Meantone family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 318447614 - Original comment: ** |
Wikispaces>Kosmorsky **Imported revision 319331034 - Original comment: ** |
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<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: | : This revision was by author [[User:Kosmorsky|Kosmorsky]] and made on <tt>2012-04-11 00:57:56 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>319331034</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> | ||
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Badness: 0.0259 | Badness: 0.0259 | ||
===Meridetone=== | ===Meridetone=== | ||
Commas: 78/77, 81/80, 99/98, 126/125 | Commas: 78/77, 81/80, 99/98, 126/125 | ||
| Line 216: | Line 216: | ||
Badness: 0.0220 | Badness: 0.0220 | ||
==Arnold== | ==Arnold== | ||
Commas: 22/21, 33/32, 36/35 | Commas: 22/21, 33/32, 36/35 | ||
POTE generator: ~3/2 | POTE generator: ~3/2 | ||
Map: [<1 0 -4 6 5|, <0 1 4 -2 -1|] | Map: [<1 0 -4 6 5|, <0 1 4 -2 -1|] | ||
| Line 225: | Line 225: | ||
Badness: 0.0261 | Badness: 0.0261 | ||
==13-limit== | ==13-limit== | ||
Map: [<1 0 -4 6 5 -1|, <0 1 4 -2 -1 3|] | Map: [<1 0 -4 6 5 -1|, <0 1 4 -2 -1 3|] | ||
| Line 231: | Line 231: | ||
Badness: 0.0233 | Badness: 0.0233 | ||
==Dominatrix== | ==Dominatrix== | ||
Commas: 27/26 36/35 45/44 64/63 | Commas: 27/26 36/35 45/44 64/63 | ||
| Line 252: | Line 252: | ||
[[Badness]]: 0.0248 | [[Badness]]: 0.0248 | ||
=Meansept= | =Meansept= | ||
Commas: 15/14, 81/80 | Commas: 15/14, 81/80 | ||
| Line 262: | Line 262: | ||
Badness: 0.0453 | Badness: 0.0453 | ||
==11-limit== | ==11-limit== | ||
Commas: 15/14, 22/21, 125/121 | Commas: 15/14, 22/21, 125/121 | ||
| Line 306: | Line 306: | ||
Badness: 0.0216 | Badness: 0.0216 | ||
==Lahoh== | ==Lahoh== | ||
Commas: 50/49, 56/55, 81/77 | Commas: 50/49, 56/55, 81/77 | ||
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Badness: 0.0285 | Badness: 0.0285 | ||
==Varan== | ==Varan== | ||
Commas: 49/48, 77/75, 81/80 | Commas: 49/48, 77/75, 81/80 | ||
| Line 355: | Line 355: | ||
Badness: 0.0396 | Badness: 0.0396 | ||
==Baragon== | ==Baragon== | ||
Commas: 49/48, 56/55, 81/80 | Commas: 49/48, 56/55, 81/80 | ||
| Line 443: | Line 443: | ||
Badness: 0.0255 | Badness: 0.0255 | ||
=Mohamaq= | =Mohamaq= | ||
Commas: 81/80, 392/375 | Commas: 81/80, 392/375 | ||
| Line 452: | Line 452: | ||
Badness: 0.0777 | Badness: 0.0777 | ||
==11-limit== | ==11-limit== | ||
Commas: 56/55, 77/75, 243/242 | Commas: 56/55, 77/75, 243/242 | ||
| Line 584: | Line 584: | ||
[[Badness]]: 0.0255 | [[Badness]]: 0.0255 | ||
==Agora== | ==Agora== | ||
Commas: 81/80, 99/98, 105/104, 121/120 | Commas: 81/80, 99/98, 105/104, 121/120 | ||
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EDOs: 17c, 19, 36, 91ce | EDOs: 17c, 19, 36, 91ce | ||
Badness: 0.0407 | Badness: 0.0407 | ||
==13-limit== | |||
Commas: 81/80, 686/675, 540/539, ? | |||
Liese is a very natural 13-limit tuning, given the generator is so near 13/9. | |||
POTE generator: ~13/9 = 633 ? | |||
Map: [<1 0 -4 -3 4 0|, <0 3 12 11 -1 7|] | |||
EDOs: 17, 19 exetra | |||
Badness? Not bad at all! | |||
==Elisa== | ==Elisa== | ||
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Badness: 0.0209 | Badness: 0.0209 | ||
=Meanmag= | =Meanmag= | ||
Commas: 81/80, 3125/3072 | Commas: 81/80, 3125/3072 | ||
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Map: [<19 30 44 53 0|, <0 0 0 0 1|] | Map: [<19 30 44 53 0|, <0 0 0 0 1|] | ||
EDOs: 19, 38d | EDOs: 19, 38d | ||
Badness: 0.0364</pre></div> | Badness: 0.0364 | ||
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 7822.5px; width: 1px;"> | |||
==ese== | |||
