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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
The 87 equal temperament, often abbreviated 87-tET, 87-EDO, or 87-ET, is the scale derived by dividing the octave into 87 equally-sized steps, where each step represents a frequency ratio of 13.79 [[cent|cent]]s. It is solid as both a [[13-limit|13-limit]] (or 15 odd limit) and as a [[5-limit|5-limit]] system, and of course does well enough in any limit in between. It represents the [[13-limit|13-limit]] [[Tonality_diamond|tonality diamond]] both uniquely and [[consistent|consistent]]ly, and is the smallest equal temperament to do so.
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:bootmii|bootmii]] and made on <tt>2016-12-23 21:33:22 UTC</tt>.<br>
: The original revision id was <tt>602790088</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>
<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">The 87 equal temperament, often abbreviated 87-tET, 87-EDO, or 87-ET, is the scale derived by dividing the octave into 87 equally-sized steps, where each step represents a frequency ratio of 13.79 [[cent]]s. It is solid as both a [[13-limit]] (or 15 odd limit) and as a [[5-limit]] system, and of course does well enough in any limit in between. It represents the [[13-limit]] [[tonality diamond]] both uniquely and [[consistent]]ly, and is the smallest equal temperament to do so.


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.


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.
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=
 
{| class="wikitable"
|-
! | Periods


=Rank two temperaments=
||~ Periods
per
per
octave ||~ Generator ||~ Cents ||~ Associated
 
ratio ||~ Temperament ||
octave
||&gt; 1 ||&gt; 4\87 ||&gt; 55.172 ||= 33/32 ||&lt; [[Sensa]] ||
! | Generator
||&gt; 1 ||&gt; 10\87 ||&gt; 137.931 ||= 13/12 || [[Quartemka]] ||
! | Cents
||&gt; 1 ||&gt; 14\87 ||&gt; 193.103 ||= 28/25 || [[Luna]]/[[Hemithirds|hemithirds]] ||
! | Associated
||&gt; 1 ||&gt; 17\87 ||&gt; 234.483 ||= 8/7 || [[Rodan]] ||
 
||&gt; 1 ||&gt; 23\87 ||&gt; 317.241 ||= 6/5 || [[Hanson]]/[[countercata]]/[[metakleismic]] ||
ratio
||&gt; 1 ||&gt; 32\87 ||&gt; 441.379 ||= 9/7 || [[Clyde]] ||
! | Temperament
||&gt; 1 ||&gt; 38\87 ||&gt; 524.138 ||= 65/48 ||&lt; [[Widefourth]] ||
|-
||&gt; 1 ||&gt; 40\87 ||&gt; 551.724 ||= 11/8 || [[Emkay]] ||
| style="text-align:right;" | 1
||&gt; 3 ||&gt; 23\87 ||&gt; 317.241 ||= 6/5 || [[Tritikleismic]] ||
| style="text-align:right;" | 4\87
||&gt; 29 ||&gt; 28\87 ||&gt; 386.207 ||= 5/4 || [[Mystery]] ||
| style="text-align:right;" | 55.172
| style="text-align:center;" | 33/32
| | [[Sensa|Sensa]]
|-
| style="text-align:right;" | 1
| style="text-align:right;" | 10\87
| style="text-align:right;" | 137.931
| style="text-align:center;" | 13/12
| | [[Quartemka|Quartemka]]
|-
| style="text-align:right;" | 1
| style="text-align:right;" | 14\87
| style="text-align:right;" | 193.103
| style="text-align:center;" | 28/25
| | [[Luna|Luna]]/[[Hemithirds|hemithirds]]
|-
| style="text-align:right;" | 1
| style="text-align:right;" | 17\87
| style="text-align:right;" | 234.483
| style="text-align:center;" | 8/7
| | [[Rodan|Rodan]]
|-
| style="text-align:right;" | 1
| style="text-align:right;" | 23\87
| style="text-align:right;" | 317.241
| style="text-align:center;" | 6/5
| | [[Hanson|Hanson]]/[[Countercata|countercata]]/[[metakleismic|metakleismic]]
|-
| style="text-align:right;" | 1
| style="text-align:right;" | 32\87
| style="text-align:right;" | 441.379
| style="text-align:center;" | 9/7
| | [[Clyde|Clyde]]
|-
| style="text-align:right;" | 1
| style="text-align:right;" | 38\87
| style="text-align:right;" | 524.138
| style="text-align:center;" | 65/48
| | [[Widefourth|Widefourth]]
|-
| style="text-align:right;" | 1
| style="text-align:right;" | 40\87
| style="text-align:right;" | 551.724
| style="text-align:center;" | 11/8
| | [[Emkay|Emkay]]
|-
| style="text-align:right;" | 3
| style="text-align:right;" | 23\87
| style="text-align:right;" | 317.241
| style="text-align:center;" | 6/5
| | [[Tritikleismic|Tritikleismic]]
|-
| style="text-align:right;" | 29
| style="text-align:right;" | 28\87
| style="text-align:right;" | 386.207
| style="text-align:center;" | 5/4
| | [[mystery|Mystery]]
|}


