87edo: Difference between revisions

Wikispaces>xenwolf
**Imported revision 239564621 - Original comment: **
Wikispaces>Gedankenwelt
**Imported revision 479841768 - 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:xenwolf|xenwolf]] and made on <tt>2011-06-30 18:06:34 UTC</tt>.<br>
: This revision was by author [[User:Gedankenwelt|Gedankenwelt]] and made on <tt>2013-12-30 05:06:31 UTC</tt>.<br>
: The original revision id was <tt>239564621</tt>.<br>
: The original revision id was <tt>479841768</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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87et [[tempering out|tempers out]] 196/195, 325/324, 352/351, 364/363, 385/384, 441/440, 625/624, 676/675, and 1001/1000 as well as the 29-comma, &lt;46 -29|, the misty comma, &lt;26 -12 -3|, the kleisma, 15625/15552, 245/243, 1029/1024, 3136/3125, and 5120/5103.
87et [[tempering out|tempers out]] 196/195, 325/324, 352/351, 364/363, 385/384, 441/440, 625/624, 676/675, and 1001/1000 as well as the 29-comma, &lt;46 -29|, the misty comma, &lt;26 -12 -3|, the kleisma, 15625/15552, 245/243, 1029/1024, 3136/3125, and 5120/5103.


Some 13-limit rank two temperaments supported by 87et are these:
87et is a particularly good tuning for [[Gamelismic clan|rodan temperament]]. The 8/7 generator of 17\87 is a remarkable 0.00062 cents sharper than the 13-limit [[POTE tuning|POTE]] generator and is close to the 11-limit POTE generator also. Also, the 32/87 generator for [[Kleismic family|clyde temperament]] is 0.04455 cents sharp of the 7-limit POTE generator.


tritikleismic 72&amp;87 &lt;&lt;18 15 -6 9 42 ... ||
=Rank two temperaments=
rodan 41&amp;87 &lt;&lt;3 17 -1 -13 -22 ... ||
||~ Periods
mystery 29&amp;58 &lt;&lt;0 29 29 29 29 ... ||
per
countercata 34&amp;87 &lt;&lt;6 5 -31 32 14 ... ||
octave ||~ Generator ||~ Cents ||~ Associated
hemithirds 31&amp;87 &lt;&lt;15 -2 -5 22 -23 ... ||
ratio ||~ Temperament ||~ 13-limit wedgie ||
||&gt; 1 ||&gt; 4\87 ||&gt; 55.172 ||= 33/32 ||&lt; [[Sensa]] ||  ||
||&gt; 1 ||&gt; 10\87 ||&gt; 137.931 ||= 13/12 || [[Quartemka]] ||  ||
||&gt; 1 ||&gt; 14\87 ||&gt; 193.103 ||= 28/25 || [[Luna]]/[[Hemithirds]] || &lt;&lt;15 -2 -5 22 -23 ... ||
||
||&gt; 1 ||&gt; 17\87 ||&gt; 234.483 ||= 8/7 || [[Rodan]] || &lt;&lt;3 17 -1 -13 -22 ... ||
||
||&gt; 1 ||&gt; 23\87 ||&gt; 317.241 ||= 6/5 || [[Countercata]] || &lt;&lt;6 5 -31 32 14 ... ||
||
||&gt; 1 ||&gt; 32\87 ||&gt; 441.379 ||= 9/7 || [[Clyde]] ||  ||
||&gt; 1 ||&gt; 40\87 ||&gt; 551.724 ||= 11/8 || [[Emkay]] || &lt;&lt;27 8 -67 -1 5 ...||
||
||&gt; 3 ||&gt; 23\87 ||&gt; 317.241 ||= 6/5 || [[Tritikleismic]] || &lt;&lt;18 15 -6 9 42 ... ||
||
||&gt; 29 ||&gt; 28\87 ||&gt; 386.207 ||= 5/4 || [[Mystery]] || &lt;&lt;0 29 29 29 29 ... ||
||


87 can serve as a MOS in these:
87 can serve as a MOS in these:
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270&amp;87 &lt;&lt;24 -9 -66 12 27 ... ||
270&amp;87 &lt;&lt;24 -9 -66 12 27 ... ||
494&amp;87 &lt;&lt;51 -1 -133 11 32 ... ||
494&amp;87 &lt;&lt;51 -1 -133 11 32 ... ||
224&amp;87 &lt;&lt;27 8 -67 -1 5 ...||
87et is a particularly good tuning for [[Gamelismic clan|rodan temperament]]. The 8/7 generator of 17\87 is a remarkable 0.00062 cents sharper than the 13-limit [[POTE tuning|POTE]] generator and is close to the 11-limit POTE generator also. Also, the 32/87 generator for [[Kleismic family|clyde temperament]] is 0.04455 cents sharp of the 7-limit POTE generator.


