Ragismic microtemperaments: Difference between revisions
Wikispaces>genewardsmith **Imported revision 300513944 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 301310262 - 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>2012-02- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-02-13 13:35:07 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>301310262</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 295: | Line 295: | ||
EDOs: 164, 224, 388, 612, 836, 1448f, 2284f | EDOs: 164, 224, 388, 612, 836, 1448f, 2284f | ||
Badness: 0.0295 | Badness: 0.0295 | ||
=Semidimfourth= | |||
Commas: 4375/4374, 235298/234375 | |||
POTE generator: ~35/27 = 448.457 | |||
Map: [<1 21 28 36|, <0 -31 -41 -53|] | |||
Wedgie: <<31 41 53 -7 -3 8|| | |||
EDOs: 91, 99, 289, 388, 875, 1263d, 1651d | |||
Badness: 0.0552 | |||
=Nearly Micro= | =Nearly Micro= | ||
| Line 510: | Line 520: | ||
</pre></div> | </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"><html><head><title>Ragismic microtemperaments</title></head><body><!-- ws:start:WikiTextTocRule: | <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>Ragismic microtemperaments</title></head><body><!-- ws:start:WikiTextTocRule:112:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:112 --><!-- ws:start:WikiTextTocRule:113: --><div style="margin-left: 1em;"><a href="#Ennealimmal">Ennealimmal</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:113 --><!-- ws:start:WikiTextTocRule:114: --><div style="margin-left: 2em;"><a href="#Ennealimmal-11 limit hemiennealimmal">11 limit hemiennealimmal</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:114 --><!-- ws:start:WikiTextTocRule:115: --><div style="margin-left: 2em;"><a href="#Ennealimmal-13 limit hemiennealimmal">13 limit hemiennealimmal</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:115 --><!-- ws:start:WikiTextTocRule:116: --><div style="margin-left: 2em;"><a href="#Ennealimmal-Semiennealimmal">Semiennealimmal</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:116 --><!-- ws:start:WikiTextTocRule:117: --><div style="margin-left: 3em;"><a href="#Ennealimmal-Semiennealimmal-13 limit semiennealimmal">13 limit semiennealimmal</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:117 --><!-- ws:start:WikiTextTocRule:118: --><div style="margin-left: 2em;"><a href="#Ennealimmal-Ennealimmic">Ennealimmic</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:118 --><!-- ws:start:WikiTextTocRule:119: --><div style="margin-left: 3em;"><a href="#Ennealimmal-Ennealimmic-13 limit ennealimmic">13 limit ennealimmic</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:119 --><!-- ws:start:WikiTextTocRule:120: --><div style="margin-left: 4em;"><a href="#Ennealimmal-Ennealimmic-13 limit ennealimmic-17 limit ennealimmic">17 limit ennealimmic</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:120 --><!-- ws:start:WikiTextTocRule:121: --><div style="margin-left: 3em;"><a href="#Ennealimmal-Ennealimmic-Ennealimnic">Ennealimnic</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:121 --><!-- ws:start:WikiTextTocRule:122: --><div style="margin-left: 2em;"><a href="#Ennealimmal-Ennealiminal">Ennealiminal</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:122 --><!-- ws:start:WikiTextTocRule:123: --><div style="margin-left: 2em;"><a href="#Ennealimmal-Semihemiennealimmal">Semihemiennealimmal</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:123 --><!-- ws:start:WikiTextTocRule:124: --><div style="margin-left: 1em;"><a href="#Gamera">Gamera</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:124 --><!-- ws:start:WikiTextTocRule:125: --><div style="margin-left: 1em;"><a href="#Supermajor">Supermajor</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:125 --><!-- ws:start:WikiTextTocRule:126: --><div style="margin-left: 2em;"><a href="#Supermajor-Semisupermajor">Semisupermajor</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:126 --><!-- ws:start:WikiTextTocRule:127: --><div style="margin-left: 1em;"><a href="#Enneadecal">Enneadecal</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:127 --><!