87 can serve as a MOS in these:
87 can serve as a MOS in these:


[[M&amp;N temperaments|270&amp;87]] &lt;&lt;24 -9 -66 12 27 ... ||
[[M&N_temperaments|270&amp;87]] &lt;&lt;24 -9 -66 12 27 ... ||
[[M&amp;N temperaments|494&amp;87]] &lt;&lt;51 -1 -133 11 32 ... ||


=13-limit detempering of 87et=  
[[M&N_temperaments|494&amp;87]] &lt;&lt;51 -1 -133 11 32 ... ||
 
=13-limit detempering of 87et=
[91/90, 49/48, 40/39, 28/27, 25/24, 21/20, 35/33, 16/15, 14/13, 13/12, 12/11, 11/10, 10/9, 28/25, 9/8, 25/22, 8/7, 15/13, 7/6, 75/64, 13/11, 25/21, 6/5, 40/33, 11/9, 16/13, 26/21, 5/4, 44/35, 14/11, 32/25, 9/7, 13/10, 21/16, 33/25, 4/3, 35/26, 27/20, 15/11, 11/8, 18/13, 7/5, 45/32, 64/45, 10/7, 13/9, 16/11, 22/15, 40/27, 52/35, 3/2, 50/33, 32/21, 20/13, 14/9, 25/16, 11/7, 35/22, 8/5, 21/13, 13/8, 18/11, 33/20, 5/3, 42/25, 22/13, 75/44, 12/7, 26/15, 7/4, 44/25, 16/9, 25/14, 9/5, 20/11, 11/6, 24/13, 13/7, 15/8, 66/35, 21/11, 25/13, 27/14, 39/20, 55/28, 99/50, 2]
[91/90, 49/48, 40/39, 28/27, 25/24, 21/20, 35/33, 16/15, 14/13, 13/12, 12/11, 11/10, 10/9, 28/25, 9/8, 25/22, 8/7, 15/13, 7/6, 75/64, 13/11, 25/21, 6/5, 40/33, 11/9, 16/13, 26/21, 5/4, 44/35, 14/11, 32/25, 9/7, 13/10, 21/16, 33/25, 4/3, 35/26, 27/20, 15/11, 11/8, 18/13, 7/5, 45/32, 64/45, 10/7, 13/9, 16/11, 22/15, 40/27, 52/35, 3/2, 50/33, 32/21, 20/13, 14/9, 25/16, 11/7, 35/22, 8/5, 21/13, 13/8, 18/11, 33/20, 5/3, 42/25, 22/13, 75/44, 12/7, 26/15, 7/4, 44/25, 16/9, 25/14, 9/5, 20/11, 11/6, 24/13, 13/7, 15/8, 66/35, 21/11, 25/13, 27/14, 39/20, 55/28, 99/50, 2]


=Music=  
=Music=
 
[[http://www.archive.org/details/Pianodactyl|Pianodactyl]] [[http://www.archive.org/download/Pianodactyl/pianodactyl.mp3|play]] by [[Gene Ward Smith]]</pre></div>
<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;87edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 87 equal temperament, often abbreviated 87-tET, 87-EDO, or 87-ET, is the scale derived by dividing the octave into 87 equally-sized steps, where each step represents a frequency ratio of 13.79 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s. It is solid as both a &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt; (or 15 odd limit) and as a &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt; system, and of course does well enough in any limit in between. It represents the &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt; &lt;a class="wiki_link" href="/tonality%20diamond"&gt;tonality diamond&lt;/a&gt; both uniquely and &lt;a class="wiki_link" href="/consistent"&gt;consistent&lt;/a&gt;ly, and is the smallest equal temperament to do so.&lt;br /&gt;
&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;
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;!-- 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;
 
