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Wikispaces>genewardsmith
**Imported revision 262893656 - Original comment: **
Wikispaces>genewardsmith
**Imported revision 262894236 - 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>2011-10-08 20:58:34 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-10-08 21:02:49 UTC</tt>.<br>
: The original revision id was <tt>262893656</tt>.<br>
: The original revision id was <tt>262894236</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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Once again, if a+b+c is odd, then define note(t) as -note(-n, [-1-a -1-b -1-c]). If t = [n, w], where w is a 3-tuple, then [note([n, w)), note(n+1, w), note(n+2), w), note(n+3, w), note(n+4), w)] is a complete 9-odd-limit quintad, where &lt;5 8 12 14|note(n, t) = n.
Once again, if a+b+c is odd, then define note(t) as -note(-n, [-1-a -1-b -1-c]). If t = [n, w], where w is a 3-tuple, then [note([n, w)), note(n+1, w), note(n+2), w), note(n+3, w), note(n+4), w)] is a complete 9-odd-limit quintad, where &lt;5 8 12 14|note(n, t) = n.
==The meantone add6/9 tablet==
The meantone add6/9 tablet is based on the [[meantone add6-9 quintad|meantone add6/9 quintad]], which can also be called the add2/9 quintad, the meantone pentatonic scale or Meantone[5]. The tablet is extremly simple, consiting of an ordered pair [n, c], where we have a meantone transversal for the notes defined by u = n-8c, where
* If u mod 5 = 0 then
note(n, c) = |u/5 c&gt;
* If u mod 5 = 1 then
note(n, c) = |(u-1)/5-3 c+2&gt;
* If u mod 5 = 2 then
note(n, c) = |(u-2)/5-6 c+4&gt;
* If u mod 5 = 3 then
note(n, c) = |(u-3)/5-1 c+1&gt;
* If u mod 5 = 4 then
note(n, c) = |(u-4)/5-4 c+3&gt;
In all cases &lt;5 8|note(n, c) = n. Tempering the the Pythgorean transversal by flattening 3 gives, as usual, a meantone tuning.
==The 5et portent tablet==
This is based on the following twelve chords, which are expressed in terms of the 2.5.7 transversal of the 11-limit rank three temperament portent, which tempers out 385/384, 441/440 and hence also 1029/1024 and 3025/3024.
chords = [[1, 131072/117649, 5/4, 512/343, 7/4],
[1, 131072/117649, 1048576/823543, 512/343, 1048576/588245],
[1, 131072/117649, 16384/12005, 512/343, 7/4],
[1, 131072/117649, 1048576/823543, 512/343, 80/49],
[1, 2048/1715, 16384/12005, 512/343, 7/4],
[1, 35/32, 5/4, 512/343, 4096/2401],
[1, 35/32, 5/4, 12005/8192, 7/4],
[1, 35/32, 5/4, 512/343, 7/4],
[1, 131072/117649, 5/4, 10/7,7/4],
[1, 588245/524288, 5/4, 10/7, 7/4],
[1, 131072/117649, 16384/12005, 131072/84035, 7/4],
[16384/16807, 131072/117649, 5/4, 10/7, 7/4]]
If now we set a chord identifier c = [c[1] c[2] c[3]], where c[1] ranges from 1 to 12, picking out the corresponding chord in the chords list. The other two values, c[2] and c[3], transpose the root of the chords by 5^c[2] 7^c[3]. If u = n - 12c[2] - 14c[3], and if v is the reduction of u mod 5, then
note(n, [c[1] c[2] c[3]]) = 2^((u-v)/5) 5^c[2] 7^c[3] chords(v+1)
Once again, &lt;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 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&gt;. This gives a 3-limit interval which tempers to a note of tutone satisfying the identity &lt;12 19|note(n, c) = 2n. We can also express this in terms of a subgroup monzo as &lt;6 19|note(n, c) = n, where note(n, c) in subgroup monzo terms is |(u-i)/6-3i c+i&gt;.


