td>246.1538<br />
</td>
<td>15/13<br />
</td>
<td>247.7411<br />
</td>
<td>-1.5873<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>3t<br />
</td>
<td>276.9231<br />
</td>
<td>27/23<br />
</td>
<td>277.5907<br />
</td>
<td>-0.6676<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>3<br />
</td>
<td>307.6923<br />
</td>
<td>43/36<br />
</td>
<td>307.6077<br />
</td>
<td>+0.0846<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>3|<br />
</td>
<td>338.4615<br />
</td>
<td>17/14<br />
</td>
<td>336.1295<br />
</td>
<td>+2.332<br />
</td>
</tr>
<tr>
<td><strong>12·</strong><br />
</td>
<td><strong>3#</strong><br />
</td>
<td><strong>369.2308</strong><br />
</td>
<td><strong>26/21</strong><br />
</td>
<td><strong>369.7468</strong><br />
</td>
<td><strong>-0.516</strong><br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>4b<br />
</td>
<td>400<br />
</td>
<td>34/27<br />
</td>
<td>399.0904<br />
</td>
<td>+0.9096<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>4t<br />
</td>
<td>430.7692<br />
</td>
<td>41/32<br />
</td>
<td>429.0624<br />
</td>
<td>+1.7068<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>4<br />
</td>
<td>461.5385<br />
</td>
<td>30/23<br />
</td>
<td>459.9944<br />
</td>
<td>+1.5441<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>4| (5t)<br />
</td>
<td>492.3077<br />
</td>
<td>85/64<br />
</td>
<td>491.2691<br />
</td>
<td>+1.0386<br />
</td>
</tr>
<tr>
<td><strong>17·</strong><br />
</td>
<td><strong>5</strong><br />
</td>
<td><strong>523.0769</strong><br />
</td>
<td><strong>23/17</strong><br />
</td>
<td><strong>523.3189</strong><br />
</td>
<td><strong>-0.242</strong><br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>5|<br />
</td>
<td>553.8462<br />
</td>
<td>11/8<br />
</td>
<td>551.3179<br />
</td>
<td>+2.5283<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>5#<br />
</td>
<td>584.6154<br />
</td>
<td>7/5<br />
</td>
<td>582.5122<br />
</td>
<td>+2.1032<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>6b<br />
</td>
<td>615.3846<br />
</td>
<td>10/7<br />
</td>
<td>617.4878<br />
</td>
<td>-2.1032<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>6t<br />
</td>
<td>646.1538<br />
</td>
<td>16/11<br />
</td>
<td>648.6821<br />
</td>
<td>-2.5283<br />
</td>
</tr>
<tr>
<td><strong>22·</strong><br />
</td>
<td><strong>6</strong><br />
</td>
<td><strong>676.9231</strong><br />
</td>
<td><strong>34/23</strong><br />
</td>
<td><strong>676.6811</strong><br />
</td>
<td><strong>+0.242</strong><br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>6|<br />
</td>
<td>707.6923<br />
</td>
<td>128/85<br />
</td>
<td>708.7309<br />
</td>
<td>-1.0386<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>6#<br />
</td>
<td>738.4615<br />
</td>
<td>23/15<br />
</td>
<td>740.0056<br />
</td>
<td>-1.5441<br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>7b<br />
</td>
<td>769.2308<br />
</td>
<td>64/41<br />
</td>
<td>770.9376<br />
</td>
<td>-1.7068<br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>7t<br />
</td>
<td>800<br />
</td>
<td>27/17<br />
</td>
<td>800.9096<br />
</td>
<td>-0.9096<br />
</td>
</tr>
<tr>
<td><strong>27·</strong><br />
</td>
<td><strong>7</strong><br />
</td>
<td><strong>830.7692</strong><br />
</td>
<td><strong>21/13</strong><br />
</td>
<td><strong>830.2532</strong><br />
</td>
<td><strong>+0.516</strong><br />
</td>
</tr>
<tr>
<td>28<br />
</td>
<td>7|<br />
</td>
<td>861.5385<br />
</td>
<td>28/17<br />
</td>
<td>863.8705<br />
</td>
