Swetismic chords: Difference between revisions
Wikispaces>genewardsmith **Imported revision 403175376 - Original comment: ** |
Wikispaces>Andrew_Heathwaite **Imported revision 490838432 - 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:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2014-02-20 16:03:18 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>490838432</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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">A //swetismic chord// is a swetismic (540/539) 11-odd-limit [[dyadic chord|essentially tempered chord]]. | <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">A //swetismic chord// is a swetismic (540/539) 11-odd-limit [[dyadic chord|essentially tempered chord]]. | ||
There are six swetismic triads, consisting of three pairs of chords in inverse relationship: 1-7/5-12/7 with steps 7/5-11/9-7/6 and 1-7/6-10/7 with steps 7/6-11/9-7/5; 1-7/6-9/7 with steps 7/6-11/10-14/9 and 1-14/9-12/7 with steps 14/9-11/10-7/6; and 1-9/7-7/5 with steps 9/7-12/11-10/7 and 1-10/7-14/9 with steps 10/7-12/11-9/7. | There are six swetismic triads, consisting of three pairs of chords in inverse relationship: | ||
* 1-7/5-12/7 with steps 7/5-11/9-7/6 and 1-7/6-10/7 with steps 7/6-11/9-7/5; | |||
* 1-7/6-9/7 with steps 7/6-11/10-14/9 and 1-14/9-12/7 with steps 14/9-11/10-7/6; | |||
* and 1-9/7-7/5 with steps 9/7-12/11-10/7 and 1-10/7-14/9 with steps 10/7-12/11-9/7. | |||
There are fifteen swetismic tetrads, consisting of three palindromic (self-inverse) chords and six pairs of chords in inverse relationship. | There are fifteen swetismic tetrads, consisting of three palindromic (self-inverse) chords and six pairs of chords in inverse relationship. The palindromic tetrads are: | ||
* 1-7/6-9/7-3/2 with steps 7/6-11/10-7/6-4/3; | |||
* 1-6/5-7/5-12/7 with steps 6/5-7/6-11/9-7/6; | |||
* and 1-9/7-7/5-9/5 with steps 9/7-12/11-9/7-10/9. | |||
The six pairs are: | |||
* 1-9/7-3/2-11/6 with steps 9/7-7/6-11/9-12/11 and 1-7/6-3/2-18/11 with steps 7/6-9/7-12/11-11/9; | |||
* 1-7/6-9/7-10/7 with steps 7/6-11/10-10/9-7/5 and 1-7/5-14/9-12/7 with steps 7/5-10/9-11/10-7/6; | |||
* 1-7/6-9/7-18/11 with steps 7/6-11/10-14/11-11/9 and 1-14/11-7/5-18/11 with steps 14/11-11/10-7/6-11/9; | |||
* 1-7/6-10/7-11/6 with steps 7/6-11/9-9/7-12/11 and 1-9/7-11/7-11/6 with steps 9/7-11/9-7/6-12/11; | |||
* 1-7/6-9/7-11/6 with steps 7/6-11/10-10/7-12/11 and 1-10/7-11/7-11/6 with steps 10/7-11/10-7/6-12/11; | |||
* and 1-10/7-14/9-12/7 with steps 10/7-12/11-11/10-7/6 and 1-7/6-9/7-7/5 with steps 7/6-11/10-12/11-10/7. | |||
Finally, there are six swetismic pentads coming in three pairs: 1-7/6-9/7-3/2-11/6 with steps 7/6-11/10-7/6-11/9-12/11 and 1-7/6-9/7-3/2-18/11 with steps 7/6-11/10-7/6-12/11-11/9; 1-7/6-10/7-5/3-11/6 with steps 7/6-11/9-7/6-11/10-12/11 and 1-7/6-10/7-5/3-20/11 with steps 7/6-11/9-7/6-12/11-11/10; and 1-7/6-9/7-10/7-11/6 with steps 7/6-11/10-10/9-9/7-12/11 and 1-9/7-10/7-11/7-11/6 with steps 9/7-10/9-11/10-7/6-12/11. | Finally, there are six swetismic pentads coming in three pairs: | ||
* 1-7/6-9/7-3/2-11/6 with steps 7/6-11/10-7/6-11/9-12/11 and 1-7/6-9/7-3/2-18/11 with steps 7/6-11/10-7/6-12/11-11/9; | |||
* 1-7/6-10/7-5/3-11/6 with steps 7/6-11/9-7/6-11/10-12/11 and 1-7/6-10/7-5/3-20/11 with steps 7/6-11/9-7/6-12/11-11/10; | |||
