Tablet: Difference between revisions
Wikispaces>genewardsmith **Imported revision 262894236 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 262968596 - 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>2011-10- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-10-09 10:53:22 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>262968596</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">[[toc | <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">[[toc]] | ||
=What is a tablet?= | =What is a tablet?= | ||
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Once again, <5 8 12 14 17|note(n, c) = c. | Once again, <5 8 12 14 17|note(n, c) = c. | ||
The selection of these particular representatives for each of the twelve types of chords is based on each of them having a common triad--three common notes--in common with the utonal pentad, the first chord in the chords list. | The selection of these particular representatives for each of the twelve types of chords is based on each of them having a common triad--three common notes--in common with the utonal pentad, the first chord in the chords list. The chord representatives do not need to be given in terms of a 2.5.7 subgroup transversal, and a more perspicuous way of expressing the same portent temperament pentads is | ||
* JI pentads | |||
1-9/8-5/4-3/2-7/4 | |||
1-9/8-9/7-3/2-9/5 | |||
1-9/8-11/8-3/2-7/4 | |||
1-9/8-9/7-3/2-18/11 | |||
* Keenanismic (385/384 essentially tempered) pentads | |||
1-6/5-11/8-3/2-7/4 | |||
1-12/11-5/4-3/2-12/7 | |||
1-12/11-5/4-16/11-7/4 | |||
1-12/11-5/4-3/2-7/4 | |||
* Werckismic (441/440 essentially tempered) pentads | |||
1-9/8-5/4-10/7-7/4 | |||
1-10/9-5/4-10/7-7/4 | |||
1-9/8-11/8-11/7-7/4 | |||
55/56-9/8-5/4-10/7-7/4 | |||
=The tutone tutonic tablet= | Each of the other eleven chords shares a triad with the first, otonal, pentad, and all of the chords can be related by an infinite but locally finite graph by drawing an edge between chords with a common triad. | ||
=The 6et tutone tutonic tablet= | |||
This tablet is based on the [[tutonic sextad]], which in terms of the 99/98 (Huygens) version of 11-limit meantone consists of a chain of five tones, followed by an augmented second; in other words a {81/80, 126/125, 99/98}-tempered version of 9/9-9/8-9/8-9/8-9/8-8/7, which in terms of notes rather than steps is a tempered 1-9/8-5/4-7/5-11/7-7/4. Using this chord as the basis for harmony puts one in [[Chromatic pairs#Tutone|tutone temperament]], a 2.9.7.11 subgroup temperament, and the sextad can be called Tutone[6], the tutone haplotonic scale. | This tablet is based on the [[tutonic sextad]], which in terms of the 99/98 (Huygens) version of 11-limit meantone consists of a chain of five tones, followed by an augmented second; in other words a {81/80, 126/125, 99/98}-tempered version of 9/9-9/8-9/8-9/8-9/8-8/7, which in terms of notes rather than steps is a tempered 1-9/8-5/4-7/5-11/7-7/4. Using this chord as the basis for harmony puts one in [[Chromatic pairs#Tutone|tutone temperament]], a 2.9.7.11 subgroup temperament, and the sextad can be called Tutone[6], the tutone haplotonic scale. | ||
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</pre></div> | </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>Tablets</title></head><body><!-- ws:start:WikiTextTocRule:24:&lt;img id=&quot;wikitext@@toc@@ | <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>Tablets</title></head><body><!-- ws:start:WikiTextTocRule:24:&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:24 --><!-- ws:start:WikiTextTocRule:25: --><div style="margin-left: 1em;"><a href="#What is a tablet?">What is a tablet?</a></div> | ||
<!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --><div style="margin-left: 1em;"><a href="#The 5-limit 3et tablet">The 5-limit 3et tablet</a></div> | |||
<!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --><div style="margin-left: 1em;"><a href="#x4et tablets">4et tablets</a></div> | |||
<!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --><div style="margin-left: 2em;"><a href="#x4et tablets-The 7-limit 4et tablet">The 7-limit 4et tablet</a></div> | |||
<!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --><div style="margin-left: 2em;"><a href="#x4et tablets-The keenanismic tablet">The keenanismic tablet</a></div> | |||
<!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --><div style="margin-left: 1em;"><a href="#x5et tablets">5et tablets</a></div> | |||
<!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --><div style="margin-left: 2em;"><a href="#x5et tablets-The 7-limit 5et tablet">The 7-limit 5et tablet</a></div> | |||