=The 13-limit 7et tablet=
=The 13-limit 7et tablet=
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The tablet satisfies the identity  
The tablet satisfies the identity  
&lt;7 11 16 20 24 26|note(n, [r e3 e5 e7 e11 e13]) = n.
&lt;7 11 16 20 24 26|note(n, [r e3 e5 e7 e11 e13]) = n.
==The meantone add6/9 tablet==
The meantone add6/9 tablet is based on the [[meantone add6-9 quintad|meantone add6/9 quintad]], which can also be called the add2/9 quintad, the meantone pentatonic scale or Meantone[5]. The tablet is extremly simple, consiting of an ordered pair [n, c], where we have a meantone transversal for the notes defined by u = n-8c, where
* If u mod 5 = 0 then
note(n, c) = |u/5 c&gt;
* If u mod 5 = 1 then
note(n, c) = |(u-1)/5-3 c+2&gt;
* If u mod 5 = 2 then
note(n, c) = |(u-2)/5-6 c+4&gt;
* If u mod 5 = 3 then
note(n, c) = |(u-3)/5-1 c+1&gt;
* If u mod 5 = 4 then
note(n, c) = |(u-4)/5-4 c+3&gt;
In all cases &lt;5 8|note(n, c) = n. Tempering the the Pythgorean transversal by flattening 3 gives, as usual, a meantone tuning.
==The 5et portent tablet=
This is based on the following twelve chords, which are expressed in terms of the 2.5.7 transversal of the 11-limit rank three temperament portent, which tempers out 385/384, 441/440 and hence also 1029/1024 and 3025/3024.
chords = [[1, 131072/117649, 5/4, 512/343, 7/4],
[1, 131072/117649, 1048576/823543, 512/343, 1048576/588245],
[1, 131072/117649, 16384/12005, 512/343, 7/4],
[1, 131072/117649, 1048576/823543, 512/343, 80/49],
[1, 2048/1715, 16384/12005, 512/343, 7/4],
[1, 35/32, 5/4, 512/343, 4096/2401],
[1, 35/32, 5/4, 12005/8192, 7/4],
[1, 35/32, 5/4, 512/343, 7/4],
[1, 131072/117649, 5/4, 10/7,7/4],
[1, 588245/524288, 5/4, 10/7, 7/4],
[1, 131072/117649, 16384/12005, 131072/84035, 7/4],
[16384/16807, 131072/117649, 5/4, 10/7, 7/4]]
If now we set a chord identifier c = [c[1] c[2] c[3]], where c[1] ranges from 1 to 12, picking out the corresponding chord in the chords list. The other two values, c[2] and c[3], transpose the root of the chords by 5^c[2] 7^c[3]. If u = n - 12c[2] - 14c[3], and if v is the reduction of u mod 5, then
note(n, [c[1] c[2] c[3]]) = 2^((u-v)/5) 5^c[2] 7^c[3] chords(v+1)
Once again, &lt;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 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&gt;. This gives a 3-limit interval which tempers to a note of tutone satisfying the identity &lt;12 19|note(n, c) = 2n. We can also express this in terms of a subgroup monzo as &lt;6 19|note(n, c) = n, where note(n, c) in subgroup monzo terms is |(u-i)/6-3i c+i&gt;.


=The orwell nonad tablet=
=The orwell nonad tablet=
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note(n, c) = |(u-i)/9-(i+9)/2 (1-i)/2-c 1 (i+1)/2+c&gt;
note(n, c) = |(u-i)/9-(i+9)/2 (1-i)/2-c 1 (i+1)/2+c&gt;
if i is odd. We then have &lt;9 14 21 25|note(n, c) = n.
if i is odd. We then have &lt;9 14 21 25|note(n, c) = n.