=Music=  
=Music=  
Line 34: Line 46:
87et &lt;a class="wiki_link" href="/tempering%20out"&gt;tempers out&lt;/a&gt; 196/195, 325/324, 352/351, 364/363, 385/384, 441/440, 625/624, 676/675, and 1001/1000 as well as the 29-comma, &amp;lt;46 -29|, the misty comma, &amp;lt;26 -12 -3|, the kleisma, 15625/15552, 245/243, 1029/1024, 3136/3125, and 5120/5103.&lt;br /&gt;
87et &lt;a class="wiki_link" href="/tempering%20out"&gt;tempers out&lt;/a&gt; 196/195, 325/324, 352/351, 364/363, 385/384, 441/440, 625/624, 676/675, and 1001/1000 as well as the 29-comma, &amp;lt;46 -29|, the misty comma, &amp;lt;26 -12 -3|, the kleisma, 15625/15552, 245/243, 1029/1024, 3136/3125, and 5120/5103.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Some 13-limit rank two temperaments supported by 87et are these:&lt;br /&gt;
87et is a particularly good tuning for &lt;a class="wiki_link" href="/Gamelismic%20clan"&gt;rodan temperament&lt;/a&gt;. The 8/7 generator of 17\87 is a remarkable 0.00062 cents sharper than the 13-limit &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE&lt;/a&gt; generator and is close to the 11-limit POTE generator also. Also, the 32/87 generator for &lt;a class="wiki_link" href="/Kleismic%20family"&gt;clyde temperament&lt;/a&gt; is 0.04455 cents sharp of the 7-limit POTE generator.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
tritikleismic 72&amp;amp;87 &amp;lt;&amp;lt;18 15 -6 9 42 ... ||&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Rank two temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Rank two temperaments&lt;/h1&gt;
rodan 41&amp;amp;87 &amp;lt;&amp;lt;3 17 -1 -13 -22 ... ||&lt;br /&gt;
mystery 29&amp;amp;58 &amp;lt;&amp;lt;0 29 29 29 29 ... ||&lt;br /&gt;
 
countercata 34&amp;amp;87 &amp;lt;&amp;lt;6 5 -31 32 14 ... ||&lt;br /&gt;
&lt;table class="wiki_table"&gt;
hemithirds 31&amp;amp;87 &amp;lt;&amp;lt;15 -2 -5 22 -23 ... ||&lt;br /&gt;
    &lt;tr&gt;
        &lt;th&gt;Periods&lt;br /&gt;
per&lt;br /&gt;
octave&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Generator&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Cents&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Associated&lt;br /&gt;
ratio&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Temperament&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;13-limit wedgie&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: right;"&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;4\87&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;55.172&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;33/32&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;a class="wiki_link" href="/Sensa"&gt;Sensa&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: right;"&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;10\87&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;137.931&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;13/12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Quartemka"&gt;Quartemka&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: right;"&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;14\87&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;193.103&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;28/25&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Luna"&gt;Luna&lt;/a&gt;/&lt;a class="wiki_link" href="/Hemithirds"&gt;Hemithirds&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&amp;lt;&amp;lt;15 -2 -5 22 -23 ...&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
||&lt;br /&gt;
    &lt;tr&gt;
        &lt;td style="text-align: right;"&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;17\87&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;234.483&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;8/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Rodan"&gt;Rodan&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&amp;lt;&amp;lt;3 17 -1 -13 -22 ...&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
||&lt;br /&gt;
    &lt;tr&gt;
        &lt;td style="text-align: right;"&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;23\87&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;317.241&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Countercata"&gt;Countercata&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&amp;lt;&amp;lt;6 5 -31 32 14 ...&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
||&lt;br /&gt;
    &lt;tr&gt;
        &lt;td style="text-align: right;"&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;32\87&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;441.379&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;9/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Clyde"&gt;Clyde&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: right;"&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;40\87&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;551.724&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;11/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Emkay"&gt;Emkay&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&amp;lt;&amp;lt;27 8 -67 -1 5 ...&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
||&lt;br /&gt;
    &lt;tr&gt;
        &lt;td style="text-align: right;"&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;23\87&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;317.241&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Tritikleismic"&gt;Tritikleismic&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&amp;lt;&amp;lt;18 15 -6 9 42 ...&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
||&lt;br /&gt;
    &lt;tr&gt;
        &lt;td style="text-align: right;"&gt;29&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;28\87&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;386.207&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Mystery"&gt;Mystery&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&amp;lt;&amp;lt;0 29 29 29 29 ...&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
||&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
87 can serve as a MOS in these:&lt;br /&gt;
87 can serve as a MOS in these:&lt;br /&gt;
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270&amp;amp;87 &amp;lt;&amp;lt;24 -9 -66 12 27 ... ||&lt;br /&gt;
270&amp;amp;87 &amp;lt;&amp;lt;24 -9 -66 12 27 ... ||&lt;br /&gt;
494&amp;amp;87 &amp;lt;&amp;lt;51 -1 -133 11 32 ... ||&lt;br /&gt;
494&amp;amp;87 &amp;lt;&amp;lt;51 -1 -133 11 32 ... ||&lt;br /&gt;
224&amp;amp;87 &amp;lt;&amp;lt;27 8 -67 -1 5 ...||&lt;br /&gt;
&lt;br /&gt;
87et is a particularly good tuning for &lt;a class="wiki_link" href="/Gamelismic%20clan"&gt;rodan temperament&lt;/a&gt;. The 8/7 generator of 17\87 is a remarkable 0.00062 cents sharper than the 13-limit &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE&lt;/a&gt; generator and is close to the 11-limit POTE generator also. Also, the 32/87 generator for &lt;a class="wiki_link" href="/Kleismic%20family"&gt;clyde temperament&lt;/a&gt; is 0.04455 cents sharp of the 7-limit POTE generator.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Music&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Music&lt;/h1&gt;
  &lt;br /&gt;
  &lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://www.archive.org/details/Pianodactyl" rel="nofollow"&gt;Pianodactyl&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://www.archive.org/download/Pianodactyl/pianodactyl.mp3" rel="nofollow"&gt;play&lt;/a&gt; by &lt;a class="wiki_link" href="/Gene%20Ward%20Smith"&gt;Gene Ward Smith&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
&lt;a class="wiki_link_ext" href="http://www.archive.org/details/Pianodactyl" rel="nofollow"&gt;Pianodactyl&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://www.archive.org/download/Pianodactyl/pianodactyl.mp3" rel="nofollow"&gt;play&lt;/a&gt; by &lt;a class="wiki_link" href="/Gene%20Ward%20Smith"&gt;Gene Ward Smith&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>