* and 1-7/6-9/7-10/7-11/6 with steps 7/6-11/10-10/9-9/7-12/11 and 1-9/7-10/7-11/7-11/6 with steps 9/7-10/9-11/10-7/6-12/11. | |||
The 11 limit swetismic chords number triads: 6, tetrads: 15, pentads: 6 for a total of 27. | The 11 limit swetismic chords number triads: 6, tetrads: 15, pentads: 6 for a total of 27. | ||
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Equal temperaments with swetismic chords include 19, 22, 31, 41, 53, 58, 72, 80, 94, 103, 111, 121, 130, 152, 183, 205, 224, 354, 537, 578, 761d, 1115de, 1339de, 1491de, 1715de and 1845de.</pre></div> | Equal temperaments with swetismic chords include 19, 22, 31, 41, 53, 58, 72, 80, 94, 103, 111, 121, 130, 152, 183, 205, 224, 354, 537, 578, 761d, 1115de, 1339de, 1491de, 1715de and 1845de.</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>swetismic chords</title></head><body>A <em>swetismic chord</em> is a swetismic (540/539) 11-odd-limit <a class="wiki_link" href="/dyadic%20chord">essentially tempered chord</a> | <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>swetismic chords</title></head><body>A <em>swetismic chord</em> is a swetismic (540/539) 11-odd-limit <a class="wiki_link" href="/dyadic%20chord">essentially tempered chord</a>.<br /> | ||
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There are six swetismic triads, consisting of three pairs of chords in inverse relationship:<br /> | |||
<ul><li>1-7/5-12/7 with steps 7/5-11/9-7/6 and 1-7/6-10/7 with steps 7/6-11/9-7/5;</li><li>1-7/6-9/7 with steps 7/6-11/10-14/9 and 1-14/9-12/7 with steps 14/9-11/10-7/6;</li><li>and 1-9/7-7/5 with steps 9/7-12/11-10/7 and 1-10/7-14/9 with steps 10/7-12/11-9/7.</li></ul><br /> | |||
There are fifteen swetismic tetrads, consisting of three palindromic (self-inverse) chords and six pairs of chords in inverse relationship. The palindromic tetrads are:<br /> | |||
<ul><li>1-7/6-9/7-3/2 with steps 7/6-11/10-7/6-4/3;</li><li>1-6/5-7/5-12/7 with steps 6/5-7/6-11/9-7/6;</li><li>and 1-9/7-7/5-9/5 with steps 9/7-12/11-9/7-10/9.</li></ul>The six pairs are:<br /> | |||
<ul><li>1-9/7-3/2-11/6 with steps 9/7-7/6-11/9-12/11 and 1-7/6-3/2-18/11 with steps 7/6-9/7-12/11-11/9;</li><li>1-7/6-9/7-10/7 with steps 7/6-11/10-10/9-7/5 and 1-7/5-14/9-12/7 with steps 7/5-10/9-11/10-7/6;</li><li>1-7/6-9/7-18/11 with steps 7/6-11/10-14/11-11/9 and 1-14/11-7/5-18/11 with steps 14/11-11/10-7/6-11/9;</li><li>1-7/6-10/7-11/6 with steps 7/6-11/9-9/7-12/11 and 1-9/7-11/7-11/6 with steps 9/7-11/9-7/6-12/11;</li><li>1-7/6-9/7-11/6 with steps 7/6-11/10-10/7-12/11 and 1-10/7-11/7-11/6 with steps 10/7-11/10-7/6-12/11;</li><li>and 1-10/7-14/9-12/7 with steps 10/7-12/11-11/10-7/6 and 1-7/6-9/7-7/5 with steps 7/6-11/10-12/11-10/7.</li></ul><br /> | |||
Finally, there are six swetismic pentads coming in three pairs:<br /> | |||
<ul><li>1-7/6-9/7-3/2-11/6 with steps 7/6-11/10-7/6-11/9-12/11 and 1-7/6-9/7-3/2-18/11 with steps 7/6-11/10-7/6-12/11-11/9;</li><li>1-7/6-10/7-5/3-11/6 with steps 7/6-11/9-7/6-11/10-12/11 and 1-7/6-10/7-5/3-20/11 with steps 7/6-11/9-7/6-12/11-11/10;</li><li>and 1-7/6-9/7-10/7-11/6 with steps 7/6-11/10-10/9-9/7-12/11 and 1-9/7-10/7-11/7-11/6 with steps 9/7-10/9-11/10-7/6-12/11.</li></ul><br /> | |||
The 11 limit swetismic chords number triads: 6, tetrads: 15, pentads: 6 for a total of 27.<br /> | The 11 limit swetismic chords number triads: 6, tetrads: 15, pentads: 6 for a total of 27.<br /> | ||
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