205edo: Difference between revisions

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Wikispaces>xenwolf
**Imported revision 573739635 - Original comment: H-Pi moved to domain zentral.zone**
Wikispaces>JosephRuhf
**Imported revision 601651598 - 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>2016-02-02 18:21:22 UTC</tt>.<br>
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-07 15:45:15 UTC</tt>.<br>
: The original revision id was <tt>573739635</tt>.<br>
: The original revision id was <tt>601651598</tt>.<br>
: The revision comment was: <tt>H-Pi moved to domain zentral.zone</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>
<h4>Original Wikitext content:</h4>
<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">205EDO divides the octave into 205 parts of 5.854 cents each. It can serve as a tuning for various temperaments, such as [[Ragismic microtemperaments|amity]] or [[Hemifamity family|laka]], and supplies the optimal patent val for [[Hemifamity temperaments#Quanic|quanic]] in the 7-, 11-, 13-, 17- and 19-limits, and for 13-limit amity, as well as other temperaments tempering out the huntma, 640/637, the rank five temperament for which it also supplies the optimal patent val. In the 5-limit it tempers out 1600000/1594323, the amity comma, and |38 -2 -15&gt;, the hemithirds comma, and is an excellent tuning for 5-limit amity. The patent val tempers out 4375/4374, 5120/5103, 6144/6125 and 540/539. Using its alternative mapping &lt;205 325 476 525| it can also be used for [[Gamelismic clan|hemithirds temperament]]; the 13-limit version of this, &lt;205 325 476 575 709 759|, is especially noteworthy. It factors into primes as 5 * 41, a fact some advocates of the division make use of; it is also 2460/12, so that a single step is precisely 12 [[mina|minas]].
<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">205EDO divides the octave into 205 parts of 5.854 cents each. It can serve as a tuning for various temperaments, such as [[Ragismic microtemperaments|amity]] or [[Hemifamity family|laka]], and supplies the optimal patent val for [[Hemifamity temperaments#Quanic|quanic]] in the 7-, 11-, 13-, 17- and 19-limits, and for 13-limit amity, as well as other temperaments tempering out the huntma, 640/637, the rank five temperament for which it also supplies the optimal patent val. In the 5-limit it tempers out [[tel:1600000/1594323|1600000/1594323]], the amity comma, and |38 -2 -15&gt;, the hemithirds comma, and is an excellent tuning for 5-limit amity. The patent val tempers out 4375/4374, 5120/5103, 6144/6125 and 540/539. Using its alternative mapping &lt;[[tel:205 325 476|205 325 476]] 525| it can also be used for [[Gamelismic clan|hemithirds temperament]]; the 13-limit version of this, &lt;[[tel:205 325 476 575 709|205 325 476 575 709]] 759|, is especially noteworthy. It factors into primes as 5 * 41, a fact some advocates of the division make use of; it is also 2460/12, so that a single step is precisely 12 [[mina|minas]].


205et tempers out 540/539, so that it allows [[swetismic chords]]; 640/637, so that it allows [[huntmic chords]]; 352/351, so that it allows [[minthmic chords]]; 1188/1183 and 540/539, so that it allows [[kestrel chords]]; and 847/845, so that it allows the [[cuthbert triad]]. This makes it a tuning of exceptional fludity for its degree of accuracy.
205et tempers out 540/539, so that it allows [[swetismic chords]]; 640/637, so that it allows [[huntmic chords]]; 352/351, so that it allows [[minthmic chords]]; 1188/1183 and 540/539, so that it allows [[kestrel chords]]; and 847/845, so that it allows the [[cuthbert triad]]. This makes it a tuning of exceptional fludity for its degree of accuracy.


=Temperament generators and Tonal Plexus=
=Temperament generators and Tonal Plexus=  
205edo is the default tuning for the [[http://hpi.zentral.zone/tonalplexus|Tonal Plexus midi controller]]. See the [[http://musictheory.zentral.zone/huntsystem1.html|theory part]] on the same website. Aside from the 24\205 generator of quanic, the 58\205 generator of amity, and the 33\205 generator of hemithirds, 205edo supplies an excellent [[meantone]] fifth in 119\205, an excellent [[myna]] generator in 53\205, and a very good [[porcupine]] generator with 28\205, which is also an excellent generator for the higher-limit extension porky, and when sliced in half to 14\205, can even be used for nautilus. These facts are all potentially of significance to anyone using a 205edo based system such as the Tonal Plexus.
205edo is the default tuning for the [[http://hpi.zentral.zone/tonalplexus|Tonal Plexus midi controller]]. See the [[http://musictheory.zentral.zone/huntsystem1.html|theory part]] on the same website. Aside from the 24\205 generator of quanic, the 58\205 generator of amity, and the 33\205 generator of hemithirds, 205edo supplies an excellent [[meantone]] fifth in 119\205, an excellent [[myna]] generator in 53\205, and a very good [[porcupine]] generator with 28\205, which is also an excellent generator for the higher-limit extension porky, and when sliced in half to 14\205, can even be used for nautilus. These facts are all potentially of significance to anyone using a 205edo based system such as the Tonal Plexus.


The 119\205 meantone fifth is extremely close to the 1/4-comma fifth, being only 0.007 cents sharp of it. Moreover the steps are half a cent flat of 1/4 of a syntonic comma. This makes the Tonal Plexus keyboard potentially of use in implementing [[http://en.wikipedia.org/wiki/Nicola_Vicentino|Nicola Vicentino]]'s [[http://www.tonalsoft.com/monzo/vicentino/vicentino.aspx|adaptive-JI scheme of 1555]]. It also means that authentic 1/4-comma meantone tuning is, for practical purposes, available in 205 and allows for historically authentic performances of 1/4-comma music on the historically newfangled Tonal Plexus.
The 119\205 meantone fifth is extremely close to the 1/4-comma fifth, being only 0.007 cents sharp of it. Moreover the steps are half a cent flat of 1/4 of a syntonic comma. This makes the Tonal Plexus keyboard potentially of use in implementing [[http://en.wikipedia.org/wiki/Nicola_Vicentino|Nicola Vicentino]]'s [[http://www.tonalsoft.com/monzo/vicentino/vicentino.aspx|adaptive-JI scheme of 1555]]. It also means that authentic 1/4-comma meantone tuning is, for practical purposes, available in 205 and allows for historically authentic performances of 1/4-comma music on the historically newfangled Tonal Plexus.


