205edo
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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>, 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 <<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, <<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:<h1> --><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 /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="x205edo MOS"></a><!-- ws:end:WikiTextHeadingRule:2 -->205edo MOS</h1> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="x205edo MOS-Quanic (24\205) MOS"></a><!-- ws:end:WikiTextHeadingRule:4 -->Quanic (24\205) MOS</h2> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h3> --><h3 id="toc3"><a name="x205edo MOS-Quanic (24\205) MOS-17 note"></a><!-- ws:end:WikiTextHeadingRule:6 -->17 note</h3> <a class="wiki_link" href="http://tel.wikispaces.com/11%2013%2011%2013%2011%2013%2011">11 13 11 13 11 13 11</a> <a class="wiki_link" href="http://tel.wikispaces.com/13%2011%2013%2011%2013%2011%2013">13 11 13 11 13 11 13</a> 11 13 13<br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h3> --><h3 id="toc4"><a name="x205edo MOS-Quanic (24\205) MOS-26 note"></a><!-- ws:end:WikiTextHeadingRule:8 -->26 note</h3> <a class="wiki_link" href="http://tel.wikispaces.com/11%2011%202%2011%2011%202%2011%2011">11 11 2 11 11 2 11 11</a> <a class="wiki_link" href="http://tel.wikispaces.com/2%2011%2011%202%2011%2011%202%2011%2011">2 11 11 2 11 11 2 11 11</a> <a class="wiki_link" href="http://tel.wikispaces.com/2%2011%2011%202%2011%2011%202%2011%202">2 11 11 2 11 11 2 11 2</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h2> --><h2 id="toc5"><a name="x205edo MOS-Amity (58\205) MOS"></a><!-- ws:end:WikiTextHeadingRule:10 -->Amity (58\205) MOS</h2> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h3> --><h3 id="toc6"><a name="x205edo MOS-Amity (58\205) MOS-11 note"></a><!-- ws:end:WikiTextHeadingRule:12 -->11 note</h3> <a class="wiki_link" href="http://tel.wikispaces.com/27%2027%204%2027%2027%204%2027%2027">27 27 4 27 27 4 27 27</a> 4 27 4<br /> <br /> <!-- ws:start:WikiTextHeadingRule:14:<h3> --><h3 id="toc7"><a name="x205edo MOS-Amity (58\205) MOS-18 note"></a><!-- ws:end:WikiTextHeadingRule:14 -->18 note</h3> <a class="wiki_link" href="http://tel.wikispaces.com/23%204%2023%204%204%2023%204%2023%204">23 4 23 4 4 23 4 23 4</a> <a class="wiki_link" href="http://tel.wikispaces.com/4%2023%204%2023%204%204%2023%204%204">4 23 4 23 4 4 23 4 4</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:16:<h3> --><h3 id="toc8"><a name="x205edo MOS-Amity (58\205) MOS-25 note"></a><!-- ws:end:WikiTextHeadingRule:16 -->25 note</h3> <a class="wiki_link" href="http://tel.wikispaces.com/19%204%204%2019%204%204%204%2019%204">19 4 4 19 4 4 4 19 4</a> <a class="wiki_link" href="http://tel.wikispaces.com/4%2019%204%204%204%2019%204%204%2019%204">4 19 4 4 4 19 4 4 19 4</a> 4 4 19 4 4 4<br /> <br /> <!-- ws:start:WikiTextHeadingRule:18:<h2> --><h2 id="toc9"><a name="x205edo MOS-Hemithirds (33\205) MOS"></a><!-- ws:end:WikiTextHeadingRule:18 -->Hemithirds (33\205) MOS</h2> <br /> <!-- ws:start:WikiTextHeadingRule:20:<h3> --><h3 id="toc10"><a name="x205edo MOS-Hemithirds (33\205) MOS-13 note"></a><!-- ws:end:WikiTextHeadingRule:20 -->13 note</h3> <a class="wiki_link" href="http://tel.wikispaces.com/26%207%2026%207%2026%207%2026%207%2026">26 7 26 7 26 7 26 7 26</a> 7 26 7 7<br /> <br /> <!-- ws:start:WikiTextHeadingRule:22:<h3> --><h3 id="toc11"><a name="x205edo MOS-Hemithirds (33\205) MOS-19 note"></a><!-- ws:end:WikiTextHeadingRule:22 -->19 note</h3> <a class="wiki_link" href="http://tel.wikispaces.com/19%207%207%2019%207%207%2019%207%207">19 7 7 19 7 7 19 7 7</a> <a class="wiki_link" href="http://tel.wikispaces.com/19%207%207%2019%207%207%2019%207%207">19 7 7 19 7 7 19 7 7</a> 7<br /> <br /> <!-- ws:start:WikiTextHeadingRule:24:<h3> --><h3 id="toc12"><a name="x205edo MOS-Hemithirds (33\205) MOS-25 note"></a><!-- ws:end:WikiTextHeadingRule:24 -->25 note</h3> <a class="wiki_link" href="http://tel.wikispaces.com/12%207%207%207%2012%207%207%207%2012">12 7 7 7 12 7 7 7 12</a> 7 7 <a class="wiki_link" href="http://tel.wikispaces.com/7%2012%207%207%207%2012%207%207%207%2012">7 12 7 7 7 12 7 7 7 12</a> 7 7 7 7<br /> <br /> <!