</span></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>Meantone family</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>Meantone family</title></head><body><!-- ws:start:WikiTextTocRule:134:&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:134 --><!-- ws:start:WikiTextTocRule:135: --><div style="margin-left: 2em;"><a href="#x-Seven limit children">Seven limit children</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:135 --><!-- ws:start:WikiTextTocRule:136: --><div style="margin-left: 1em;"><a href="#Septimal meantone">Septimal meantone</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:136 --><!-- ws:start:WikiTextTocRule:137: --><div style="margin-left: 2em;"><a href="#Septimal meantone-Unidecimal meantone aka Huygens">Unidecimal meantone aka Huygens</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:137 --><!-- ws:start:WikiTextTocRule:138: --><div style="margin-left: 3em;"><a href="#Septimal meantone-Unidecimal meantone aka Huygens-Tridecimal meantone">Tridecimal meantone</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:138 --><!-- ws:start:WikiTextTocRule:139: --><div style="margin-left: 3em;"><a href="#Septimal meantone-Unidecimal meantone aka Huygens-Grosstone">Grosstone</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:139 --><!-- ws:start:WikiTextTocRule:140: --><div style="margin-left: 3em;"><a href="#Septimal meantone-Unidecimal meantone aka Huygens-Meridetone">Meridetone</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:140 --><!-- ws:start:WikiTextTocRule:141: --><div style="margin-left: 2em;"><a href="#Septimal meantone-Meanpop">Meanpop</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:141 --><!-- ws:start:WikiTextTocRule:142: --><div style="margin-left: 3em;"><a href="#Septimal meantone-Meanpop-13-limit Meanpop">13-limit Meanpop</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:142 --><!-- ws:start:WikiTextTocRule:143: --><div style="margin-left: 3em;"><a href="#Septimal meantone-Meanpop-Meanplop">Meanplop</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:143 --><!-- ws:start:WikiTextTocRule:144: --><div style="margin-left: 2em;"><a href="#Septimal meantone-Meanenneadecal">Meanenneadecal</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:144 --><!-- ws:start:WikiTextTocRule:145: --><div style="margin-left: 3em;"><a href="#Septimal meantone-Meanenneadecal-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:145 --><!-- ws:start:WikiTextTocRule:146: --><div style="margin-left: 2em;"><a href="#Septimal meantone-Meanundeci">Meanundeci</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:146 --><!-- ws:start:WikiTextTocRule:147: --><div style="margin-left: 1em;"><a href="#Flattone">Flattone</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:147 --><!-- ws:start:WikiTextTocRule:148: --><div style="margin-left: 2em;"><a href="#Flattone-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:148 --><!-- ws:start:WikiTextTocRule:149: --><div style="margin-left: 2em;"><a href="#Flattone-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:149 --><!-- ws:start:WikiTextTocRule:150: --><div style="margin-left: 1em;"><a href="#Dominant">Dominant</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:150 --><!-- ws:start:WikiTextTocRule:151: --><div style="margin-left: 2em;"><a href="#Dominant-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:151 --><!-- ws:start:WikiTextTocRule:152: --><div style="margin-left: 2em;"><a href="#Dominant-Domineering">Domineering</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:152 --><!-- ws:start:WikiTextTocRule:153: --><div style="margin-left: 2em;"><a href="#Dominant-Arnold">Arnold</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:153 --><!-- ws:start:WikiTextTocRule:154: --><div style="margin-left: 2em;"><a href="#Dominant-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:154 --><!-- ws:start:WikiTextTocRule:155: --><div style="margin-left: 2em;"><a href="#Dominant-Dominatrix">Dominatrix</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:155 --><!