=205edo MOS=
=205edo MOS=  
==Quanic (24\205) MOS==
==Quanic (24\205) MOS==  


===17 note===
===17 note===  
11 13 11 13 11 13 11 13 11 13 11 13 11 13 11 13 13
[[tel:11 13 11 13 11 13 11|11 13 11 13 11 13 11]] [[tel:13 11 13 11 13 11 13|13 11 13 11 13 11 13]] 11 13 13


===26 note===
===26 note===  
11 11 2 11 11 2 11 11 2 11 11 2 11 11 2 11 11 2 11 11 2 11 11 2 11 2
[[tel:11 11 2 11 11 2 11 11|11 11 2 11 11 2 11 11]] [[tel:2 11 11 2 11 11 2 11 11|2 11 11 2 11 11 2 11 11]] [[tel:2 11 11 2 11 11 2 11 2|2 11 11 2 11 11 2 11 2]]


==Amity (58\205) MOS==
==Amity (58\205) MOS==  


===11 note===
===11 note===  
27 27 4 27 27 4 27 27 4 27 4
[[tel:27 27 4 27 27 4 27 27|27 27 4 27 27 4 27 27]] 4 27 4


===18 note===
===18 note===  
23 4 23 4 4 23 4 23 4 4 23 4 23 4 4 23 4 4
[[tel:23 4 23 4 4 23 4 23 4|23 4 23 4 4 23 4 23 4]] [[tel:4 23 4 23 4 4 23 4 4|4 23 4 23 4 4 23 4 4]]


===25 note===
===25 note===  
19 4 4 19 4 4 4 19 4 4 19 4 4 4 19 4 4 19 4 4 4 19 4 4 4
[[tel:19 4 4 19 4 4 4 19 4|19 4 4 19 4 4 4 19 4]] [[tel:4 19 4 4 4 19 4 4 19 4|4 19 4 4 4 19 4 4 19 4]] 4 4 19 4 4 4


==Hemithirds (33\205) MOS==
==Hemithirds (33\205) MOS==  


===13 note===
===13 note===  
26 7 26 7 26 7 26 7 26 7 26 7 7
[[tel:26 7 26 7 26 7 26 7 26|26 7 26 7 26 7 26 7 26]] 7 26 7 7


===19 note===
===19 note===  
19 7 7 19 7 7 19 7 7 19 7 7 19 7 7 19 7 7 7
[[tel:19 7 7 19 7 7 19 7 7|19 7 7 19 7 7 19 7 7]] [[tel:19 7 7 19 7 7 19 7 7|19 7 7 19 7 7 19 7 7]] 7


===25 note===
===25 note===  
12 7 7 7 12 7 7 7 12 7 7 7 12 7 7 7 12 7 7 7 12 7 7 7 7
[[tel:12 7 7 7 12 7 7 7 12|12 7 7 7 12 7 7 7 12]] 7 7 [[tel:7 12 7 7 7 12 7 7 7 12|7 12 7 7 7 12 7 7 7 12]] 7 7 7 7


===31 notes===
===31 notes===  
5 7 7 7 7 5 7 7 7 7 5 7 7 7 7 5 7 7 7 7 5 7 7 7 7 5 7 7 7 7 7
5 7 7 7 7 5 7 7 7 7 5 7 7 7 7 5 7 7 7 7 5 7 7 7 7 5 7 7 7 7 7


==Meantone (119\205) MOS==
==Meantone (119\205) MOS==  


===12 note===
===12 note===  
13 20 13 20 13 20 20 13 20 13 20 20
[[tel:13 20 13 20 13 20 20|13 20 13 20 13 20 20]] [[tel:13 20 13 20 20|13 20 13 20 20]]


===19 note===
===19 note===  
13 13 7 13 13 7 13 13 7 13 7 13 13 7 13 13 7 13 7
[[tel:13 13 7 13 13 7 13 13|13 13 7 13 13 7 13 13]] [[tel:7 13 7 13 13 7 13 13 7|7 13 7 13 13 7 13 13 7]] 13 7


===31 notes===
===31 notes===  
6 7 6 7 7 6 7 6 7 7 6 7 6 7 7 6 7 7 6 7 6 7 7 6 7 6 7 7 6 7 7
6 7 6 7 7 6 7 6 7 7 6 7 6 7 7 6 7 7 6 7 6 7 7 6 7 6 7 7 6 7 7


==Myna (53\205) MOS==
==Myna (53\205) MOS==  


===11 note===
===11 note===  
7 7 39 7 7 39 7 7 39 7 39
7 [[tel:7 39 7 7 39 7 7 39 7 39|7 39 7 7 39 7 7 39 7 39]]


===15 note===
===15 note===  
7 7 7 32 7 7 7 32 7 7 7 32 7 7 32
7 7 [[tel:7 32 7 7 7 32 7 7 7 32|7 32 7 7 7 32 7 7 7 32]] 7 7 32


===19 note===
===19 note===  
7 7 7 7 25 7 7 7 7 25 7 7 7 7 25 7 7 7 25
7 7 7 [[tel:7 25 7 7 7 7 25 7 7 7 7|7 25 7 7 7 7 25 7 7 7 7]] [[tel:25 7 7 7 25|25 7 7 7 25]]


===23 note===
===23 note===  
7 7 7 7 7 18 7 7 7 7 7 18 7 7 7 7 7 18 7 7 7 7 18
7 7 7 7 [[tel:7 18 7 7 7 7 7 18 7 7 7|7 18 7 7 7 7 7 18 7 7 7]] 7 [[tel:7 18 7 7 7 7 18|7 18 7 7 7 7 18]]


===27 note===
===27 note===  
7 7 7 7 7 7 11 7 7 7 7 7 7 11 7 7 7 7 7 7 11 7 7 7 7 7 11
7 7 7 7 7 [[tel:7 11 7 7 7 7 7 7 11 7 7|7 11 7 7 7 7 7 7 11 7 7]] 7 7 7 [[tel:7 11 7 7 7 7 7 11|7 11 7 7 7 7 7 11]]


