205edo: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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>

<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>, 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 <205 325 476 525| it can also be used for [[Gamelismic clan|hemithirds temperament]]; the 13-limit version of this, <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>, 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===

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===

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==

===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===

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===

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==

===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 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===

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===

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===

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===

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===

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 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===

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===

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===

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===

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===

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===

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===

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===

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>

<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"><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 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 <a class="wiki_link" href="/Gamelismic%20clan">hemithirds temperament</a>; 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 <a class="wiki_link" href="/mina">minas</a>.<br />

<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"><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 />

<h1 id="toc0"><a name="Temperament generators and Tonal Plexus"></a>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 />

<h1 id="toc1"><a name="x205edo MOS"></a>205edo MOS</h1>

<h2 id="toc2"><a name="x205edo MOS-Quanic (24\205) MOS"></a>Quanic (24\205) MOS</h2>

<br />

<h3 id="toc3"><a name="x205edo MOS-Quanic (24\205) MOS-17 note"></a>17 note</h3>

11 13 11 13 11 13 11 13 11 13 11 13 11 13 11 13 13<br />

<br />

<h3 id="toc4"><a name="x205edo MOS-Quanic (24\205) MOS-26 note"></a>26 note</h3>

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<br />

<br />

<h2 id="toc5"><a name="x205edo MOS-Amity (58\205) MOS"></a>Amity (58\205) MOS</h2>

<br />

<h3 id="toc6"><a name="x205edo MOS-Amity (58\205) MOS-11 note"></a>11 note</h3>

27 27 4 27 27 4 27 27 4 27 4<br />

<br />

<h3 id="toc7"><a name="x205edo MOS-Amity (58\205) MOS-18 note"></a>18 note</h3>

23 4 23 4 4 23 4 23 4 4 23 4 23 4 4 23 4 4<br />

<br />

<h3 id="toc8"><a name="x205edo MOS-Amity (58\205) MOS-25 note"></a>25 note</h3>

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<br />

<br />

<h2 id="toc9"><a name="x205edo MOS-Hemithirds (33\205) MOS"></a>Hemithirds (33\205) MOS</h2>

<br />

<h3 id="toc10"><a name="x205edo MOS-Hemithirds (33\205) MOS-13 note"></a>13 note</h3>

26 7 26 7 26 7 26 7 26 7 26 7 7<br />

<br />

<h3 id="toc11"><a name="x205edo MOS-Hemithirds (33\205) MOS-19 note"></a>19 note</h3>

19 7 7 19 7 7 19 7 7 19 7 7 19 7 7 19 7 7 7<br />

<br />

<h3 id="toc12"><a name="x205edo MOS-Hemithirds (33\205) MOS-25 note"></a>25 note</h3>

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<br />

<br />

<h3 id="toc13"><a name="x205edo MOS-Hemithirds (33\205) MOS-31 notes"></a>31 notes</h3>

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<br />

<br />

<h2 id="toc14"><a name="x205edo MOS-Meantone (119\205) MOS"></a>Meantone (119\205) MOS</h2>

<br />

<h3 id="toc15"><a name="x205edo MOS-Meantone (119\205) MOS-12 note"></a>12 note</h3>

13 20 13 20 13 20 20 13 20 13 20 20<br />

<br />

<h3 id="toc16"><a name="x205edo MOS-Meantone (119\205) MOS-19 note"></a>19 note</h3>

13 13 7 13 13 7 13 13 7 13 7 13 13 7 13 13 7 13 7<br />

<br />

<h3 id="toc17"><a name="x205edo MOS-Meantone (119\205) MOS-31 notes"></a>31 notes</h3>

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<br />

<br />

<h2 id="toc18"><a name="x205edo MOS-Myna (53\205) MOS"></a>Myna (53\205) MOS</h2>

<br />

<h3 id="toc19"><a name="x205edo MOS-Myna (53\205) MOS-11 note"></a>11 note</h3>

7 7 39 7 7 39 7 7 39 7 39<br />

7 <a class="wiki_link" href="http://tel.wikispaces.com/7%2039%207%207%2039%207%207%2039%207%2039">7 39 7 7 39 7 7 39 7 39</a><br />

<br />

<h3 id="toc20"><a name="x205edo MOS-Myna (53\205) MOS-15 note"></a>15 note</h3>

7 7 7 32 7 7 7 32 7 7 7 32 7 7 32<br />

7 7 <a class="wiki_link" href="http://tel.wikispaces.com/7%2032%207%207%207%2032%207%207%207%2032">7 32 7 7 7 32 7 7 7 32</a> 7 7 32<br />