-- ws:start:WikiTextTocRule:128: --><div style="margin-left: 1em;"><a href="#Deca">Deca</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:128 --><!-- ws:start:WikiTextTocRule:129: --><div style="margin-left: 2em;"><a href="#Deca-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:129 --><!-- ws:start:WikiTextTocRule:130: --><div style="margin-left: 2em;"><a href="#Deca-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:130 --><!-- ws:start:WikiTextTocRule:131: --><div style="margin-left: 1em;"><a href="#Mitonic">Mitonic</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:131 --><!-- ws:start:WikiTextTocRule:132: --><div style="margin-left: 1em;"><a href="#Abigail">Abigail</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:132 --><!-- ws:start:WikiTextTocRule:133: --><div style="margin-left: 2em;"><a href="#Abigail-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:133 --><!-- ws:start:WikiTextTocRule:134: --><div style="margin-left: 2em;"><a href="#Abigail-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:134 --><!-- ws:start:WikiTextTocRule:135: --><div style="margin-left: 1em;"><a href="#Semidimi">Semidimi</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:135 --><!-- ws:start:WikiTextTocRule:136: --><div style="margin-left: 1em;"><a href="#Brahmagupta">Brahmagupta</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:136 --><!-- ws:start:WikiTextTocRule:137: --><div style="margin-left: 2em;"><a href="#Brahmagupta-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:137 --><!-- ws:start:WikiTextTocRule:138: --><div style="margin-left: 1em;"><a href="#Neusec">Neusec</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:138 --><!-- ws:start:WikiTextTocRule:139: --><div style="margin-left: 2em;"><a href="#Neusec-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:139 --><!-- ws:start:WikiTextTocRule:140: --><div style="margin-left: 1em;"><a href="#Quasithird">Quasithird</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:140 --><!-- ws:start:WikiTextTocRule:141: --><div style="margin-left: 2em;"><a href="#Quasithird-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:141 --><!-- ws:start:WikiTextTocRule:142: --><div style="margin-left: 2em;"><a href="#Quasithird-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:142 --><!-- ws:start:WikiTextTocRule:143: --><div style="margin-left: 1em;"><a href="#Semidimfourth">Semidimfourth</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:143 --><!-- ws:start:WikiTextTocRule:144: --><div style="margin-left: 1em;"><a href="#Nearly Micro">Nearly Micro</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:144 --><!-- ws:start:WikiTextTocRule:145: --><div style="margin-left: 1em;"><a href="#Octoid">Octoid</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:145 --><!-- ws:start:WikiTextTocRule:146: --><div style="margin-left: 2em;"><a href="#Octoid-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:146 --><!-- ws:start:WikiTextTocRule:147: --><div style="margin-left: 2em;"><a href="#Octoid-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:147 --><!-- ws:start:WikiTextTocRule:148: --><div style="margin-left: 2em;"><a href="#Octoid-Music">Music</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:148 --><!-- ws:start:WikiTextTocRule:149: --><div style="margin-left: 2em;"><a href="#Octoid-Octopus">Octopus</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:149 --><!-- ws:start:WikiTextTocRule:150: --><div style="margin-left: 1em;"><a href="#Amity">Amity</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:150 --><!-- ws:start:WikiTextTocRule:151: --><div style="margin-left: 2em;"><a href="#Amity-5-limit">5-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:151 --><!-- ws:start:WikiTextTocRule:152: --><div style="margin-left: 2em;"><a href="#Amity-7-limit">7-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:152 --><!-- ws:start:WikiTextTocRule:153: --><div style="margin-left: 2em;"><a href="#Amity-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:153 --><!