===31 notes===
===31 notes===  
7 7 7 7 7 7 7 4 7 7 7 7 7 7 7 4 7 7 7 7 7 7 7 4 7 7 7 7 7 7 4
7 7 7 7 7 7 7 4 7 7 7 7 7 7 7 4 7 7 7 7 7 7 7 4 7 7 7 7 7 7 4


==Porcupine (28\205) MOS==
==Porcupine (28\205) MOS==  


===15 note===
===15 note===  
19 9 19 9 19 9 19 9 19 9 19 9 19 9 9
[[tel:19 9 19 9 19 9 19 9 19|19 9 19 9 19 9 19 9 19]] [[tel:9 19 9 19 9 9|9 19 9 19 9 9]]


===22 note===
===22 note===  
10 9 9 10 9 9 10 9 9 10 9 9 10 9 9 10 9 9 10 9 9 9
[[tel:10 9 9 10 9 9 10 9 9|10 9 9 10 9 9 10 9 9]] [[tel:10 9 9 10 9 9 10 9 9|10 9 9 10 9 9 10 9 9]] 10 9 9 9


===29 note===
===29 note===  
1 9 9 9 1 9 9 9 1 9 9 9 1 9 9 9 1 9 9 9 1 9 9 9 1 9 9 9 9</pre></div>
1 9 9 9 1 9 9 9 1 9 9 9 1 9 9 9 1 9 9 9 1 9 9 9 1 9 9 9 9</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;205edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;205EDO divides the octave into 205 parts of 5.854 cents each. It can serve as a tuning for various temperaments, such as &lt;a class="wiki_link" href="/Ragismic%20microtemperaments"&gt;amity&lt;/a&gt; or &lt;a class="wiki_link" href="/Hemifamity%20family"&gt;laka&lt;/a&gt;, and supplies the optimal patent val for &lt;a class="wiki_link" href="/Hemifamity%20temperaments#Quanic"&gt;quanic&lt;/a&gt; in the 7-, 11-, 13-, 17- and 19-limits, and for 13-limit amity, as well as other temperaments tempering out the huntma, 640/637, the rank five temperament for which it also supplies the optimal patent val. In the 5-limit it tempers out 1600000/1594323, the amity comma, and |38 -2 -15&amp;gt;, the hemithirds comma, and is an excellent tuning for 5-limit amity. The patent val tempers out 4375/4374, 5120/5103, 6144/6125 and 540/539. Using its alternative mapping &amp;lt;205 325 476 525| it can also be used for &lt;a class="wiki_link" href="/Gamelismic%20clan"&gt;hemithirds temperament&lt;/a&gt;; the 13-limit version of this, &amp;lt;205 325 476 575 709 759|, is especially noteworthy. It factors into primes as 5 * 41, a fact some advocates of the division make use of; it is also 2460/12, so that a single step is precisely 12 &lt;a class="wiki_link" href="/mina"&gt;minas&lt;/a&gt;.&lt;br /&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;205edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;205EDO divides the octave into 205 parts of 5.854 cents each. It can serve as a tuning for various temperaments, such as &lt;a class="wiki_link" href="/Ragismic%20microtemperaments"&gt;amity&lt;/a&gt; or &lt;a class="wiki_link" href="/Hemifamity%20family"&gt;laka&lt;/a&gt;, and supplies the optimal patent val for &lt;a class="wiki_link" href="/Hemifamity%20temperaments#Quanic"&gt;quanic&lt;/a&gt; in the 7-, 11-, 13-, 17- and 19-limits, and for 13-limit amity, as well as other temperaments tempering out the huntma, 640/637, the rank five temperament for which it also supplies the optimal patent val. In the 5-limit it tempers out [[tel:1600000/1594323|1600000/1594323]], the amity comma, and |38 -2 -15&amp;gt;, the hemithirds comma, and is an excellent tuning for 5-limit amity. The patent val tempers out 4375/4374, 5120/5103, 6144/6125 and 540/539. Using its alternative mapping &amp;lt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/205%20325%20476"&gt;205 325 476&lt;/a&gt; 525| it can also be used for &lt;a class="wiki_link" href="/Gamelismic%20clan"&gt;hemithirds temperament&lt;/a&gt;; the 13-limit version of this, &amp;lt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/205%20325%20476%20575%20709"&gt;205 325 476 575 709&lt;/a&gt; 759|, is especially noteworthy. It factors into primes as 5 * 41, a fact some advocates of the division make use of; it is also 2460/12, so that a single step is precisely 12 &lt;a class="wiki_link" href="/mina"&gt;minas&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
205et tempers out 540/539, so that it allows &lt;a class="wiki_link" href="/swetismic%20chords"&gt;swetismic chords&lt;/a&gt;; 640/637, so that it allows &lt;a class="wiki_link" href="/huntmic%20chords"&gt;huntmic chords&lt;/a&gt;; 352/351, so that it allows &lt;a class="wiki_link" href="/minthmic%20chords"&gt;minthmic chords&lt;/a&gt;; 1188/1183 and 540/539, so that it allows &lt;a class="wiki_link" href="/kestrel%20chords"&gt;kestrel chords&lt;/a&gt;; and 847/845, so that it allows the &lt;a class="wiki_link" href="/cuthbert%20triad"&gt;cuthbert triad&lt;/a&gt;. This makes it a tuning of exceptional fludity for its degree of accuracy.&lt;br /&gt;
205et tempers out 540/539, so that it allows &lt;a class="wiki_link" href="/swetismic%20chords"&gt;swetismic chords&lt;/a&gt;; 640/637, so that it allows &lt;a class="wiki_link" href="/huntmic%20chords"&gt;huntmic chords&lt;/a&gt;; 352/351, so that it allows &lt;a class="wiki_link" href="/minthmic%20chords"&gt;minthmic chords&lt;/a&gt;; 1188/1183 and 540/539, so that it allows &lt;a class="wiki_link" href="/kestrel%20chords"&gt;kestrel chords&lt;/a&gt;; and 847/845, so that it allows the &lt;a class="wiki_link" href="/cuthbert%20triad"&gt;cuthbert triad&lt;/a&gt;. This makes it a tuning of exceptional fludity for its degree of accuracy.&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="Temperament generators and Tonal Plexus"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Temperament generators and Tonal Plexus&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Temperament generators and Tonal Plexus"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Temperament generators and Tonal Plexus&lt;/h1&gt;