-- ws:start:WikiTextTocRule:156: --><div style="margin-left: 1em;"><a href="#Sharptone">Sharptone</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:156 --><!-- ws:start:WikiTextTocRule:157: --><div style="margin-left: 1em;"><a href="#Meansept">Meansept</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:157 --><!-- ws:start:WikiTextTocRule:158: --><div style="margin-left: 2em;"><a href="#Meansept-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:158 --><!-- ws:start:WikiTextTocRule:159: --><div style="margin-left: 1em;"><a href="#Injera">Injera</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:159 --><!-- ws:start:WikiTextTocRule:160: --><div style="margin-left: 2em;"><a href="#Injera-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:160 --><!-- ws:start:WikiTextTocRule:161: --><div style="margin-left: 2em;"><a href="#Injera-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:161 --><!-- ws:start:WikiTextTocRule:162: --><div style="margin-left: 2em;"><a href="#Injera-Lahoh">Lahoh</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:162 --><!-- ws:start:WikiTextTocRule:163: --><div style="margin-left: 1em;"><a href="#Godzilla">Godzilla</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:163 --><!-- ws:start:WikiTextTocRule:164: --><div style="margin-left: 2em;"><a href="#Godzilla-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:164 --><!-- ws:start:WikiTextTocRule:165: --><div style="margin-left: 2em;"><a href="#Godzilla-Semafour">Semafour</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:165 --><!-- ws:start:WikiTextTocRule:166: --><div style="margin-left: 2em;"><a href="#Godzilla-Varan">Varan</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:166 --><!-- ws:start:WikiTextTocRule:167: --><div style="margin-left: 2em;"><a href="#Godzilla-Baragon">Baragon</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:167 --><!-- ws:start:WikiTextTocRule:168: --><div style="margin-left: 2em;"><a href="#Godzilla-Music">Music</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:168 --><!-- ws:start:WikiTextTocRule:169: --><div style="margin-left: 1em;"><a href="#Mohajira">Mohajira</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:169 --><!-- ws:start:WikiTextTocRule:170: --><div style="margin-left: 2em;"><a href="#Mohajira-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:170 --><!-- ws:start:WikiTextTocRule:171: --><div style="margin-left: 2em;"><a href="#Mohajira-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:171 --><!-- ws:start:WikiTextTocRule:172: --><div style="margin-left: 1em;"><a href="#Maqamic">Maqamic</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:172 --><!-- ws:start:WikiTextTocRule:173: --><div style="margin-left: 2em;"><a href="#Maqamic-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:173 --><!-- ws:start:WikiTextTocRule:174: --><div style="margin-left: 1em;"><a href="#Migration">Migration</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:174 --><!-- ws:start:WikiTextTocRule:175: --><div style="margin-left: 1em;"><a href="#Mohamaq">Mohamaq</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:175 --><!-- ws:start:WikiTextTocRule:176: --><div style="margin-left: 2em;"><a href="#Mohamaq-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:176 --><!-- ws:start:WikiTextTocRule:177: --><div style="margin-left: 1em;"><a href="#Orphic">Orphic</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:177 --><!-- ws:start:WikiTextTocRule:178: --><div style="margin-left: 2em;"><a href="#Orphic-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:178 --><!-- ws:start:WikiTextTocRule:179: --><div style="margin-left: 2em;"><a href="#Orphic-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:179 --><!-- ws:start:WikiTextTocRule:180: --><div style="margin-left: 1em;"><a href="#Mothra">Mothra</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:180 --><!