-- ws:start:WikiTextTocRule:154: --><div style="margin-left: 2em;"><a href="#Amity-Hitchcock">Hitchcock</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:154 --><!-- ws:start:WikiTextTocRule:155: --><div style="margin-left: 2em;"><a href="#Amity-Hemiamity">Hemiamity</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:155 --><!-- ws:start:WikiTextTocRule:156: --><div style="margin-left: 1em;"><a href="#Parakleismic">Parakleismic</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:156 --><!-- ws:start:WikiTextTocRule:157: --><div style="margin-left: 2em;"><a href="#Parakleismic-7-limit">7-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:157 --><!-- ws:start:WikiTextTocRule:158: --><div style="margin-left: 2em;"><a href="#Parakleismic-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:158 --><!-- ws:start:WikiTextTocRule:159: --><div style="margin-left: 2em;"><a href="#Parakleismic-Parkleismic">Parkleismic</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:159 --><!-- ws:start:WikiTextTocRule:160: --><div style="margin-left: 3em;"><a href="#Parakleismic-Parkleismic-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:160 --><!-- ws:start:WikiTextTocRule:161: --><div style="margin-left: 2em;"><a href="#Parakleismic-Paradigmic">Paradigmic</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:161 --><!-- ws:start:WikiTextTocRule:162: --><div style="margin-left: 3em;"><a href="#Parakleismic-Paradigmic-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:162 --><!-- ws:start:WikiTextTocRule:163: --><div style="margin-left: 1em;"><a href="#Semiparakleismic">Semiparakleismic</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:163 --><!-- ws:start:WikiTextTocRule:164: --><div style="margin-left: 1em;"><a href="#Quincy">Quincy</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:164 --><!-- ws:start:WikiTextTocRule:165: --><div style="margin-left: 2em;"><a href="#Quincy-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:165 --><!-- ws:start:WikiTextTocRule:166: --><div style="margin-left: 2em;"><a href="#Quincy-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:166 --><!-- ws:start:WikiTextTocRule:167: --><div style="margin-left: 2em;"><a href="#Quincy-17-limit">17-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:167 --><!-- ws:start:WikiTextTocRule:168: --><div style="margin-left: 2em;"><a href="#Quincy-19-limit">19-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:168 --><!-- ws:start:WikiTextTocRule:169: --></div> | ||
<!-- ws:end:WikiTextTocRule:169 -->The ragisma is 4375/4374 with a monzo of |-1 -7 4 1&gt;, the smallest 7-limit superparticular ratio. Since (10/9)^4 4375/4374 * 32/21, the minor tone 10/9 tends to be an interval of relatively low complexity in temperaments tempering out the ragisma, though when looking at microtemperaments the word &quot;relatively&quot; should be emphasized. Even so mitonic uses it as a generator, which ennealimmal and enneadecal can do also, and amity reaches it in three generators. We also have 7/6 = 4375/4374 * (27/25)^2, so 27/25 also tends to relatively low complexity, with the same caveat about &quot;relatively&quot;; however 27/25 is the period for ennealimmal.<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Ennealimmal"></a><!-- ws:end:WikiTextHeadingRule:0 -->Ennealimmal</h1> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Ennealimmal"></a><!-- ws:end:WikiTextHeadingRule:0 -->Ennealimmal</h1> | ||
| Line 855: | Line 866: | ||
Badness: 0.0295<br /> | Badness: 0.0295<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:60:&lt;h1&gt; --><h1 id="toc30"><a name="Nearly Micro"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:60:&lt;h1&gt; --><h1 id="toc30"><a name="Semidimfourth"></a><!-- ws:end:WikiTextHeadingRule:60 -->Semidimfourth</h1> | ||
Commas: 4375/4374, 235298/234375<br /> | |||
<br /> | |||
POTE generator: ~35/27 = 448.457<br /> | |||
<br /> | |||
Map: [&lt;1 21 28 36|, &lt;0 -31 -41 -53|]<br /> | |||
Wedgie: &lt;&lt;31 41 53 -7 -3 8||<br /> | |||