205edo is the default tuning for the &lt;a class="wiki_link_ext" href="http://hpi.zentral.zone/tonalplexus" rel="nofollow"&gt;Tonal Plexus midi controller&lt;/a&gt;. See the &lt;a class="wiki_link_ext" href="http://musictheory.zentral.zone/huntsystem1.html" rel="nofollow"&gt;theory part&lt;/a&gt; on the same website. Aside from the 24\205 generator of quanic, the 58\205 generator of amity, and the 33\205 generator of hemithirds, 205edo supplies an excellent &lt;a class="wiki_link" href="/meantone"&gt;meantone&lt;/a&gt; fifth in 119\205, an excellent &lt;a class="wiki_link" href="/myna"&gt;myna&lt;/a&gt; generator in 53\205, and a very good &lt;a class="wiki_link" href="/porcupine"&gt;porcupine&lt;/a&gt; generator with 28\205, which is also an excellent generator for the higher-limit extension porky, and when sliced in half to 14\205, can even be used for nautilus. These facts are all potentially of significance to anyone using a 205edo based system such as the Tonal Plexus.&lt;br /&gt;
205edo is the default tuning for the &lt;a class="wiki_link_ext" href="http://hpi.zentral.zone/tonalplexus" rel="nofollow"&gt;Tonal Plexus midi controller&lt;/a&gt;. See the &lt;a class="wiki_link_ext" href="http://musictheory.zentral.zone/huntsystem1.html" rel="nofollow"&gt;theory part&lt;/a&gt; on the same website. Aside from the 24\205 generator of quanic, the 58\205 generator of amity, and the 33\205 generator of hemithirds, 205edo supplies an excellent &lt;a class="wiki_link" href="/meantone"&gt;meantone&lt;/a&gt; fifth in 119\205, an excellent &lt;a class="wiki_link" href="/myna"&gt;myna&lt;/a&gt; generator in 53\205, and a very good &lt;a class="wiki_link" href="/porcupine"&gt;porcupine&lt;/a&gt; generator with 28\205, which is also an excellent generator for the higher-limit extension porky, and when sliced in half to 14\205, can even be used for nautilus. These facts are all potentially of significance to anyone using a 205edo based system such as the Tonal Plexus.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The 119\205 meantone fifth is extremely close to the 1/4-comma fifth, being only 0.007 cents sharp of it. Moreover the steps are half a cent flat of 1/4 of a syntonic comma. This makes the Tonal Plexus keyboard potentially of use in implementing &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Nicola_Vicentino" rel="nofollow"&gt;Nicola Vicentino&lt;/a&gt;'s &lt;a class="wiki_link_ext" href="http://www.tonalsoft.com/monzo/vicentino/vicentino.aspx" rel="nofollow"&gt;adaptive-JI scheme of 1555&lt;/a&gt;. It also means that authentic 1/4-comma meantone tuning is, for practical purposes, available in 205 and allows for historically authentic performances of 1/4-comma music on the historically newfangled Tonal Plexus.&lt;br /&gt;
The 119\205 meantone fifth is extremely close to the 1/4-comma fifth, being only 0.007 cents sharp of it. Moreover the steps are half a cent flat of 1/4 of a syntonic comma. This makes the Tonal Plexus keyboard potentially of use in implementing &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Nicola_Vicentino" rel="nofollow"&gt;Nicola Vicentino&lt;/a&gt;'s &lt;a class="wiki_link_ext" href="http://www.tonalsoft.com/monzo/vicentino/vicentino.aspx" rel="nofollow"&gt;adaptive-JI scheme of 1555&lt;/a&gt;. It also means that authentic 1/4-comma meantone tuning is, for practical purposes, available in 205 and allows for historically authentic performances of 1/4-comma music on the historically newfangled Tonal Plexus.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="x205edo MOS"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;205edo MOS&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="x205edo MOS"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;205edo MOS&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x205edo MOS-Quanic (24\205) MOS"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Quanic (24\205) MOS&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x205edo MOS-Quanic (24\205) MOS"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Quanic (24\205) MOS&lt;/h2&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="x205edo MOS-Quanic (24\205) MOS-17 note"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;17 note&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="x205edo MOS-Quanic (24\205) MOS-17 note"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;17 note&lt;/h3&gt;
11 13 11 13 11 13 11 13 11 13 11 13 11 13 11 13 13&lt;br /&gt;
&lt;a class="wiki_link" href="http://tel.wikispaces.com/11%2013%2011%2013%2011%2013%2011"&gt;11 13 11 13 11 13 11&lt;/a&gt; &lt;a class="wiki_link" href="http://tel.wikispaces.com/13%2011%2013%2011%2013%2011%2013"&gt;13 11 13 11 13 11 13&lt;/a&gt; 11 13 13&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc4"&gt;&lt;a name="x205edo MOS-Quanic (24\205) MOS-26 note"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;26 note&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc4"&gt;&lt;a name="x205edo MOS-Quanic (24\205) MOS-26 note"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;26 note&lt;/h3&gt;
11 11 2 11 11 2 11 11 2 11 11 2 11 11 2 11 11 2 11 11 2 11 11 2 11 2&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="x205edo MOS-Amity (58\205) MOS"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Amity (58\205) MOS&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="x205edo MOS-Amity (58\205) MOS"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Amity (58\205) MOS&lt;/h2&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc6"&gt;&lt;a name="x205edo MOS-Amity (58\205) MOS-11 note"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;11 note&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc6"&gt;&lt;a name="x205edo MOS-Amity (58\205) MOS-11 note"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;11 note&lt;/h3&gt;
27 27 4 27 27 4 27 27 4 27 4&lt;br /&gt;
&lt;a class="wiki_link" href="http://tel.wikispaces.com/27%2027%204%2027%2027%204%2027%2027"&gt;27 27 4 27 27 4 27 27&lt;/a&gt; 4 27 4&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc7"&gt;&lt;a name="x205edo MOS-Amity (58\205) MOS-18 note"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;18 note&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc7"&gt;&lt;a name="x205edo MOS-Amity (58\205) MOS-18 note"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;18 note&lt;/h3&gt;