<td>-2.332<br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td>7# (A)<br />
</td>
<td>892.3077<br />
</td>
<td>72/43<br />
</td>
<td>892.3923<br />
</td>
<td>-0.0846<br />
</td>
</tr>
<tr>
<td>30<br />
</td>
<td>8b<br />
</td>
<td>923.0769<br />
</td>
<td>46/27<br />
</td>
<td>922.4093<br />
</td>
<td>+0.6676<br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td>8t<br />
</td>
<td>953.8462<br />
</td>
<td>26/15<br />
</td>
<td>952.2589<br />
</td>
<td>+1.5873<br />
</td>
</tr>
<tr>
<td><strong>32·</strong><br />
</td>
<td><strong>8</strong><br />
</td>
<td><strong>984.6154</strong><br />
</td>
<td><strong>30/17</strong><br />
</td>
<td><strong>983.3133</strong><br />
</td>
<td><strong>+1.3021</strong><br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td>8|<br />
</td>
<td>1015.3846<br />
</td>
<td>9/5<br />
</td>
<td>1017.5963<br />
</td>
<td>-2.2117<br />
</td>
</tr>
<tr>
<td>34<br />
</td>
<td>8#<br />
</td>
<td>1046.1538<br />
</td>
<td>64/35<br />
</td>
<td>1044.8604<br />
</td>
<td>+1.2934<br />
</td>
</tr>
<tr>
<td>35<br />
</td>
<td>9b<br />
</td>
<td>1076.9231<br />
</td>
<td>41/22<br />
</td>
<td>1077.7445<br />
</td>
<td>-0.8214<br />
</td>
</tr>
<tr>
<td>36<br />
</td>
<td>9t<br />
</td>
<td>1107.6923<br />
</td>
<td>74/39<br />
</td>
<td>1108.8614<br />
</td>
<td>-1.1691<br />
</td>
</tr>
<tr>
<td>37<br />
</td>
<td>9<br />
</td>
<td>1138.4615<br />
</td>
<td>56/29<br />
</td>
<td>1139.2487<br />
</td>
<td>-0.7872<br />
</td>
</tr>
<tr>
<td>38<br />
</td>
<td>9| (1t)<br />
</td>
<td>1169.2308<br />
</td>
<td>112/57<br />
</td>
<td>1169.3579<br />
</td>
<td>-0.1271<br />
</td>
</tr>
<tr>
<td><strong>39··(or 0)</strong><br />
</td>
<td><strong>1</strong><br />
</td>
<td><strong>1200</strong><br />
</td>
<td><strong>2/1</strong><br />
</td>
<td><strong>1200</strong><br />
</td>
<td><strong>None</strong><br />
</td>
</tr>
</table>
<br />
<br />
<strong>39 tone equal <a class="wiki_link" href="/modes">modes</a>:</strong><br />
<br />
15 15 9 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/2L%201s">2L 1s</a><br />
14 14 11 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/2L%201s">2L 1s</a><br />
13 13 13 = <a class="wiki_link" href="/3edo">3edo</a><br />
11 11 11 6 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%201s">3L 1s</a><br />
10 10 10 9 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%201s">3L 1s</a><br />
11 3 11 11 3 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%202s">3L 2s</a><br />
11 3 11 3 11 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of type <span style="color: #660000; cursor: pointer;"><a class="wiki_link" href="/3L%202s">3L 2s</a></span><br />
9 6 9 9 6 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%202s">3L 2s</a><br />
9 6 9 6 9 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of type <span style="color: #660000; cursor: pointer;"><a class="wiki_link" href="/3L%202s">3L 2s</a></span><br />
9 9 9 9 3 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/4L%201s">4L 1s (bug)</a><br />
9 3 9 9 9 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of type <span style="color: #660000; cursor: pointer;"><a class="wiki_link" href="/4L%201s">4L 1s (bug)</a></span><br />
8 8 8 8 7 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/4L%201s">4L 1s (bug)</a><br />
10 3 10 3 10 3 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%203s">3L 3s</a><br />
9 4 9 4 9 4 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%203s">3L 3s</a><br />