-- ws:start:WikiTextHeadingRule:26:<h3> --><h3 id="toc13"><a name="x205edo MOS-Hemithirds (33\205) MOS-31 notes"></a><!-- ws:end:WikiTextHeadingRule:26 -->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 /> <!-- ws:start:WikiTextHeadingRule:28:<h2> --><h2 id="toc14"><a name="x205edo MOS-Meantone (119\205) MOS"></a><!-- ws:end:WikiTextHeadingRule:28 -->Meantone (119\205) MOS</h2> <br /> <!-- ws:start:WikiTextHeadingRule:30:<h3> --><h3 id="toc15"><a name="x205edo MOS-Meantone (119\205) MOS-12 note"></a><!-- ws:end:WikiTextHeadingRule:30 -->12 note</h3> <a class="wiki_link" href="http://tel.wikispaces.com/13%2020%2013%2020%2013%2020%2020">13 20 13 20 13 20 20</a> <a class="wiki_link" href="http://tel.wikispaces.com/13%2020%2013%2020%2020">13 20 13 20 20</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:32:<h3> --><h3 id="toc16"><a name="x205edo MOS-Meantone (119\205) MOS-19 note"></a><!-- ws:end:WikiTextHeadingRule:32 -->19 note</h3> <a class="wiki_link" href="http://tel.wikispaces.com/13%2013%207%2013%2013%207%2013%2013">13 13 7 13 13 7 13 13</a> <a class="wiki_link" href="http://tel.wikispaces.com/7%2013%207%2013%2013%207%2013%2013%207">7 13 7 13 13 7 13 13 7</a> 13 7<br /> <br /> <!-- ws:start:WikiTextHeadingRule:34:<h3> --><h3 id="toc17"><a name="x205edo MOS-Meantone (119\205) MOS-31 notes"></a><!-- ws:end:WikiTextHeadingRule:34 -->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 /> <!-- ws:start:WikiTextHeadingRule:36:<h2> --><h2 id="toc18"><a name="x205edo MOS-Myna (53\205) MOS"></a><!-- ws:end:WikiTextHeadingRule:36 -->Myna (53\205) MOS</h2> <br /> <!-- ws:start:WikiTextHeadingRule:38:<h3> --><h3 id="toc19"><a name="x205edo MOS-Myna (53\205) MOS-11 note"></a><!-- ws:end:WikiTextHeadingRule:38 -->11 note</h3> 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 /> <!-- ws:start:WikiTextHeadingRule:40:<h3> --><h3 id="toc20"><a name="x205edo MOS-Myna (53\205) MOS-15 note"></a><!-- ws:end:WikiTextHeadingRule:40 -->15 note</h3> 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 /> <!-- ws:start:WikiTextHeadingRule:42:<h3> --><h3 id="toc21"><a name="x205edo MOS-Myna (53\205) MOS-19 note"></a><!-- ws:end:WikiTextHeadingRule:42 -->19 note</h3> 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 /> <!-- ws:start:WikiTextHeadingRule:44:<h3> --><h3 id="toc22"><a name="x205edo MOS-Myna (53\205) MOS-23 note"></a><!-- ws:end:WikiTextHeadingRule:44 -->23 note</h3> 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 /> <!-- ws:start:WikiTextHeadingRule:46:<h3> --><h3 id="toc23"><a name="x205edo MOS-Myna (53\205) MOS-27 note"></a><!-- ws:end:WikiTextHeadingRule:46 -->27 note</h3> 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 /> <!-- ws:start:WikiTextHeadingRule:48:<h3> --><h3 id="toc24"><a name="x205edo MOS-Myna (53\205) MOS-31 notes"></a><!-- ws:end:WikiTextHeadingRule:48 -->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 /> <!-- ws:start:WikiTextHeadingRule:50:<h2> --><h2 id="toc25"><a name="x205edo MOS-Porcupine (28\205) MOS"></a><!-- ws:end:WikiTextHeadingRule:50 -->Porcupine (28\205) MOS</h2> <br /> <!-- ws:start:WikiTextHeadingRule:52:<h3> --><h3 id="toc26"><a name="x205edo MOS-Porcupine (28\205) MOS-15 note"></a><!-- ws:end:WikiTextHeadingRule:52 -->15 note</h3> <a class="wiki_link" href="http://tel.wikispaces.com/19%209%2019%209%2019%209%2019%209%2019">19 9 19 9 19 9 19 9 19</a> <a class="wiki_link" href="http://tel.wikispaces.com/9%2019%209%2019%209%209">9 19 9 19 9 9</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:54:<h3> --><h3 id="toc27"><a name="x205edo MOS-Porcupine (28\205) MOS-22 note"></a><!-- ws:end:WikiTextHeadingRule:54 -->22 note</h3> <a class="wiki_link" href="http://tel.wikispaces.com/10%209%209%2010%209%209%2010%209%209">10 9 9 10 9 9 10 9 9</a> <a class="wiki_link" href="http://tel.wikispaces.com/10%209%209%2010%209%209%2010%209%209">10 9 9 10 9 9 10 9 9</a> 10 9 9 9<br /> <br /> <!-- ws:start:WikiTextHeadingRule:56:<h3> --><h3 id="toc28"><a name="x205edo MOS-Porcupine (28\205) MOS-29 note"></a><!-- ws:end:WikiTextHeadingRule:56 -->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>