&lt;table class="wiki_table"&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;/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;/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;/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;/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;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;/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;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="/Hanson"&gt;Hanson&lt;/a&gt;/&lt;a class="wiki_link" href="/countercata"&gt;countercata&lt;/a&gt;/&lt;a class="wiki_link" href="/metakleismic"&gt;metakleismic&lt;/a&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;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;/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;38\87&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;524.138&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;65/48&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;a class="wiki_link" href="/Widefourth"&gt;Widefourth&lt;/a&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;/tr&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;/tr&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;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
[http://www.archive.org/details/Pianodactyl Pianodactyl] [http://www.archive.org/download/Pianodactyl/pianodactyl.mp3 play] by [[Gene_Ward_Smith|Gene Ward Smith]]      [[Category:87edo]]
87 can serve as a MOS in these:&lt;br /&gt;
[[Category:clyde]]
&lt;br /&gt;
[[Category:countercata]]
&lt;a class="wiki_link" href="/M%26N%20temperaments"&gt;270&amp;amp;87&lt;/a&gt; &amp;lt;&amp;lt;24 -9 -66 12 27 ... ||&lt;br /&gt;
[[Category:edo]]
&lt;a class="wiki_link" href="/M%26N%20temperaments"&gt;494&amp;amp;87&lt;/a&gt; &amp;lt;&amp;lt;51 -1 -133 11 32 ... ||&lt;br /&gt;
[[Category:hemithirds]]
&lt;br /&gt;
[[Category:listen]]
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="x13-limit detempering of 87et"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;13-limit detempering of 87et&lt;/h1&gt;
[[Category:mystery]]
[91/90, 49/48, 40/39, 28/27, 25/24, 21/20, 35/33, 16/15, 14/13, 13/12, 12/11, 11/10, 10/9, 28/25, 9/8, 25/22, 8/7, 15/13, 7/6, 75/64, 13/11, 25/21, 6/5, 40/33, 11/9, 16/13, 26/21, 5/4, 44/35, 14/11, 32/25, 9/7, 13/10, 21/16, 33/25, 4/3, 35/26, 27/20, 15/11, 11/8, 18/13, 7/5, 45/32, 64/45, 10/7, 13/9, 16/11, 22/15, 40/27, 52/35, 3/2, 50/33, 32/21, 20/13, 14/9, 25/16, 11/7, 35/22, 8/5, 21/13, 13/8, 18/11, 33/20, 5/3, 42/25, 22/13, 75/44, 12/7, 26/15, 7/4, 44/25, 16/9, 25/14, 9/5, 20/11, 11/6, 24/13, 13/7, 15/8, 66/35, 21/11, 25/13, 27/14, 39/20, 55/28, 99/50, 2]&lt;br /&gt;
[[Category:rodan]]
&lt;br /&gt;
[[Category:theory]]
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Music&lt;/h1&gt;
[[Category:tritikleismic]]
&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>

Revision as of 00:00, 17 July 2018

The 87 equal temperament, often abbreviated 87-tET, 87-EDO, or 87-ET, is the scale derived by dividing the octave into 87 equally-sized steps, where each step represents a frequency ratio of 13.79 cents. It is solid as both a 13-limit (or 15 odd limit) and as a 5-limit system, and of course does well enough in any limit in between. It represents the 13-limit tonality diamond both uniquely and consistently, and is the smallest equal temperament to do so.

87et 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 rodan temperament. The 8/7 generator of 17\87 is a remarkable 0.00062 cents sharper than the 13-limit POTE generator and is close to the 11-limit POTE generator also. Also, the 32\87 generator for clyde temperament is 0.04455 cents sharp of the 7-limit POTE generator.

Rank two temperaments

Periods

per

octave

Generator Cents Associated

ratio

Temperament
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
1 17\87 234.483 8/7 Rodan
1 23\87 317.241 6/5 Hanson/countercata/metakleismic
1 32\87 441.379 9/7 Clyde
1 38\87 524.138 65/48 Widefourth
1 40\87 551.724 11/8 Emkay
3 23\87 317.241 6/5 Tritikleismic
29 28\87 386.207 5/4 Mystery

87 can serve as a MOS in these:

270&87 <<24 -9 -66 12 27 ... ||

494&87 <<51 -1 -133 11 32 ... ||

13-limit detempering of 87et

[91/90, 49/48, 40/39, 28/27, 25/24, 21/20, 35/33, 16/15, 14/13, 13/12, 12/11, 11/10, 10/9, 28/25, 9/8, 25/22, 8/7, 15/13, 7/6, 75/64, 13/11, 25/21, 6/5, 40/33, 11/9, 16/13, 26/21, 5/4, 44/35, 14/11, 32/25, 9/7, 13/10, 21/16, 33/25, 4/3, 35/26, 27/20, 15/11, 11/8, 18/13, 7/5, 45/32, 64/45, 10/7, 13/9, 16/11, 22/15, 40/27, 52/35, 3/2, 50/33, 32/21, 20/13, 14/9, 25/16, 11/7, 35/22, 8/5, 21/13, 13/8, 18/11, 33/20, 5/3, 42/25, 22/13, 75/44, 12/7, 26/15, 7/4, 44/25, 16/9, 25/14, 9/5, 20/11, 11/6, 24/13, 13/7, 15/8, 66/35, 21/11, 25/13, 27/14, 39/20, 55/28, 99/50, 2]

Music

Pianodactyl play by Gene Ward Smith

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