Tablet: Difference between revisions
Wikispaces>genewardsmith **Imported revision 255453394 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 256942162 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<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>2011-09- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-09-22 07:22:52 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>256942162</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> | ||
| Line 143: | Line 143: | ||
=The tutone tutonic tablet= | =The 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. | |||
If the tablet is the ordered pair [n, c] and if u = n-19c, then if i = u mod 6, define note(n, c) = |(u-i)/6-3i 2c+2i>. This gives a 3-limit interval which tempers to a note of tutone satisfying the identity <12 19|note(n, c)> = 2n. We can also express this in terms of a subgroup monzo as <6 19|note(n, c)| = n, where note(n, c) in subgroup monzo terms is |(u-i)/6-3i c+i>.</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: | <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:16:&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:16 --><!-- ws:start:WikiTextTocRule:17: --><a href="#What is a tablet?">What is a tablet?</a><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --> | <a href="#The 5-limit 3et tablet">The 5-limit 3et tablet</a><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --> | <a href="#The 7-limit 4et tablet">The 7-limit 4et tablet</a><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --> | <a href="#The 7-limit 5et tablet">The 7-limit 5et tablet</a><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --> | <a href="#The 13-limit 7et tablet">The 13-limit 7et tablet</a><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --> | <a href="#The meantone add6/9 tablet">The meantone add6/9 tablet</a><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --> | <a href="#The tutone tutonic tablet">The tutone tutonic tablet</a><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --> | <a href="#x2n. We can also express this in terms of a subgroup monzo as"> 2n. We can also express this in terms of a subgroup monzo as &lt;6 19|note(n, c)| </a><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:25 --><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> | ||
By a <em>tablet</em> (the name by analogy with tablature) is meant a pair [n, c] consisting of an approximate note-number n (an integer) and a chord denoting element c, typically a <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Tuple" rel="nofollow">tuple</a> of integers, which defines a type of chord up to octave equivalence. Together they define a note in a just intonation group or regular temperament. The representation of the note is non-unique, as for any note there will be a variety of tablets for it depending on the specified type of chord and chord element, but by means of a val or val-like mapping, the number n in the tablet is definable from the note.<br /> | By a <em>tablet</em> (the name by analogy with tablature) is meant a pair [n, c] consisting of an approximate note-number n (an integer) and a chord denoting element c, typically a <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Tuple" rel="nofollow">tuple</a> of integers, which defines a type of chord up to octave equivalence. Together they define a note in a just intonation group or regular temperament. The representation of the note is non-unique, as for any note there will be a variety of tablets for it depending on the specified type of chord and chord element, but by means of a val or val-like mapping, the number n in the tablet is definable from the note.<br /> | ||
| Line 250: | Line 250: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="The tutone tutonic tablet"></a><!-- ws:end:WikiTextHeadingRule:12 -->The tutone tutonic tablet</h1> | <!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="The tutone tutonic tablet"></a><!-- ws:end:WikiTextHeadingRule:12 -->The tutone tutonic tablet</h1> | ||
</body></html></pre></div> | 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 /> | |||
If the tablet is the ordered pair [n, c] and if u = n-19c, then if i = u mod 6, define note(n, c) = |(u-i)/6-3i 2c+2i&gt;. This gives a 3-limit interval which tempers to a note of tutone satisfying the identity &lt;12 19|note(n, c)&gt; <!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc7"><a name="x2n. We can also express this in terms of a subgroup monzo as"></a><!-- ws:end:WikiTextHeadingRule:14 --> 2n. We can also express this in terms of a subgroup monzo as &lt;6 19|note(n, c)| </h1> | |||
n, where note(n, c) in subgroup monzo terms is |(u-i)/6-3i c+i&gt;.</body></html></pre></div> | |||