EDOs: 91, 99, 289, 388, 875, 1263d, 1651d<br /> | |||
Badness: 0.0552<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:62:&lt;h1&gt; --><h1 id="toc31"><a name="Nearly Micro"></a><!-- ws:end:WikiTextHeadingRule:62 -->Nearly Micro</h1> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:64:&lt;h1&gt; --><h1 id="toc32"><a name="Octoid"></a><!-- ws:end:WikiTextHeadingRule:64 -->Octoid</h1> | ||
Commas: 4375/4374, 16875/16807<br /> | Commas: 4375/4374, 16875/16807<br /> | ||
<br /> | <br /> | ||
| Line 867: | Line 888: | ||
Badness: 0.0427<br /> | Badness: 0.0427<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:66:&lt;h2&gt; --><h2 id="toc33"><a name="Octoid-11-limit"></a><!-- ws:end:WikiTextHeadingRule:66 -->11-limit</h2> | ||
Commas: 540/539, 1375/1372, 4000/3993<br /> | Commas: 540/539, 1375/1372, 4000/3993<br /> | ||
<br /> | <br /> | ||
| Line 876: | Line 897: | ||
Badness: 0.0141<br /> | Badness: 0.0141<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:68:&lt;h2&gt; --><h2 id="toc34"><a name="Octoid-13-limit"></a><!-- ws:end:WikiTextHeadingRule:68 -->13-limit</h2> | ||
Commas: 540/539, 1375/1372, 4000/3993, 625/624<br /> | Commas: 540/539, 1375/1372, 4000/3993, 625/624<br /> | ||
<br /> | <br /> | ||
| Line 885: | Line 906: | ||
Badness: 0.0153<br /> | Badness: 0.0153<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:70:&lt;h2&gt; --><h2 id="toc35"><a name="Octoid-Music"></a><!-- ws:end:WikiTextHeadingRule:70 -->Music</h2> | ||
<!-- ws:start:WikiTextUrlRule: | <!-- ws:start:WikiTextUrlRule:643:http://www.archive.org/details/Dreyfus --><a class="wiki_link_ext" href="http://www.archive.org/details/Dreyfus" rel="nofollow">http://www.archive.org/details/Dreyfus</a><!-- ws:end:WikiTextUrlRule:643 --><br /> | ||
<a class="wiki_link_ext" href="http://www.archive.org/download/Dreyfus/Genewardsmith-Dreyfus.mp3" rel="nofollow">play</a><br /> | <a class="wiki_link_ext" href="http://www.archive.org/download/Dreyfus/Genewardsmith-Dreyfus.mp3" rel="nofollow">play</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:72:&lt;h2&gt; --><h2 id="toc36"><a name="Octoid-Octopus"></a><!-- ws:end:WikiTextHeadingRule:72 -->Octopus</h2> | ||
Commas: 169/168, 325/324, 364/363, 540/539<br /> | Commas: 169/168, 325/324, 364/363, 540/539<br /> | ||
<br /> | <br /> | ||
| Line 898: | Line 919: | ||
Badness: 0.0217<br /> | Badness: 0.0217<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:74:&lt;h1&gt; --><h1 id="toc37"><a name="Amity"></a><!-- ws:end:WikiTextHeadingRule:74 -->Amity</h1> | ||
The generator for amity temperament is the acute minor third, which means an ordinary 6/5 minor third raised by an 81/80 comma to 243/200, and from this it derives its name. Aside from the ragisma it tempers out the 5-limit amity comma, 1600000/1594323, 5120/5103 and 6144/6125. It can also be described as the 46&amp;53 temperament, or by its wedgie, &lt;&lt;5 13 -17 9 -41 -76||. <a class="wiki_link" href="/99edo">99edo</a> is a good tuning for amity, with generator 28/99, and MOS of 11, 18, 25, 32, 46 or 53 notes are available. If you are looking for a different kind of neutral third this could be the temperament for you.<br /> | The generator for amity temperament is the acute minor third, which means an ordinary 6/5 minor third raised by an 81/80 comma to 243/200, and from this it derives its name. Aside from the ragisma it tempers out the 5-limit amity comma, 1600000/1594323, 5120/5103 and 6144/6125. It can also be described as the 46&amp;53 temperament, or by its wedgie, &lt;&lt;5 13 -17 9 -41 -76||. <a class="wiki_link" href="/99edo">99edo</a> is a good tuning for amity, with generator 28/99, and MOS of 11, 18, 25, 32, 46 or 53 notes are available. If you are looking for a different kind of neutral third this could be the temperament for you.<br /> | ||
<br /> | <br /> | ||