<br />

<h3 id="toc21"><a name="x205edo MOS-Myna (53\205) MOS-19 note"></a>19 note</h3>

7 7 7 7 25 7 7 7 7 25 7 7 7 7 25 7 7 7 25<br />

7 7 7 <a class="wiki_link" href="http://tel.wikispaces.com/7%2025%207%207%207%207%2025%207%207%207%207">7 25 7 7 7 7 25 7 7 7 7</a> <a class="wiki_link" href="http://tel.wikispaces.com/25%207%207%207%2025">25 7 7 7 25</a><br />

<br />

<h3 id="toc22"><a name="x205edo MOS-Myna (53\205) MOS-23 note"></a>23 note</h3>

7 7 7 7 7 18 7 7 7 7 7 18 7 7 7 7 7 18 7 7 7 7 18<br />

7 7 7 7 <a class="wiki_link" href="http://tel.wikispaces.com/7%2018%207%207%207%207%207%2018%207%207%207">7 18 7 7 7 7 7 18 7 7 7</a> 7 <a class="wiki_link" href="http://tel.wikispaces.com/7%2018%207%207%207%207%2018">7 18 7 7 7 7 18</a><br />

<br />

<h3 id="toc23"><a name="x205edo MOS-Myna (53\205) MOS-27 note"></a>27 note</h3>

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<br />

7 7 7 7 7 <a class="wiki_link" href="http://tel.wikispaces.com/7%2011%207%207%207%207%207%207%2011%207%207">7 11 7 7 7 7 7 7 11 7 7</a> 7 7 7 <a class="wiki_link" href="http://tel.wikispaces.com/7%2011%207%207%207%207%207%2011">7 11 7 7 7 7 7 11</a><br />

<br />

<h3 id="toc24"><a name="x205edo MOS-Myna (53\205) MOS-31 notes"></a>31 notes</h3>

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<br />

<br />

<h2 id="toc25"><a name="x205edo MOS-Porcupine (28\205) MOS"></a>Porcupine (28\205) MOS</h2>

<br />

<h3 id="toc26"><a name="x205edo MOS-Porcupine (28\205) MOS-15 note"></a>15 note</h3>

19 9 19 9 19 9 19 9 19 9 19 9 19 9 9<br />

<br />

<h3 id="toc27"><a name="x205edo MOS-Porcupine (28\205) MOS-22 note"></a>22 note</h3>

10 9 9 10 9 9 10 9 9 10 9 9 10 9 9 10 9 9 10 9 9 9<br />

<br />

<h3 id="toc28"><a name="x205edo MOS-Porcupine (28\205) MOS-29 note"></a>29 note</h3>

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</body></html></pre></div>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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>
 <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]].
 et 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=
 edo 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===
-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===
-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==
 ===11 note===
-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===
-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===
-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==
 ===13 note===
-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===
-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===
-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===
 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===
-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===
-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===
 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 39 7 7 39 7 7 39 7 39
+[[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 32 7 7 7 32 7 7 7 32 7 7 32
+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 25 7 7 7 7 25 7 7 7 7 25 7 7 7 25
+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 18 7 7 7 7 7 18 7 7 7 7 7 18 7 7 7 7 18
+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 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 [[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 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===
-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===
-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===
 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>
-<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;
 et 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;!-- 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;
 edo 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;
 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;!-- 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;
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-&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;
-13 11 13 11 13 11 13 11 13 11 13 11 13 11 13 13&lt;br /&gt;
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 &lt;br /&gt;
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-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;br /&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;
-&lt;br /&gt;
+ &lt;br /&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 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;
 &lt;br /&gt;
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-4 23 4 4 23 4 23 4 4 23 4 23 4 4 23 4 4&lt;br /&gt;
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 &lt;br /&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;
-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;
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 &lt;br /&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;
-&lt;br /&gt;
+ &lt;br /&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;
-7 26 7 26 7 26 7 26 7 26 7 7&lt;br /&gt;
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 &lt;br /&gt;
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-7 7 19 7 7 19 7 7 19 7 7 19 7 7 19 7 7 7&lt;br /&gt;
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 &lt;br /&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;
-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;
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 &lt;br /&gt;
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-&lt;br /&gt;
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