23 4 23 4 4 23 4 23 4 4 23 4 23 4 4 23 4 4&lt;br /&gt;
&lt;a class="wiki_link" href="http://tel.wikispaces.com/23%204%2023%204%204%2023%204%2023%204"&gt;23 4 23 4 4 23 4 23 4&lt;/a&gt; &lt;a class="wiki_link" href="http://tel.wikispaces.com/4%2023%204%2023%204%204%2023%204%204"&gt;4 23 4 23 4 4 23 4 4&lt;/a&gt;&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc8"&gt;&lt;a name="x205edo MOS-Amity (58\205) MOS-25 note"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;25 note&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc8"&gt;&lt;a name="x205edo MOS-Amity (58\205) MOS-25 note"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;25 note&lt;/h3&gt;
19 4 4 19 4 4 4 19 4 4 19 4 4 4 19 4 4 19 4 4 4 19 4 4 4&lt;br /&gt;
&lt;a class="wiki_link" href="http://tel.wikispaces.com/19%204%204%2019%204%204%204%2019%204"&gt;19 4 4 19 4 4 4 19 4&lt;/a&gt; &lt;a class="wiki_link" href="http://tel.wikispaces.com/4%2019%204%204%204%2019%204%204%2019%204"&gt;4 19 4 4 4 19 4 4 19 4&lt;/a&gt; 4 4 19 4 4 4&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="x205edo MOS-Hemithirds (33\205) MOS"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Hemithirds (33\205) MOS&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="x205edo MOS-Hemithirds (33\205) MOS"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Hemithirds (33\205) MOS&lt;/h2&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc10"&gt;&lt;a name="x205edo MOS-Hemithirds (33\205) MOS-13 note"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;13 note&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc10"&gt;&lt;a name="x205edo MOS-Hemithirds (33\205) MOS-13 note"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;13 note&lt;/h3&gt;
26 7 26 7 26 7 26 7 26 7 26 7 7&lt;br /&gt;
&lt;a class="wiki_link" href="http://tel.wikispaces.com/26%207%2026%207%2026%207%2026%207%2026"&gt;26 7 26 7 26 7 26 7 26&lt;/a&gt; 7 26 7 7&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc11"&gt;&lt;a name="x205edo MOS-Hemithirds (33\205) MOS-19 note"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;19 note&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc11"&gt;&lt;a name="x205edo MOS-Hemithirds (33\205) MOS-19 note"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;19 note&lt;/h3&gt;
19 7 7 19 7 7 19 7 7 19 7 7 19 7 7 19 7 7 7&lt;br /&gt;
&lt;a class="wiki_link" href="http://tel.wikispaces.com/19%207%207%2019%207%207%2019%207%207"&gt;19 7 7 19 7 7 19 7 7&lt;/a&gt; &lt;a class="wiki_link" href="http://tel.wikispaces.com/19%207%207%2019%207%207%2019%207%207"&gt;19 7 7 19 7 7 19 7 7&lt;/a&gt; 7&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc12"&gt;&lt;a name="x205edo MOS-Hemithirds (33\205) MOS-25 note"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;25 note&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc12"&gt;&lt;a name="x205edo MOS-Hemithirds (33\205) MOS-25 note"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;25 note&lt;/h3&gt;
12 7 7 7 12 7 7 7 12 7 7 7 12 7 7 7 12 7 7 7 12 7 7 7 7&lt;br /&gt;
&lt;a class="wiki_link" href="http://tel.wikispaces.com/12%207%207%207%2012%207%207%207%2012"&gt;12 7 7 7 12 7 7 7 12&lt;/a&gt; 7 7 &lt;a class="wiki_link" href="http://tel.wikispaces.com/7%2012%207%207%207%2012%207%207%207%2012"&gt;7 12 7 7 7 12 7 7 7 12&lt;/a&gt; 7 7 7 7&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc13"&gt;&lt;a name="x205edo MOS-Hemithirds (33\205) MOS-31 notes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;31 notes&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc13"&gt;&lt;a name="x205edo MOS-Hemithirds (33\205) MOS-31 notes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;31 notes&lt;/h3&gt;
5 7 7 7 7 5 7 7 7 7 5 7 7 7 7 5 7 7 7 7 5 7 7 7 7 5 7 7 7 7 7&lt;br /&gt;
5 7 7 7 7 5 7 7 7 7 5 7 7 7 7 5 7 7 7 7 5 7 7 7 7 5 7 7 7 7 7&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc14"&gt;&lt;a name="x205edo MOS-Meantone (119\205) MOS"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;Meantone (119\205) MOS&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc14"&gt;&lt;a name="x205edo MOS-Meantone (119\205) MOS"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;Meantone (119\205) MOS&lt;/h2&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc15"&gt;&lt;a name="x205edo MOS-Meantone (119\205) MOS-12 note"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;12 note&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc15"&gt;&lt;a name="x205edo MOS-Meantone (119\205) MOS-12 note"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;12 note&lt;/h3&gt;
13 20 13 20 13 20 20 13 20 13 20 20&lt;br /&gt;
&lt;a class="wiki_link" href="http://tel.wikispaces.com/13%2020%2013%2020%2013%2020%2020"&gt;13 20 13 20 13 20 20&lt;/a&gt; &lt;a class="wiki_link" href="http://tel.wikispaces.com/13%2020%2013%2020%2020"&gt;13 20 13 20 20&lt;/a&gt;&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc16"&gt;&lt;a name="x205edo MOS-Meantone (119\205) MOS-19 note"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;19 note&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc16"&gt;&lt;a name="x205edo MOS-Meantone (119\205) MOS-19 note"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;19 note&lt;/h3&gt;
13 13 7 13 13 7 13 13 7 13 7 13 13 7 13 13 7 13 7&lt;br /&gt;
&lt;a class="wiki_link" href="http://tel.wikispaces.com/13%2013%207%2013%2013%207%2013%2013"&gt;13 13 7 13 13 7 13 13&lt;/a&gt; &lt;a class="wiki_link" href="http://tel.wikispaces.com/7%2013%207%2013%2013%207%2013%2013%207"&gt;7 13 7 13 13 7 13 13 7&lt;/a&gt; 13 7&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc17"&gt;&lt;a name="x205edo MOS-Meantone (119\205) MOS-31 notes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;31 notes&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc17"&gt;&lt;a name="x205edo MOS-Meantone (119\205) MOS-31 notes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;31 notes&lt;/h3&gt;