</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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Tablets&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:24:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:24 --&gt;&lt;!-- ws:start:WikiTextTocRule:25: --&gt;&lt;a href="#What is a tablet?"&gt;What is a tablet?&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:25 --&gt;&lt;!-- ws:start:WikiTextTocRule:26: --&gt; | &lt;a href="#The 5-limit 3et tablet"&gt;The 5-limit 3et tablet&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:26 --&gt;&lt;!-- ws:start:WikiTextTocRule:27: --&gt; | &lt;a href="#x4et tablets"&gt;4et tablets&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:27 --&gt;&lt;!-- ws:start:WikiTextTocRule:28: --&gt;&lt;!-- ws:end:WikiTextTocRule:28 --&gt;&lt;!-- ws:start:WikiTextTocRule:29: --&gt;&lt;!-- ws:end:WikiTextTocRule:29 --&gt;&lt;!-- ws:start:WikiTextTocRule:30: --&gt; | &lt;a href="#x5et tablets"&gt;5et tablets&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:30 --&gt;&lt;!-- ws:start:WikiTextTocRule:31: --&gt;&lt;!-- ws:end:WikiTextTocRule:31 --&gt;&lt;!-- ws:start:WikiTextTocRule:32: --&gt; | &lt;a href="#The 13-limit 7et tablet"&gt;The 13-limit 7et tablet&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:32 --&gt;&lt;!-- ws:start:WikiTextTocRule:33: --&gt;&lt;!-- ws:end:WikiTextTocRule:33 --&gt;&lt;!-- ws:start:WikiTextTocRule:34: --&gt; | &lt;a href="#x=The 5et portent tablet"&gt;=The 5et portent tablet&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:34 --&gt;&lt;!-- ws:start:WikiTextTocRule:35: --&gt; | &lt;a href="#The tutone tutonic tablet"&gt;The tutone tutonic tablet&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:35 --&gt;&lt;!-- ws:start:WikiTextTocRule:36: --&gt; | &lt;a href="#The orwell nonad tablet"&gt;The orwell nonad tablet&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:36 --&gt;&lt;!-- ws:start:WikiTextTocRule:37: --&gt;
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Tablets&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:24:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:24 --&gt;&lt;!-- ws:start:WikiTextTocRule:25: --&gt;&lt;a href="#What is a tablet?"&gt;What is a tablet?&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:25 --&gt;&lt;!-- ws:start:WikiTextTocRule:26: --&gt; | &lt;a href="#The 5-limit 3et tablet"&gt;The 5-limit 3et tablet&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:26 --&gt;&lt;!-- ws:start:WikiTextTocRule:27: --&gt; | &lt;a href="#x4et tablets"&gt;4et tablets&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:27 --&gt;&lt;!-- ws:start:WikiTextTocRule:28: --&gt;&lt;!-- ws:end:WikiTextTocRule:28 --&gt;&lt;!-- ws:start:WikiTextTocRule:29: --&gt;&lt;!-- ws:end:WikiTextTocRule:29 --&gt;&lt;!-- ws:start:WikiTextTocRule:30: --&gt; | &lt;a href="#x5et tablets"&gt;5et tablets&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:30 --&gt;&lt;!-- ws:start:WikiTextTocRule:31: --&gt;&lt;!-- ws:end:WikiTextTocRule:31 --&gt;&lt;!-- ws:start:WikiTextTocRule:32: --&gt;&lt;!-- ws:end:WikiTextTocRule:32 --&gt;&lt;!-- ws:start:WikiTextTocRule:33: --&gt;&lt;!-- ws:end:WikiTextTocRule:33 --&gt;&lt;!-- ws:start:WikiTextTocRule:34: --&gt; | &lt;a href="#The tutone tutonic tablet"&gt;The tutone tutonic tablet&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:34 --&gt;&lt;!-- ws:start:WikiTextTocRule:35: --&gt; | &lt;a href="#The 13-limit 7et tablet"&gt;The 13-limit 7et tablet&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:35 --&gt;&lt;!-- ws:start:WikiTextTocRule:36: --&gt; | &lt;a href="#The orwell nonad tablet"&gt;The orwell nonad tablet&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:36 --&gt;&lt;!-- ws:start:WikiTextTocRule:37: --&gt;