8 5 8 5 8 5 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%203s">3L 3s</a><br />
7 7 7 7 7 4 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/5L%201s">5L 1s (Grumpy hexatonic)</a><br />
7 4 7 7 7 7 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of type <span style="cursor: pointer;"><a class="wiki_link" href="/5L%201s">5L 1s (Grumpy hexatonic)</a></span><br />
3 9 3 9 3 9 3 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%204s">3L 4s</a><br />
5 5 7 5 5 5 7 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/2L%205s">2L 5s (mavila)</a><br />
5 5 5 7 5 5 7 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/2L%205s">2L 5s (mavila)</a><br />
5 7 5 5 7 5 5 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/2L%205s">2L 5s (mavila)</a><br />
6 3 6 6 3 6 6 3 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/5L%203s">5L 3s</a><br />
5 5 5 5 5 5 5 4 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/7L%201s">7L 1s (Grumpy octatonic)</a><br />
5 4 5 5 5 5 5 5 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/7L%201s">7L 1s (Grumpy octatonic)</a><br />
<strong>5 5 5 2 5 5 5 5 2</strong> - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/7L%202s">7L 2s (unfair mavila)</a><br />
5 5 2 5 5 5 2 5 5 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/7L%202s">7L 2s (unfair mavila)</a><br />
5 5 3 5 5 3 5 5 3 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/6L%203s">6L 3s (unfair augmented)</a><br />
5 4 4 5 4 4 5 4 4 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%206s">3L 6s (fair augmented)</a><br />
4 4 4 4 4 4 4 4 4 3 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/9L%201s">9L 1s (Grumpy decatonic)</a><br />
4 4 3 4 4 4 4 4 4 4 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/9L%201s">9L 1s (Grumpy decatonic)</a><br />
<strong>3 3 5 3 3 3 5 3 3 3 5</strong> - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%208s">3L 8s</a><br />
3 3 3 3 3 3 3 3 3 3 3 3 3 = <a class="wiki_link" href="/13edo">13edo</a><br />
<strong>3 3 3 2 3 3 3 3 2 3 3 3 3 2</strong> - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/11L%203s">11L 3s</a><br />
3 2 3 3 2 3 2 3 3 2 3 2 3 3 2 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/9L%206s">9L 6s</a><br />
3 2 3 2 3 2 2 3 2 3 2 3 2 3 2 2 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/7L%209s">7L 9s</a><br />
<strong>2 2 3 2 2 2 3 2 2 3 2 2 3 2 2 2 3</strong> - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/5L%2012s">5L 12s</a><br />
2 2 2 2 2 3 2 2 2 2 2 3 2 2 2 2 2 3 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%2015s">3L 15s</a><br />
<strong>3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3</strong> - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of type <a class="wiki_link" href="/10L%209s">10L 9s</a><br />
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/19L%201s">19L 1s</a><br />
2 2 2 1 2 2 2 1 2 2 2 1 2 2 2 2 1 2 2 2 2 1 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/17L%205s">17L 5s</a><br />
<strong>2 2 1 2 2 1 2 2 1 2 2 1 2 2 1 2 2 2 1 2 2 2 1</strong> - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/16L%207s">16L 7s</a><br />
2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/13L%2013s">13L 13s</a><br />
<strong>2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1</strong> - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/10L%2019s">10L 19s</a><br />
2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/8L%2023s">8L 23s</a><br />
2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/6L%2027s">6L 27s</a></body></html>