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