&lt;!-- ws:end:WikiTextTocRule:37 --&gt;&lt;br /&gt;
&lt;!-- ws:end:WikiTextTocRule:37 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="What is a tablet?"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;What is a tablet?&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="What is a tablet?"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;What is a tablet?&lt;/h1&gt;
Line 280: Line 281:
Once again, if a+b+c is odd, then define note(t) as -note(-n, [-1-a -1-b -1-c]). If t = [n, w], where w is a 3-tuple, then [note([n, w)), note(n+1, w), note(n+2), w), note(n+3, w), note(n+4), w)] is a complete 9-odd-limit quintad, where &amp;lt;5 8 12 14|note(n, t) = n.&lt;br /&gt;
Once again, if a+b+c is odd, then define note(t) as -note(-n, [-1-a -1-b -1-c]). If t = [n, w], where w is a 3-tuple, then [note([n, w)), note(n+1, w), note(n+2), w), note(n+3, w), note(n+4), w)] is a complete 9-odd-limit quintad, where &amp;lt;5 8 12 14|note(n, t) = n.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="The 13-limit 7et tablet"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;The 13-limit 7et tablet&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="x5et tablets-The meantone add6/9 tablet"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;The meantone add6/9 tablet&lt;/h2&gt;
The meantone add6/9 tablet is based on the &lt;a class="wiki_link" href="/meantone%20add6-9%20quintad"&gt;meantone add6/9 quintad&lt;/a&gt;, which can also be called the add2/9 quintad, the meantone pentatonic scale or Meantone[5]. The tablet is extremly simple, consiting of an ordered pair [n, c], where we have a meantone transversal for the notes defined by u = n-8c, where &lt;br /&gt;
&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;If u mod 5 = 0 then&lt;/li&gt;&lt;/ul&gt;note(n, c) = |u/5 c&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;If u mod 5 = 1 then&lt;/li&gt;&lt;/ul&gt;note(n, c) = |(u-1)/5-3 c+2&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;If u mod 5 = 2 then&lt;/li&gt;&lt;/ul&gt;note(n, c) = |(u-2)/5-6 c+4&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;If u mod 5 = 3 then&lt;/li&gt;&lt;/ul&gt;note(n, c) = |(u-3)/5-1 c+1&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;If u mod 5 = 4 then&lt;/li&gt;&lt;/ul&gt;note(n, c) = |(u-4)/5-4 c+3&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In all cases &amp;lt;5 8|note(n, c) = n. Tempering the the Pythgorean transversal by flattening 3 gives, as usual, a meantone tuning.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="x5et tablets-The 5et portent tablet"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;The 5et portent tablet&lt;/h2&gt;
This is based on the following twelve chords, which are expressed in terms of the 2.5.7 transversal of the 11-limit rank three temperament portent, which tempers out 385/384, 441/440 and hence also 1029/1024 and 3025/3024. &lt;br /&gt;
&lt;br /&gt;
chords = [[1, 131072/117649, 5/4, 512/343, 7/4], [1, 131072/117649, 1048576/823543, 512/343, 1048576/588245], [1, 131072/117649, 16384/12005, 512/343, 7/4], [1, 131072/117649, 1048576/823543, 512/343, 80/49], [1, 2048/1715, 16384/12005, 512/343, 7/4], [1, 35/32, 5/4, 512/343, 4096/2401], [1, 35/32, 5/4, 12005/8192, 7/4], [1, 35/32, 5/4, 512/343, 7/4], [1, 131072/117649, 5/4, 10/7,7/4], [1, 588245/524288, 5/4, 10/7, 7/4], [1, 131072/117649, 16384/12005, 131072/84035, 7/4], [16384/16807, 131072/117649, 5/4, 10/7, 7/4]]&lt;br /&gt;