-- ws:start:WikiTextTocRule:181: --><div style="margin-left: 2em;"><a href="#Mothra-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:181 --><!-- ws:start:WikiTextTocRule:182: --><div style="margin-left: 2em;"><a href="#Mothra-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:182 --><!-- ws:start:WikiTextTocRule:183: --><div style="margin-left: 2em;"><a href="#Mothra-Mosura">Mosura</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:183 --><!-- ws:start:WikiTextTocRule:184: --><div style="margin-left: 3em;"><a href="#Mothra-Mosura-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:184 --><!-- ws:start:WikiTextTocRule:185: --><div style="margin-left: 1em;"><a href="#Squares">Squares</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:185 --><!-- ws:start:WikiTextTocRule:186: --><div style="margin-left: 2em;"><a href="#Squares-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:186 --><!-- ws:start:WikiTextTocRule:187: --><div style="margin-left: 2em;"><a href="#Squares-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:187 --><!-- ws:start:WikiTextTocRule:188: --><div style="margin-left: 2em;"><a href="#Squares-Agora">Agora</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:188 --><!-- ws:start:WikiTextTocRule:189: --><div style="margin-left: 1em;"><a href="#Cuboctahedra">Cuboctahedra</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:189 --><!-- ws:start:WikiTextTocRule:190: --><div style="margin-left: 2em;"><a href="#Cuboctahedra-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:190 --><!-- ws:start:WikiTextTocRule:191: --><div style="margin-left: 1em;"><a href="#Liese">Liese</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:191 --><!-- ws:start:WikiTextTocRule:192: --><div style="margin-left: 2em;"><a href="#Liese-Liesel">Liesel</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:192 --><!-- ws:start:WikiTextTocRule:193: --><div style="margin-left: 2em;"><a href="#Liese-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:193 --><!-- ws:start:WikiTextTocRule:194: --><div style="margin-left: 2em;"><a href="#Liese-Elisa">Elisa</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:194 --><!-- ws:start:WikiTextTocRule:195: --><div style="margin-left: 1em;"><a href="#Jerome">Jerome</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:195 --><!-- ws:start:WikiTextTocRule:196: --><div style="margin-left: 2em;"><a href="#Jerome-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:196 --><!-- ws:start:WikiTextTocRule:197: --><div style="margin-left: 2em;"><a href="#Jerome-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:197 --><!-- ws:start:WikiTextTocRule:198: --><div style="margin-left: 2em;"><a href="#Jerome-17-limit">17-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:198 --><!-- ws:start:WikiTextTocRule:199: --><div style="margin-left: 1em;"><a href="#Meanmag">Meanmag</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:199 --><!-- ws:start:WikiTextTocRule:200: --><div style="margin-left: 1em;"><a href="#Undevigintone">Undevigintone</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:200 --><!-- ws:start:WikiTextTocRule:201: --><div style="margin-left: 2em;"><a href="#Undevigintone-ese">ese</a></div> | ||
<!-- ws:end:WikiTextTocRule:201 --><!-- ws:start:WikiTextTocRule:202: --></div> | |||
<!-- ws:end:WikiTextTocRule:202 -->The <a class="wiki_link" href="/5-limit">5-limit</a> parent <a class="wiki_link" href="/Comma">comma</a> of the <a class="wiki_link" href="/meantone">meantone</a> family is the Didymus or <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Syntonic_comma" rel="nofollow">syntonic comma</a>, 81/80. This is the one they all temper out. The <a class="wiki_link" href="/Monzos%20and%20Interval%20Space">monzo</a> for 81/80 goes |-4 4 -1&gt;, and that can be flipped around to the corresponding <a class="wiki_link" href="/Wedgies%20and%20Multivals">wedgie</a>, &lt;&lt;1 4 4||, which tells us that the period is an octave, the generator is a fifth, and four fifths go to make up a 5/1 interval.<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 696.239<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 696.239<br /> | ||