6 7 6 7 7 6 7 6 7 7 6 7 6 7 7 6 7 7 6 7 6 7 7 6 7 6 7 7 6 7 7&lt;br /&gt;
6 7 6 7 7 6 7 6 7 7 6 7 6 7 7 6 7 7 6 7 6 7 7 6 7 6 7 7 6 7 7&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc18"&gt;&lt;a name="x205edo MOS-Myna (53\205) MOS"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;Myna (53\205) MOS&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc18"&gt;&lt;a name="x205edo MOS-Myna (53\205) MOS"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;Myna (53\205) MOS&lt;/h2&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc19"&gt;&lt;a name="x205edo MOS-Myna (53\205) MOS-11 note"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;11 note&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc19"&gt;&lt;a name="x205edo MOS-Myna (53\205) MOS-11 note"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;11 note&lt;/h3&gt;
7 7 39 7 7 39 7 7 39 7 39&lt;br /&gt;
7 &lt;a class="wiki_link" href="http://tel.wikispaces.com/7%2039%207%207%2039%207%207%2039%207%2039"&gt;7 39 7 7 39 7 7 39 7 39&lt;/a&gt;&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc20"&gt;&lt;a name="x205edo MOS-Myna (53\205) MOS-15 note"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;15 note&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc20"&gt;&lt;a name="x205edo MOS-Myna (53\205) MOS-15 note"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;15 note&lt;/h3&gt;
7 7 7 32 7 7 7 32 7 7 7 32 7 7 32&lt;br /&gt;
7 7 &lt;a class="wiki_link" href="http://tel.wikispaces.com/7%2032%207%207%207%2032%207%207%207%2032"&gt;7 32 7 7 7 32 7 7 7 32&lt;/a&gt; 7 7 32&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc21"&gt;&lt;a name="x205edo MOS-Myna (53\205) MOS-19 note"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;19 note&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc21"&gt;&lt;a name="x205edo MOS-Myna (53\205) MOS-19 note"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;19 note&lt;/h3&gt;
7 7 7 7 25 7 7 7 7 25 7 7 7 7 25 7 7 7 25&lt;br /&gt;
7 7 7 &lt;a class="wiki_link" href="http://tel.wikispaces.com/7%2025%207%207%207%207%2025%207%207%207%207"&gt;7 25 7 7 7 7 25 7 7 7 7&lt;/a&gt; &lt;a class="wiki_link" href="http://tel.wikispaces.com/25%207%207%207%2025"&gt;25 7 7 7 25&lt;/a&gt;&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc22"&gt;&lt;a name="x205edo MOS-Myna (53\205) MOS-23 note"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;23 note&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc22"&gt;&lt;a name="x205edo MOS-Myna (53\205) MOS-23 note"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;23 note&lt;/h3&gt;
7 7 7 7 7 18 7 7 7 7 7 18 7 7 7 7 7 18 7 7 7 7 18&lt;br /&gt;
7 7 7 7 &lt;a class="wiki_link" href="http://tel.wikispaces.com/7%2018%207%207%207%207%207%2018%207%207%207"&gt;7 18 7 7 7 7 7 18 7 7 7&lt;/a&gt; 7 &lt;a class="wiki_link" href="http://tel.wikispaces.com/7%2018%207%207%207%207%2018"&gt;7 18 7 7 7 7 18&lt;/a&gt;&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc23"&gt;&lt;a name="x205edo MOS-Myna (53\205) MOS-27 note"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;27 note&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc23"&gt;&lt;a name="x205edo MOS-Myna (53\205) MOS-27 note"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;27 note&lt;/h3&gt;
7 7 7 7 7 7 11 7 7 7 7 7 7 11 7 7 7 7 7 7 11 7 7 7 7 7 11&lt;br /&gt;
7 7 7 7 7 &lt;a class="wiki_link" href="http://tel.wikispaces.com/7%2011%207%207%207%207%207%207%2011%207%207"&gt;7 11 7 7 7 7 7 7 11 7 7&lt;/a&gt; 7 7 7 &lt;a class="wiki_link" href="http://tel.wikispaces.com/7%2011%207%207%207%207%207%2011"&gt;7 11 7 7 7 7 7 11&lt;/a&gt;&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc24"&gt;&lt;a name="x205edo MOS-Myna (53\205) MOS-31 notes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;31 notes&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc24"&gt;&lt;a name="x205edo MOS-Myna (53\205) MOS-31 notes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;31 notes&lt;/h3&gt;
7 7 7 7 7 7 7 4 7 7 7 7 7 7 7 4 7 7 7 7 7 7 7 4 7 7 7 7 7 7 4&lt;br /&gt;
7 7 7 7 7 7 7 4 7 7 7 7 7 7 7 4 7 7 7 7 7 7 7 4 7 7 7 7 7 7 4&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:50:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc25"&gt;&lt;a name="x205edo MOS-Porcupine (28\205) MOS"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;Porcupine (28\205) MOS&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:50:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc25"&gt;&lt;a name="x205edo MOS-Porcupine (28\205) MOS"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;Porcupine (28\205) MOS&lt;/h2&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:52:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc26"&gt;&lt;a name="x205edo MOS-Porcupine (28\205) MOS-15 note"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;15 note&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:52:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc26"&gt;&lt;a name="x205edo MOS-Porcupine (28\205) MOS-15 note"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;15 note&lt;/h3&gt;
19 9 19 9 19 9 19 9 19 9 19 9 19 9 9&lt;br /&gt;
&lt;a class="wiki_link" href="http://tel.wikispaces.com/19%209%2019%209%2019%209%2019%209%2019"&gt;19 9 19 9 19 9 19 9 19&lt;/a&gt; &lt;a class="wiki_link" href="http://tel.wikispaces.com/9%2019%209%2019%209%209"&gt;9 19 9 19 9 9&lt;/a&gt;&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:54:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc27"&gt;&lt;a name="x205edo MOS-Porcupine (28\205) MOS-22 note"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:54 --&gt;22 note&lt;/h3&gt;
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10 9 9 10 9 9 10 9 9 10 9 9 10 9 9 10 9 9 10 9 9 9&lt;br /&gt;
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Revision as of 15:45, 7 December 2016