&lt;br /&gt;
If now we set a chord identifier c = [c[1] c[2] c[3]], where c[1] ranges from 1 to 12, picking out the corresponding chord in the chords list. The other two values, c[2] and c[3], transpose the root of the chords by 5^c[2] 7^c[3]. If u = n - 12c[2] - 14c[3], and if v is the reduction of u mod 5, then &lt;br /&gt;
note(n, [c[1] c[2] c[3]]) = 2^((u-v)/5) 5^c[2] 7^c[3] chords(v+1)&lt;br /&gt;
Once again, &amp;lt;5 8 12 14 17|note(n, c) = c.&lt;br /&gt;
&lt;br /&gt;
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.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc9"&gt;&lt;a name="The tutone tutonic tablet"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;The tutone tutonic tablet&lt;/h1&gt;
This tablet is based on the &lt;a class="wiki_link" href="/tutonic%20sextad"&gt;tutonic sextad&lt;/a&gt;, 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 &lt;a class="wiki_link" href="/Chromatic%20pairs#Tutone"&gt;tutone temperament&lt;/a&gt;, a 2.9.7.11 subgroup temperament, and the sextad can be called Tutone[6], the tutone haplotonic scale.&lt;br /&gt;
&lt;br /&gt;
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&amp;gt;. This gives a 3-limit interval which tempers to a note of tutone satisfying the identity &amp;lt;12 19|note(n, c) = 2n. We can also express this in terms of a subgroup monzo as &amp;lt;6 19|note(n, c) = n, where note(n, c) in subgroup monzo terms is |(u-i)/6-3i c+i&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc10"&gt;&lt;a name="The 13-limit 7et tablet"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;The 13-limit 7et tablet&lt;/h1&gt;
Let &amp;lt;r e3 e5 e7 e11 e13| denote an otonal 13-limit septad with root given by |* e3 e5 e7 e11 e13&amp;gt; when r is even, which in close position is 9/8-5/4-11/8-3/2-13/8-7/4-2. If r is odd, let it denote a utonal pentad which in close position is 12/11-6/5-4/3-3/2-12/7-24/13-2&lt;br /&gt;
Let &amp;lt;r e3 e5 e7 e11 e13| denote an otonal 13-limit septad with root given by |* e3 e5 e7 e11 e13&amp;gt; when r is even, which in close position is 9/8-5/4-11/8-3/2-13/8-7/4-2. If r is odd, let it denote a utonal pentad which in close position is 12/11-6/5-4/3-3/2-12/7-24/13-2&lt;br /&gt;
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The tablet satisfies the identity &lt;br /&gt;
The tablet satisfies the identity &lt;br /&gt;
&amp;lt;7 11 16 20 24 26|note(n, [r e3 e5 e7 e11 e13]) = n.&lt;br /&gt;
&amp;lt;7 11 16 20 24 26|note(n, [r e3 e5 e7 e11 e13]) = n.&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="The 13-limit 7et tablet-The meantone add6/9 tablet"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;The meantone add6/9 tablet&lt;/h2&gt;
The meantone add6/9 tablet is based on the &lt;a class="wiki_link" href="/meantone%20add6-9%20quintad"&gt;meantone add6/9 quintad&lt;/a&gt;, which can also be called the add2/9 quintad, the meantone pentatonic scale or Meantone[5]. The tablet is extremly simple, consiting of an ordered pair [n, c], where we have a meantone transversal for the notes defined by u = n-8c, where &lt;br /&gt;
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&lt;ul&gt;&lt;li&gt;If u mod 5 = 0 then&lt;/li&gt;&lt;/ul&gt;note(n, c) = |u/5 c&amp;gt;&lt;br /&gt;
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&lt;ul&gt;&lt;li&gt;If u mod 5 = 1 then&lt;/li&gt;&lt;/ul&gt;note(n, c) = |(u-1)/5-3 c+2&amp;gt;&lt;br /&gt;
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&lt;ul&gt;&lt;li&gt;If u mod 5 = 2 then&lt;/li&gt;&lt;/ul&gt;note(n, c) = |(u-2)/5-6 c+4&amp;gt;&lt;br /&gt;
