205edo: Difference between revisions
Wikispaces>genewardsmith **Imported revision 303263700 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 321208788 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<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:genewardsmith|genewardsmith]] and made on <tt>2012- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-04-16 16:44:13 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>321208788</tt>.<br> | ||
: The revision comment was: <tt></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> | ||
| Line 8: | Line 8: | ||
<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, 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. | <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, 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]] | 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= | ||
| Line 91: | Line 91: | ||
<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, 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.<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, 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.<br /> | ||
<br /> | <br /> | ||
205et tempers out 540/539, so that it allows <a class="wiki_link" href="/swetismic%20chords">swetismic chords</a> | 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 /> | <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> | <!-- 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> | ||