IMPORTED REVISION FROM WIKISPACES

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This revision was by author JosephRuhf and made on 2016-12-07 15:45:15 UTC.
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Original Wikitext content:

205EDO divides the octave into 205 parts of 5.854 cents each. It can serve as a tuning for various temperaments, such as [[Ragismic microtemperaments|amity]] or [[Hemifamity family|laka]], and supplies the optimal patent val for [[Hemifamity temperaments#Quanic|quanic]] in the 7-, 11-, 13-, 17- and 19-limits, and for 13-limit amity, as well as other temperaments tempering out the huntma, 640/637, the rank five temperament for which it also supplies the optimal patent val. In the 5-limit it tempers out [[tel:1600000/1594323|1600000/1594323]], the amity comma, and |38 -2 -15>, the hemithirds comma, and is an excellent tuning for 5-limit amity. The patent val tempers out 4375/4374, 5120/5103, 6144/6125 and 540/539. Using its alternative mapping <[[tel:205 325 476|205 325 476]] 525| it can also be used for [[Gamelismic clan|hemithirds temperament]]; the 13-limit version of this, <[[tel:205 325 476 575 709|205 325 476 575 709]] 759|, is especially noteworthy. It factors into primes as 5 * 41, a fact some advocates of the division make use of; it is also 2460/12, so that a single step is precisely 12 [[mina|minas]].

205et tempers out 540/539, so that it allows [[swetismic chords]]; 640/637, so that it allows [[huntmic chords]]; 352/351, so that it allows [[minthmic chords]]; 1188/1183 and 540/539, so that it allows [[kestrel chords]]; and 847/845, so that it allows the [[cuthbert triad]]. This makes it a tuning of exceptional fludity for its degree of accuracy.

=Temperament generators and Tonal Plexus= 
205edo is the default tuning for the [[http://hpi.zentral.zone/tonalplexus|Tonal Plexus midi controller]]. See the [[http://musictheory.zentral.zone/huntsystem1.html|theory part]] on the same website. Aside from the 24\205 generator of quanic, the 58\205 generator of amity, and the 33\205 generator of hemithirds, 205edo supplies an excellent [[meantone]] fifth in 119\205, an excellent [[myna]] generator in 53\205, and a very good [[porcupine]] generator with 28\205, which is also an excellent generator for the higher-limit extension porky, and when sliced in half to 14\205, can even be used for nautilus. These facts are all potentially of significance to anyone using a 205edo based system such as the Tonal Plexus.

The 119\205 meantone fifth is extremely close to the 1/4-comma fifth, being only 0.007 cents sharp of it. Moreover the steps are half a cent flat of 1/4 of a syntonic comma. This makes the Tonal Plexus keyboard potentially of use in implementing [[http://en.wikipedia.org/wiki/Nicola_Vicentino|Nicola Vicentino]]'s [[http://www.tonalsoft.com/monzo/vicentino/vicentino.aspx|adaptive-JI scheme of 1555]]. It also means that authentic 1/4-comma meantone tuning is, for practical purposes, available in 205 and allows for historically authentic performances of 1/4-comma music on the historically newfangled Tonal Plexus.

=205edo MOS= 
==Quanic (24\205) MOS== 

===17 note=== 
[[tel:11 13 11 13 11 13 11|11 13 11 13 11 13 11]] [[tel:13 11 13 11 13 11 13|13 11 13 11 13 11 13]] 11 13 13

===26 note=== 
[[tel:11 11 2 11 11 2 11 11|11 11 2 11 11 2 11 11]] [[tel:2 11 11 2 11 11 2 11 11|2 11 11 2 11 11 2 11 11]] [[tel:2 11 11 2 11 11 2 11 2|2 11 11 2 11 11 2 11 2]]

==Amity (58\205) MOS== 

===11 note=== 
[[tel:27 27 4 27 27 4 27 27|27 27 4 27 27 4 27 27]] 4 27 4

===18 note=== 
[[tel:23 4 23 4 4 23 4 23 4|23 4 23 4 4 23 4 23 4]] [[tel:4 23 4 23 4 4 23 4 4|4 23 4 23 4 4 23 4 4]]

===25 note=== 
[[tel:19 4 4 19 4 4 4 19 4|19 4 4 19 4 4 4 19 4]] [[tel:4 19 4 4 4 19 4 4 19 4|4 19 4 4 4 19 4 4 19 4]] 4 4 19 4 4 4

==Hemithirds (33\205) MOS== 

===13 note=== 
[[tel:26 7 26 7 26 7 26 7 26|26 7 26 7 26 7 26 7 26]] 7 26 7 7

===19 note=== 
[[tel:19 7 7 19 7 7 19 7 7|19 7 7 19 7 7 19 7 7]] [[tel:19 7 7 19 7 7 19 7 7|19 7 7 19 7 7 19 7 7]] 7

===25 note=== 
[[tel:12 7 7 7 12 7 7 7 12|12 7 7 7 12 7 7 7 12]] 7 7 [[tel:7 12 7 7 7 12 7 7 7 12|7 12 7 7 7 12 7 7 7 12]] 7 7 7 7

===31 notes=== 
5 7 7 7 7 5 7 7 7 7 5 7 7 7 7 5 7 7 7 7 5 7 7 7 7 5 7 7 7 7 7

==Meantone (119\205) MOS== 

===12 note=== 
[[tel:13 20 13 20 13 20 20|13 20 13 20 13 20 20]] [[tel:13 20 13 20 20|13 20 13 20 20]]

===19 note=== 
[[tel:13 13 7 13 13 7 13 13|13 13 7 13 13 7 13 13]] [[tel:7 13 7 13 13 7 13 13 7|7 13 7 13 13 7 13 13 7]] 13 7