| Line 829: | Line 844: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="Septimal meantone-Unidecimal meantone aka Huygens-Meridetone"></a><!-- ws:end:WikiTextHeadingRule:10 -->Meridetone</h3> | <!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="Septimal meantone-Unidecimal meantone aka Huygens-Meridetone"></a><!-- ws:end:WikiTextHeadingRule:10 -->Meridetone</h3> | ||
Commas: 78/77, 81/80, 99/98, 126/125<br /> | Commas: 78/77, 81/80, 99/98, 126/125<br /> | ||
<br /> | <br /> | ||
POTE generator: ~3/2 = 697.529<br /> | POTE generator: ~3/2 = 697.529<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:36:&lt;h2&gt; --><h2 id="toc18"><a name="Dominant-Arnold"></a><!-- ws:end:WikiTextHeadingRule:36 -->Arnold</h2> | <!-- ws:start:WikiTextHeadingRule:36:&lt;h2&gt; --><h2 id="toc18"><a name="Dominant-Arnold"></a><!-- ws:end:WikiTextHeadingRule:36 -->Arnold</h2> | ||
Commas: 22/21, 33/32, 36/35<br /> | Commas: 22/21, 33/32, 36/35<br /> | ||
<br /> | <br /> | ||
POTE generator: ~3/2 <br /> | POTE generator: ~3/2<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 0 -4 6 5|, &lt;0 1 4 -2 -1|]<br /> | Map: [&lt;1 0 -4 6 5|, &lt;0 1 4 -2 -1|]<br /> | ||
| Line 982: | Line 997: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:38:&lt;h2&gt; --><h2 id="toc19"><a name="Dominant-13-limit"></a><!-- ws:end:WikiTextHeadingRule:38 -->13-limit</h2> | <!-- ws:start:WikiTextHeadingRule:38:&lt;h2&gt; --><h2 id="toc19"><a name="Dominant-13-limit"></a><!-- ws:end:WikiTextHeadingRule:38 -->13-limit</h2> | ||
<br /> | <br /> | ||
Map: [&lt;1 0 -4 6 5 -1|, &lt;0 1 4 -2 -1 3|]<br /> | Map: [&lt;1 0 -4 6 5 -1|, &lt;0 1 4 -2 -1 3|]<br /> | ||
EDOs: 5, 7, 12ef, 19def, 31def<br /> | EDOs: 5, 7, 12ef, 19def, 31def<br /> | ||
| Line 988: | Line 1,003: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:40:&lt;h2&gt; --><h2 id="toc20"><a name="Dominant-Dominatrix"></a><!-- ws:end:WikiTextHeadingRule:40 -->Dominatrix</h2> | <!-- ws:start:WikiTextHeadingRule:40:&lt;h2&gt; --><h2 id="toc20"><a name="Dominant-Dominatrix"></a><!-- ws:end:WikiTextHeadingRule:40 -->Dominatrix</h2> | ||
Commas: 27/26 36/35 45/44 64/63<br /> | Commas: 27/26 36/35 45/44 64/63<br /> | ||
<br /> | <br /> | ||
POTE generator: ~3/2 = 698.544<br /> | POTE generator: ~3/2 = 698.544<br /> | ||
| Line 1,009: | Line 1,024: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:44:&lt;h1&gt; --><h1 id="toc22"><a name="Meansept"></a><!-- ws:end:WikiTextHeadingRule:44 -->Meansept</h1> | <!-- ws:start:WikiTextHeadingRule:44:&lt;h1&gt; --><h1 id="toc22"><a name="Meansept"></a><!-- ws:end:WikiTextHeadingRule:44 -->Meansept</h1> | ||
Commas: 15/14, 81/80<br /> | Commas: 15/14, 81/80<br /> | ||
<br /> | <br /> | ||
POTE generator: ~3/2 = 682.895<br /> | POTE generator: ~3/2 = 682.895<br /> | ||
| Line 1,019: | Line 1,034: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:46:&lt;h2&gt; --><h2 id="toc23"><a name="Meansept-11-limit"></a><!-- ws:end:WikiTextHeadingRule:46 -->11-limit</h2> | <!-- ws:start:WikiTextHeadingRule:46:&lt;h2&gt; --><h2 id="toc23"><a name="Meansept-11-limit"></a><!-- ws:end:WikiTextHeadingRule:46 -->11-limit</h2> | ||
Commas: 15/14, 22/21, 125/121<br /> | Commas: 15/14, 22/21, 125/121<br /> | ||
<br /> | <br /> | ||
POTE generator: ~3/2 = 685.234<br /> | POTE generator: ~3/2 = 685.234<br /> | ||
| Line 1,063: | Line 1,078: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:54:&lt;h2&gt; --><h2 id="toc27"><a name="Injera-Lahoh"></a><!-- ws:end:WikiTextHeadingRule:54 -->Lahoh</h2> | <!-- ws:start:WikiTextHeadingRule:54:&lt;h2&gt; --><h2 id="toc27"><a name="Injera-Lahoh"></a><!-- ws:end:WikiTextHeadingRule:54 -->Lahoh</h2> | ||
