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, 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. 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://www.h-pi.com/TPX28features.html|Tonal Plexus midi controller]]. See the [[http://www.h-pi.com/theory/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 MOS= ==Quanic (24\205) MOS== ===17 note=== 11 13 11 13 11 13 11 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 ==Amity (58\205) MOS== ===11 note=== 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 ===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 ==Hemithirds (33\205) MOS== ===13 note=== 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 ===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 ===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 ===19 note=== 13 13 7 13 13 7 13 13 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 ===15 note=== 7 7 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 ===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 ===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 ===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 ===22 note=== 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, 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 <a class="wiki_link" href="/Gamelismic%20clan">hemithirds temperament</a>; 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.<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://www.h-pi.com/TPX28features.html" rel="nofollow">Tonal Plexus midi controller</a>. See the <a class="wiki_link_ext" href="http://www.h-pi.com/theory/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 /> <!-- 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> 11 13 11 13 11 13 11 13 11 13 11 13 11 13 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> 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 /> <!-- 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> 27 27 4 27 27 4 27 27 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> 23 4 23 4 4 23 4 23 4 4 23 4 23 4 4 23 4 4<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> 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 /> <!-- 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> 26 7 26 7 26 7 26 7 26 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> 19 7 7 19 7 7 19 7 7 19 7 7 19 7 7 19 7 7 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> 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 /> <!-- 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> 13 20 13 20 13 20 20 13 20 13 20 20<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> 13 13 7 13 13 7 13 13 7 13 7 13 13 7 13 13 7 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 7 39 7 7 39 7 7 39 7 39<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 7 32 7 7 7 32 7 7 7 32 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 7 25 7 7 7 7 25 7 7 7 7 25 7 7 7 25<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 7 18 7 7 7 7 7 18 7 7 7 7 7 18 7 7 7 7 18<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 7 11 7 7 7 7 7 7 11 7 7 7 7 7 7 11 7 7 7 7 7 11<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> 19 9 19 9 19 9 19 9 19 9 19 9 19 9 9<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> 10 9 9 10 9 9 10 9 9 10 9 9 10 9 9 10 9 9 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>