<!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --><div style="margin-left: 2em;"><a href="#x5et tablets-The meantone add6/9 tablet">The meantone add6/9 tablet</a></div> | |||
<!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --><div style="margin-left: 2em;"><a href="#x5et tablets-The 5et portent tablet">The 5et portent tablet</a></div> | |||
<!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --><div style="margin-left: 1em;"><a href="#The 6et tutone tutonic tablet">The 6et tutone tutonic tablet</a></div> | |||
<!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --><div style="margin-left: 1em;"><a href="#The 13-limit 7et tablet">The 13-limit 7et tablet</a></div> | |||
<!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --><div style="margin-left: 1em;"><a href="#The orwell nonad tablet">The orwell nonad tablet</a></div> | |||
<!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --></div> | |||
<!-- ws:end:WikiTextTocRule:37 --><br /> | <!-- ws:end:WikiTextTocRule:37 --><br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="What is a tablet?"></a><!-- ws:end:WikiTextHeadingRule:0 -->What is a tablet?</h1> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="What is a tablet?"></a><!-- ws:end:WikiTextHeadingRule:0 -->What is a tablet?</h1> | ||
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Once again, &lt;5 8 12 14 17|note(n, c) = c.<br /> | Once again, &lt;5 8 12 14 17|note(n, c) = c.<br /> | ||
<br /> | <br /> | ||
The selection of these particular representatives for each of the twelve types of chords is based on each of them having a common triad--three common notes--in common with the utonal pentad, the first chord in the chords list.<br /> | The selection of these particular representatives for each of the twelve types of chords is based on each of them having a common triad--three common notes--in common with the utonal pentad, the first chord in the chords list. The chord representatives do not need to be given in terms of a 2.5.7 subgroup transversal, and a more perspicuous way of expressing the same portent temperament pentads is <br /> | ||
<ul><li>JI pentads</li></ul>1-9/8-5/4-3/2-7/4<br /> | |||
1-9/8-9/7-3/2-9/5<br /> | |||
1-9/8-11/8-3/2-7/4<br /> | |||
1-9/8-9/7-3/2-18/11<br /> | |||
<ul><li>Keenanismic (385/384 essentially tempered) pentads</li></ul>1-6/5-11/8-3/2-7/4<br /> | |||
1-12/11-5/4-3/2-12/7<br /> | |||
1-12/11-5/4-16/11-7/4<br /> | |||
1-12/11-5/4-3/2-7/4<br /> | |||
<ul><li>Werckismic (441/440 essentially tempered) pentads</li></ul>1-9/8-5/4-10/7-7/4<br /> | |||
1-10/9-5/4-10/7-7/4<br /> | |||
1-9/8-11/8-11/7-7/4<br /> | |||
55/56-9/8-5/4-10/7-7/4<br /> | |||
<br /> | |||
Each of the other eleven chords shares a triad with the first, otonal, pentad, and all of the chords can be related by an infinite but locally finite graph by drawing an edge between chords with a common triad.<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc9"><a name="The tutone tutonic tablet"></a><!-- ws:end:WikiTextHeadingRule:18 -->The tutone tutonic tablet</h1> | <!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc9"><a name="The 6et tutone tutonic tablet"></a><!-- ws:end:WikiTextHeadingRule:18 -->The 6et tutone tutonic tablet</h1> | ||
This tablet is based on the <a class="wiki_link" href="/tutonic%20sextad">tutonic sextad</a>, which in terms of the 99/98 (Huygens) version of 11-limit meantone consists of a chain of five tones, followed by an augmented second; in other words a {81/80, 126/125, 99/98}-tempered version of 9/9-9/8-9/8-9/8-9/8-8/7, which in terms of notes rather than steps is a tempered 1-9/8-5/4-7/5-11/7-7/4. Using this chord as the basis for harmony puts one in <a class="wiki_link" href="/Chromatic%20pairs#Tutone">tutone temperament</a>, a 2.9.7.11 subgroup temperament, and the sextad can be called Tutone[6], the tutone haplotonic scale.<br /> | This tablet is based on the <a class="wiki_link" href="/tutonic%20sextad">tutonic sextad</a>, which in terms of the 99/98 (Huygens) version of 11-limit meantone consists of a chain of five tones, followed by an augmented second; in other words a {81/80, 126/125, 99/98}-tempered version of 9/9-9/8-9/8-9/8-9/8-8/7, which in terms of notes rather than steps is a tempered 1-9/8-5/4-7/5-11/7-7/4. Using this chord as the basis for harmony puts one in <a class="wiki_link" href="/Chromatic%20pairs#Tutone">tutone temperament</a>, a 2.9.7.11 subgroup temperament, and the sextad can be called Tutone[6], the tutone haplotonic scale.<br /> | ||
<br /> | <br /> | ||