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&lt;ul&gt;&lt;li&gt;If u mod 5 = 3 then&lt;/li&gt;&lt;/ul&gt;note(n, c) = |(u-3)/5-1 c+1&amp;gt;&lt;br /&gt;
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&lt;ul&gt;&lt;li&gt;If u mod 5 = 4 then&lt;/li&gt;&lt;/ul&gt;note(n, c) = |(u-4)/5-4 c+3&amp;gt;&lt;br /&gt;
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In all cases &amp;lt;5 8|note(n, c) = n. Tempering the the Pythgorean transversal by flattening 3 gives, as usual, a meantone tuning.&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc9"&gt;&lt;a name="x=The 5et portent tablet"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;=The 5et portent tablet&lt;/h1&gt;
This is based on the following twelve chords, which are expressed in terms of the 2.5.7 transversal of the 11-limit rank three temperament portent, which tempers out 385/384, 441/440 and hence also 1029/1024 and 3025/3024. &lt;br /&gt;
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chords = [[1, 131072/117649, 5/4, 512/343, 7/4], [1, 131072/117649, 1048576/823543, 512/343, 1048576/588245], [1, 131072/117649, 16384/12005, 512/343, 7/4], [1, 131072/117649, 1048576/823543, 512/343, 80/49], [1, 2048/1715, 16384/12005, 512/343, 7/4], [1, 35/32, 5/4, 512/343, 4096/2401], [1, 35/32, 5/4, 12005/8192, 7/4], [1, 35/32, 5/4, 512/343, 7/4], [1, 131072/117649, 5/4, 10/7,7/4], [1, 588245/524288, 5/4, 10/7, 7/4], [1, 131072/117649, 16384/12005, 131072/84035, 7/4], [16384/16807, 131072/117649, 5/4, 10/7, 7/4]]&lt;br /&gt;
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If now we set a chord identifier c = [c[1] c[2] c[3]], where c[1] ranges from 1 to 12, picking out the corresponding chord in the chords list. The other two values, c[2] and c[3], transpose the root of the chords by 5^c[2] 7^c[3]. If u = n - 12c[2] - 14c[3], and if v is the reduction of u mod 5, then &lt;br /&gt;
note(n, [c[1] c[2] c[3]]) = 2^((u-v)/5) 5^c[2] 7^c[3] chords(v+1)&lt;br /&gt;
Once again, &amp;lt;5 8 12 14 17|note(n, c) = c.&lt;br /&gt;
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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.&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc10"&gt;&lt;a name="The tutone tutonic tablet"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;The tutone tutonic tablet&lt;/h1&gt;
This tablet is based on the &lt;a class="wiki_link" href="/tutonic%20sextad"&gt;tutonic sextad&lt;/a&gt;, 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 &lt;a class="wiki_link" href="/Chromatic%20pairs#Tutone"&gt;tutone temperament&lt;/a&gt;, a 2.9.7.11 subgroup temperament, and the sextad can be called Tutone[6], the tutone haplotonic scale.&lt;br /&gt;
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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&amp;gt;. This gives a 3-limit interval which tempers to a note of tutone satisfying the identity &amp;lt;12 19|note(n, c) = 2n. We can also express this in terms of a subgroup monzo as &amp;lt;6 19|note(n, c) = n, where note(n, c) in subgroup monzo terms is |(u-i)/6-3i c+i&amp;gt;.&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc11"&gt;&lt;a name="The orwell nonad tablet"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;The orwell nonad tablet&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc11"&gt;&lt;a name="The orwell nonad tablet"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;The orwell nonad tablet&lt;/h1&gt;
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