===31 notes=== 
6 7 6 7 7 6 7 6 7 7 6 7 6 7 7 6 7 7 6 7 6 7 7 6 7 6 7 7 6 7 7

==Myna (53\205) MOS== 

===11 note=== 
7 [[tel:7 39 7 7 39 7 7 39 7 39|7 39 7 7 39 7 7 39 7 39]]

===15 note=== 
7 7 [[tel:7 32 7 7 7 32 7 7 7 32|7 32 7 7 7 32 7 7 7 32]] 7 7 32

===19 note=== 
7 7 7 [[tel:7 25 7 7 7 7 25 7 7 7 7|7 25 7 7 7 7 25 7 7 7 7]] [[tel:25 7 7 7 25|25 7 7 7 25]]

===23 note=== 
7 7 7 7 [[tel:7 18 7 7 7 7 7 18 7 7 7|7 18 7 7 7 7 7 18 7 7 7]] 7 [[tel:7 18 7 7 7 7 18|7 18 7 7 7 7 18]]

===27 note=== 
7 7 7 7 7 [[tel:7 11 7 7 7 7 7 7 11 7 7|7 11 7 7 7 7 7 7 11 7 7]] 7 7 7 [[tel:7 11 7 7 7 7 7 11|7 11 7 7 7 7 7 11]]

===31 notes=== 
7 7 7 7 7 7 7 4 7 7 7 7 7 7 7 4 7 7 7 7 7 7 7 4 7 7 7 7 7 7 4

==Porcupine (28\205) MOS== 

===15 note=== 
[[tel:19 9 19 9 19 9 19 9 19|19 9 19 9 19 9 19 9 19]] [[tel:9 19 9 19 9 9|9 19 9 19 9 9]]

===22 note=== 
[[tel:10 9 9 10 9 9 10 9 9|10 9 9 10 9 9 10 9 9]] [[tel:10 9 9 10 9 9 10 9 9|10 9 9 10 9 9 10 9 9]] 10 9 9 9

===29 note=== 
1 9 9 9 1 9 9 9 1 9 9 9 1 9 9 9 1 9 9 9 1 9 9 9 1 9 9 9 9

Original HTML content:

<html><head><title>205edo</title></head><body>205EDO divides the octave into 205 parts of 5.854 cents each. It can serve as a tuning for various temperaments, such as <a class="wiki_link" href="/Ragismic%20microtemperaments">amity</a> or <a class="wiki_link" href="/Hemifamity%20family">laka</a>, and supplies the optimal patent val for <a class="wiki_link" href="/Hemifamity%20temperaments#Quanic">quanic</a> in the 7-, 11-, 13-, 17- and 19-limits, and for 13-limit amity, as well as other temperaments tempering out the huntma, 640/637, the rank five temperament for which it also supplies the optimal patent val. In the 5-limit it tempers out [[tel:1600000/1594323|1600000/1594323]], the amity comma, and |38 -2 -15&gt;, the hemithirds comma, and is an excellent tuning for 5-limit amity. The patent val tempers out 4375/4374, 5120/5103, 6144/6125 and 540/539. Using its alternative mapping &lt;<a class="wiki_link" href="http://tel.wikispaces.com/205%20325%20476">205 325 476</a> 525| it can also be used for <a class="wiki_link" href="/Gamelismic%20clan">hemithirds temperament</a>; the 13-limit version of this, &lt;<a class="wiki_link" href="http://tel.wikispaces.com/205%20325%20476%20575%20709">205 325 476 575 709</a> 759|, is especially noteworthy. It factors into primes as 5 * 41, a fact some advocates of the division make use of; it is also 2460/12, so that a single step is precisely 12 <a class="wiki_link" href="/mina">minas</a>.<br />
<br />
205et tempers out 540/539, so that it allows <a class="wiki_link" href="/swetismic%20chords">swetismic chords</a>; 640/637, so that it allows <a class="wiki_link" href="/huntmic%20chords">huntmic chords</a>; 352/351, so that it allows <a class="wiki_link" href="/minthmic%20chords">minthmic chords</a>; 1188/1183 and 540/539, so that it allows <a class="wiki_link" href="/kestrel%20chords">kestrel chords</a>; and 847/845, so that it allows the <a class="wiki_link" href="/cuthbert%20triad">cuthbert triad</a>. This makes it a tuning of exceptional fludity for its degree of accuracy.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Temperament generators and Tonal Plexus"></a><!-- ws:end:WikiTextHeadingRule:0 -->Temperament generators and Tonal Plexus</h1>
 205edo is the default tuning for the <a class="wiki_link_ext" href="http://hpi.zentral.zone/tonalplexus" rel="nofollow">Tonal Plexus midi controller</a>. See the <a class="wiki_link_ext" href="http://musictheory.zentral.zone/huntsystem1.html" rel="nofollow">theory part</a> on the same website. Aside from the 24\205 generator of quanic, the 58\205 generator of amity, and the 33\205 generator of hemithirds, 205edo supplies an excellent <a class="wiki_link" href="/meantone">meantone</a> fifth in 119\205, an excellent <a class="wiki_link" href="/myna">myna</a> generator in 53\205, and a very good <a class="wiki_link" href="/porcupine">porcupine</a> generator with 28\205, which is also an excellent generator for the higher-limit extension porky, and when sliced in half to 14\205, can even be used for nautilus. These facts are all potentially of significance to anyone using a 205edo based system such as the Tonal Plexus.<br />
<br />
The 119\205 meantone fifth is extremely close to the 1/4-comma fifth, being only 0.007 cents sharp of it. Moreover the steps are half a cent flat of 1/4 of a syntonic comma. This makes the Tonal Plexus keyboard potentially of use in implementing <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Nicola_Vicentino" rel="nofollow">Nicola Vicentino</a>'s <a class="wiki_link_ext" href="http://www.tonalsoft.com/monzo/vicentino/vicentino.aspx" rel="nofollow">adaptive-JI scheme of 1555</a>. It also means that authentic 1/4-comma meantone tuning is, for practical purposes, available in 205 and allows for historically authentic performances of 1/4-comma music on the historically newfangled Tonal Plexus.<br />
<br />
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