In the 5-limit amity is a genuine microtemperament, with 58/205 being a possible tuning. Another good choice is (64/5)^(1/13), which gives pure major thirds.<br /> | In the 5-limit amity is a genuine microtemperament, with 58/205 being a possible tuning. Another good choice is (64/5)^(1/13), which gives pure major thirds.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:76:&lt;h2&gt; --><h2 id="toc38"><a name="Amity-5-limit"></a><!-- ws:end:WikiTextHeadingRule:76 -->5-limit</h2> | ||
Comma: 1600000/1594323<br /> | Comma: 1600000/1594323<br /> | ||
<br /> | <br /> | ||
| Line 912: | Line 933: | ||
Badness: 0.0220<br /> | Badness: 0.0220<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:78:&lt;h2&gt; --><h2 id="toc39"><a name="Amity-7-limit"></a><!-- ws:end:WikiTextHeadingRule:78 -->7-limit</h2> | ||
Commas: 4375/4374, 5120/5103<br /> | Commas: 4375/4374, 5120/5103<br /> | ||
<br /> | <br /> | ||
| Line 922: | Line 943: | ||
Badness: 0.0236<br /> | Badness: 0.0236<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:80:&lt;h2&gt; --><h2 id="toc40"><a name="Amity-11-limit"></a><!-- ws:end:WikiTextHeadingRule:80 -->11-limit</h2> | ||
Commas: 540/539, 4375/4374, 5120/5103<br /> | Commas: 540/539, 4375/4374, 5120/5103<br /> | ||
<br /> | <br /> | ||
| Line 931: | Line 952: | ||
Badness: 0.0315<br /> | Badness: 0.0315<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:82:&lt;h2&gt; --><h2 id="toc41"><a name="Amity-Hitchcock"></a><!-- ws:end:WikiTextHeadingRule:82 -->Hitchcock</h2> | ||
Commas: 121/120, 176/175, 2200/2187<br /> | Commas: 121/120, 176/175, 2200/2187<br /> | ||
<br /> | <br /> | ||
| Line 940: | Line 961: | ||
Badness: 0.0352<br /> | Badness: 0.0352<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:84:&lt;h2&gt; --><h2 id="toc42"><a name="Amity-Hemiamity"></a><!-- ws:end:WikiTextHeadingRule:84 -->Hemiamity</h2> | ||
Commas: 4375/4374, 5120/5103, 3025/3024<br /> | Commas: 4375/4374, 5120/5103, 3025/3024<br /> | ||
<br /> | <br /> | ||
| Line 948: | Line 969: | ||
EDOs: 14, 46, 106, 152, 350<br /> | EDOs: 14, 46, 106, 152, 350<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:86:&lt;h1&gt; --><h1 id="toc43"><a name="Parakleismic"></a><!-- ws:end:WikiTextHeadingRule:86 -->Parakleismic</h1> | ||
In the 5-limit, parakleismic is an undoubted microtemperament, tempering out the parakleisma, |8 14 -13&gt;, with the <a class="wiki_link" href="/118edo">118edo</a> tuning giving errors well under a cent. It has a generator a very slightly (half a cent or less) flat 6/5, 13 of which give 32/3, and 14 64/5. However while 118 no longer has better than a cent of accuracy in the 7 or 11 limits, it is a decent temperament there nonetheless, and this allows an extension, with the 7-limit wedgie being &lt;&lt;13 14 35 -8 19 42|| and adding 3136/3125 and 4375/4374, and the 11-limit wedgie &lt;&lt;13 14 35 -36 ...|| adding 385/384. For the 7-limit <a class="wiki_link" href="/99edo">99edo</a> may be preferred, but in the 11-limit it is best to stick with 118.<br /> | In the 5-limit, parakleismic is an undoubted microtemperament, tempering out the parakleisma, |8 14 -13&gt;, with the <a class="wiki_link" href="/118edo">118edo</a> tuning giving errors well under a cent. It has a generator a very slightly (half a cent or less) flat 6/5, 13 of which give 32/3, and 14 64/5. However while 118 no longer has better than a cent of accuracy in the 7 or 11 limits, it is a decent temperament there nonetheless, and this allows an extension, with the 7-limit wedgie being &lt;&lt;13 14 35 -8 19 42|| and adding 3136/3125 and 4375/4374, and the 11-limit wedgie &lt;&lt;13 14 35 -36 ...|| adding 385/384. For the 7-limit <a class="wiki_link" href="/99edo">99edo</a> may be preferred, but in the 11-limit it is best to stick with 118.<br /> | ||
<br /> | <br /> | ||
| Line 959: | Line 980: | ||
Badness: 0.0433<br /> | Badness: 0.0433<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:88:&lt;h2&gt; --><h2 id="toc44"><a name="Parakleismic-7-limit"></a><!-- ws:end:WikiTextHeadingRule:88 -->7-limit</h2> | ||
Commas: 3136/3125, 4375/4374<br /> | Commas: 3136/3125, 4375/4374<br /> | ||
<br /> | <br /> | ||
| Line 968: | Line 989: | ||
