Just intonation subgroup: Difference between revisions
Wikispaces>genewardsmith **Imported revision 143693319 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 143694515 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-05-21 05: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-05-21 05:26:22 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>143694515</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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Ets: 5, 31, 36, 135, 571 | Ets: 5, 31, 36, 135, 571 | ||
Archytas [8/7, 32/27, 4/3, 3/2, 12/7, 16/9, 2/1] | Archytas Diatonic [8/7, 32/27, 4/3, 3/2, 12/7, 16/9, 2/1] | ||
Septimal [8/7, 9/7, 4/3, 32/21, 12/7, 16/9, 2/1] | Safi al-Din Septimal [8/7, 9/7, 4/3, 32/21, 12/7, 16/9, 2/1] | ||
[2, 5, 7] | [2, 5, 7] | ||
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Ets: 7, 15, 17, 24, 159, 494, 518, 653 | Ets: 7, 15, 17, 24, 159, 494, 518, 653 | ||
Zalzal [9/8, 27/22, 4/3, 3/2, 18/11, 16/9, 2/1] | Zalzal, al-Farabi's version [9/8, 27/22, 4/3, 3/2, 18/11, 16/9, 2/1] | ||
[2, 5, 11] | [2, 5, 11] | ||
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Ets: 9, 17, 26, 31, 41, 46, 63, 72, 135 | Ets: 9, 17, 26, 31, 41, 46, 63, 72, 135 | ||
Ptolemy [22/21, 8/7, 4/3, 3/2, 11/7, 12/7, 2/1] | Ptolemy Intense Chromatic [22/21, 8/7, 4/3, 3/2, 11/7, 12/7, 2/1] | ||
[2, 5, 7, 11] | [2, 5, 7, 11] | ||
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Ets: 7, 10, 17, 60, 70, 130, 147, 277, 424 | Ets: 7, 10, 17, 60, 70, 130, 147, 277, 424 | ||
Mustaqim [9/8, 39/32, 4/3, 3/2, 13/8, 16/9, 2/1] | Mustaqim mode, Ibn Sina [9/8, 39/32, 4/3, 3/2, 13/8, 16/9, 2/1] | ||
[2, 3, 7, 13] | [2, 3, 7, 13] | ||
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Buzurg [14/13, 16/13, 4/3, 56/39, 3/2] | Buzurg [14/13, 16/13, 4/3, 56/39, 3/2] | ||
Safi [8/7, 16/13, 4/3, 32/21, 64/39, 16/9, 2/1] | Septimal tuning, Safi al-Din [8/7, 16/13, 4/3, 32/21, 64/39, 16/9, 2/1] | ||
Ibn [14/13, 7/6, 4/3, 3/2, 21/13, 7/4, 2]</pre></div> | Septimal tuning, Ibn Sina [14/13, 7/6, 4/3, 3/2, 21/13, 7/4, 2]</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>Just intonation subgroups</title></head><body>By a just intonation subgroup is meant a <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Free_abelian_group" rel="nofollow">group</a> generated by a finite set of positive rational numbers via arbitrary multiplications and divisions. Any such group will be contained in a <a class="wiki_link" href="/Harmonic%20Limit">p-limit</a> group for some minimal choice of prime p, which is the prime limit of the subgroup. <br /> | <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>Just intonation subgroups</title></head><body>By a just intonation subgroup is meant a <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Free_abelian_group" rel="nofollow">group</a> generated by a finite set of positive rational numbers via arbitrary multiplications and divisions. Any such group will be contained in a <a class="wiki_link" href="/Harmonic%20Limit">p-limit</a> group for some minimal choice of prime p, which is the prime limit of the subgroup. <br /> | ||
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Ets: 5, 31, 36, 135, 571<br /> | Ets: 5, 31, 36, 135, 571<br /> | ||
<br /> | <br /> | ||
Archytas [8/7, 32/27, 4/3, 3/2, 12/7, 16/9, 2/1]<br /> | Archytas Diatonic [8/7, 32/27, 4/3, 3/2, 12/7, 16/9, 2/1]<br /> | ||
Septimal [8/7, 9/7, 4/3, 32/21, 12/7, 16/9, 2/1]<br /> | Safi al-Din Septimal [8/7, 9/7, 4/3, 32/21, 12/7, 16/9, 2/1]<br /> | ||
<br /> | <br /> | ||
[2, 5, 7]<br /> | [2, 5, 7]<br /> | ||
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Ets: 7, 15, 17, 24, 159, 494, 518, 653<br /> | Ets: 7, 15, 17, 24, 159, 494, 518, 653<br /> | ||
<br /> | <br /> | ||
Zalzal [9/8, 27/22, 4/3, 3/2, 18/11, 16/9, 2/1]<br /> | Zalzal, al-Farabi's version [9/8, 27/22, 4/3, 3/2, 18/11, 16/9, 2/1]<br /> | ||
<br /> | <br /> | ||
[2, 5, 11]<br /> | [2, 5, 11]<br /> | ||
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Ets: 9, 17, 26, 31, 41, 46, 63, 72, 135<br /> | Ets: 9, 17, 26, 31, 41, 46, 63, 72, 135<br /> | ||
<br /> | <br /> | ||
Ptolemy [22/21, 8/7, 4/3, 3/2, 11/7, 12/7, 2/1]<br /> | Ptolemy Intense Chromatic [22/21, 8/7, 4/3, 3/2, 11/7, 12/7, 2/1]<br /> | ||
<br /> | <br /> | ||
[2, 5, 7, 11]<br /> | [2, 5, 7, 11]<br /> | ||
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Ets: 7, 10, 17, 60, 70, 130, 147, 277, 424<br /> | Ets: 7, 10, 17, 60, 70, 130, 147, 277, 424<br /> | ||
<br /> | <br /> | ||
Mustaqim [9/8, 39/32, 4/3, 3/2, 13/8, 16/9, 2/1]<br /> | Mustaqim mode, Ibn Sina [9/8, 39/32, 4/3, 3/2, 13/8, 16/9, 2/1]<br /> | ||
<br /> | <br /> | ||
[2, 3, 7, 13]<br /> | [2, 3, 7, 13]<br /> | ||
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<br /> | <br /> | ||
Buzurg [14/13, 16/13, 4/3, 56/39, 3/2]<br /> | Buzurg [14/13, 16/13, 4/3, 56/39, 3/2]<br /> | ||
Safi [8/7, 16/13, 4/3, 32/21, 64/39, 16/9, 2/1]<br /> | Septimal tuning, Safi al-Din [8/7, 16/13, 4/3, 32/21, 64/39, 16/9, 2/1]<br /> | ||
Ibn [14/13, 7/6, 4/3, 3/2, 21/13, 7/4, 2]</body></html></pre></div> | Septimal tuning, Ibn Sina [14/13, 7/6, 4/3, 3/2, 21/13, 7/4, 2]</body></html></pre></div> | ||