Badness: 0.0274<br /> | Badness: 0.0274<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:90:&lt;h2&gt; --><h2 id="toc45"><a name="Parakleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:90 -->11-limit</h2> | ||
Commas: 385/384, 3136/3125, 4375/4374<br /> | Commas: 385/384, 3136/3125, 4375/4374<br /> | ||
<br /> | <br /> | ||
| Line 977: | Line 998: | ||
Badness: 0.0497<br /> | Badness: 0.0497<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:92:&lt;h2&gt; --><h2 id="toc46"><a name="Parakleismic-Parkleismic"></a><!-- ws:end:WikiTextHeadingRule:92 -->Parkleismic</h2> | ||
Commas: 176/175, 1375/1372, 2200/2187<br /> | Commas: 176/175, 1375/1372, 2200/2187<br /> | ||
<br /> | <br /> | ||
| Line 986: | Line 1,007: | ||
Badness: 0.0559<br /> | Badness: 0.0559<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:94:&lt;h3&gt; --><h3 id="toc47"><a name="Parakleismic-Parkleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:94 -->13-limit</h3> | ||
Commas: 169/168, 176/175, 325/324, 1375/1372<br /> | Commas: 169/168, 176/175, 325/324, 1375/1372<br /> | ||
<br /> | <br /> | ||
| Line 995: | Line 1,016: | ||
Badness: 0.0366<br /> | Badness: 0.0366<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:96:&lt;h2&gt; --><h2 id="toc48"><a name="Parakleismic-Paradigmic"></a><!-- ws:end:WikiTextHeadingRule:96 -->Paradigmic</h2> | ||
Commas: 540/539, 896/891, 3136/3125<br /> | Commas: 540/539, 896/891, 3136/3125<br /> | ||
<br /> | <br /> | ||
| Line 1,004: | Line 1,025: | ||
Badness: 0.0417<br /> | Badness: 0.0417<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:98:&lt;h3&gt; --><h3 id="toc49"><a name="Parakleismic-Paradigmic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:98 -->13-limit</h3> | ||
Commas: 169/168, 325/324, 540/539, 832/825<br /> | Commas: 169/168, 325/324, 540/539, 832/825<br /> | ||
<br /> | <br /> | ||
| Line 1,013: | Line 1,034: | ||
Badness: 0.0358<br /> | Badness: 0.0358<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:100:&lt;h1&gt; --><h1 id="toc50"><a name="Semiparakleismic"></a><!-- ws:end:WikiTextHeadingRule:100 -->Semiparakleismic</h1> | ||
Commas: 3025/3024, 3136/3125, 4375/4374<br /> | Commas: 3025/3024, 3136/3125, 4375/4374<br /> | ||
<br /> | <br /> | ||
| Line 1,022: | Line 1,043: | ||
Badness: 0.0342<br /> | Badness: 0.0342<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:102:&lt;h1&gt; --><h1 id="toc51"><a name="Quincy"></a><!-- ws:end:WikiTextHeadingRule:102 -->Quincy</h1> | ||
Commas: 4375/4374, 823543/819200<br /> | Commas: 4375/4374, 823543/819200<br /> | ||
<br /> | <br /> | ||
| Line 1,031: | Line 1,052: | ||
Badness: 0.0797<br /> | Badness: 0.0797<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:104:&lt;h2&gt; --><h2 id="toc52"><a name="Quincy-11-limit"></a><!-- ws:end:WikiTextHeadingRule:104 -->11-limit</h2> | ||
Commas: 441/440, 4000/3993, 41503/41472<br /> | Commas: 441/440, 4000/3993, 41503/41472<br /> | ||
<br /> | <br /> | ||
| Line 1,040: | Line 1,061: | ||
Badness: 0.0309<br /> | Badness: 0.0309<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:106:&lt;h2&gt; --><h2 id="toc53"><a name="Quincy-13-limit"></a><!-- ws:end:WikiTextHeadingRule:106 -->13-limit</h2> | ||
Commas: 364/363, 441/440, 676/675, 4375/4374<br /> | Commas: 364/363, 441/440, 676/675, 4375/4374<br /> | ||
<br /> | <br /> | ||
| Line 1,049: | Line 1,070: | ||
Badness: 0.0239<br /> | Badness: 0.0239<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:108:&lt;h2&gt; --><h2 id="toc54"><a name="Quincy-17-limit"></a><!-- ws:end:WikiTextHeadingRule:108 -->17-limit</h2> | ||
Commas: 364/363, 441/440, 595/594, 1001/1000, 1156/1155<br /> | Commas: 364/363, 441/440, 595/594, 1001/1000, 1156/1155<br /> | ||
<br /> | <br /> | ||
| Line 1,058: | Line 1,079: | ||
Badness: 0.0147<br /> | Badness: 0.0147<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:110:&lt;h2&gt; --><h2 id="toc55"><a name="Quincy-19-limit"></a><!-- ws:end:WikiTextHeadingRule:110 -->19-limit</h2> | ||
Commas: 343/342, 364/363, 441/440, 595/594, 676/675, 2601/2600<br /> | Commas: 343/342, 364/363, 441/440, 595/594, 676/675, 2601/2600<br /> | ||
<br /> | <br /> | ||