Commas: 50/49, 56/55, 81/77<br /> | Commas: 50/49, 56/55, 81/77<br /> | ||
<br /> | <br /> | ||
POTE generator: ~3/2 = 699.001<br /> | POTE generator: ~3/2 = 699.001<br /> | ||
| Line 1,103: | Line 1,118: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:62:&lt;h2&gt; --><h2 id="toc31"><a name="Godzilla-Varan"></a><!-- ws:end:WikiTextHeadingRule:62 -->Varan</h2> | <!-- ws:start:WikiTextHeadingRule:62:&lt;h2&gt; --><h2 id="toc31"><a name="Godzilla-Varan"></a><!-- ws:end:WikiTextHeadingRule:62 -->Varan</h2> | ||
Commas: 49/48, 77/75, 81/80<br /> | Commas: 49/48, 77/75, 81/80<br /> | ||
<br /> | <br /> | ||
POTE generator: ~8/7 = 251.079<br /> | POTE generator: ~8/7 = 251.079<br /> | ||
| Line 1,112: | Line 1,127: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:64:&lt;h2&gt; --><h2 id="toc32"><a name="Godzilla-Baragon"></a><!-- ws:end:WikiTextHeadingRule:64 -->Baragon</h2> | <!-- ws:start:WikiTextHeadingRule:64:&lt;h2&gt; --><h2 id="toc32"><a name="Godzilla-Baragon"></a><!-- ws:end:WikiTextHeadingRule:64 -->Baragon</h2> | ||
Commas: 49/48, 56/55, 81/80<br /> | Commas: 49/48, 56/55, 81/80<br /> | ||
<br /> | <br /> | ||
POTE generator: ~8/7 = 251.173<br /> | POTE generator: ~8/7 = 251.173<br /> | ||
| Line 1,200: | Line 1,215: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:80:&lt;h1&gt; --><h1 id="toc40"><a name="Mohamaq"></a><!-- ws:end:WikiTextHeadingRule:80 -->Mohamaq</h1> | <!-- ws:start:WikiTextHeadingRule:80:&lt;h1&gt; --><h1 id="toc40"><a name="Mohamaq"></a><!-- ws:end:WikiTextHeadingRule:80 -->Mohamaq</h1> | ||
Commas: 81/80, 392/375<br /> | Commas: 81/80, 392/375<br /> | ||
<br /> | <br /> | ||
POTE generator: ~25/21 = 350.586<br /> | POTE generator: ~25/21 = 350.586<br /> | ||
| Line 1,209: | Line 1,224: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:82:&lt;h2&gt; --><h2 id="toc41"><a name="Mohamaq-11-limit"></a><!-- ws:end:WikiTextHeadingRule:82 -->11-limit</h2> | <!-- ws:start:WikiTextHeadingRule:82:&lt;h2&gt; --><h2 id="toc41"><a name="Mohamaq-11-limit"></a><!-- ws:end:WikiTextHeadingRule:82 -->11-limit</h2> | ||
Commas: 56/55, 77/75, 243/242<br /> | Commas: 56/55, 77/75, 243/242<br /> | ||
<br /> | <br /> | ||
POTE generator: ~11/9 = 350.565<br /> | POTE generator: ~11/9 = 350.565<br /> | ||
| Line 1,341: | Line 1,356: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:106:&lt;h2&gt; --><h2 id="toc53"><a name="Squares-Agora"></a><!-- ws:end:WikiTextHeadingRule:106 -->Agora</h2> | <!-- ws:start:WikiTextHeadingRule:106:&lt;h2&gt; --><h2 id="toc53"><a name="Squares-Agora"></a><!-- ws:end:WikiTextHeadingRule:106 -->Agora</h2> | ||
Commas: 81/80, 99/98, 105/104, 121/120<br /> | Commas: 81/80, 99/98, 105/104, 121/120<br /> | ||
<br /> | <br /> | ||
POTE generator: ~9/7 = 426.276<br /> | POTE generator: ~9/7 = 426.276<br /> | ||
| Line 1,386: | Line 1,401: | ||
Badness: 0.0407<br /> | Badness: 0.0407<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:116:&lt;h2&gt; --><h2 id="toc58"><a name="Liese-Elisa"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:116:&lt;h2&gt; --><h2 id="toc58"><a name="Liese-13-limit"></a><!-- ws:end:WikiTextHeadingRule:116 -->13-limit</h2> | ||
Commas: 81/80, 686/675, 540/539, ?<br /> | |||
Liese is a very natural 13-limit tuning, given the generator is so near 13/9.<br /> | |||
<br /> | |||
POTE generator: ~13/9 = 633 ?<br /> | |||
<br /> | |||
Map: [&lt;1 0 -4 -3 4 0|, &lt;0 3 12 11 -1 7|]<br /> | |||
EDOs: 17, 19 exetra<br /> | |||
Badness? Not bad at all!<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:118:&lt;h2&gt; --><h2 id="toc59"><a name="Liese-Elisa"></a><!-- ws:end:WikiTextHeadingRule:118 -->Elisa</h2> | |||
Commas: 77/75, 81/80, 99/98<br /> | Commas: 77/75, 81/80, 99/98<br /> | ||
<br /> | <br /> | ||
| Line 1,395: | Line 1,420: | ||
Badness: 0.0416<br /> | Badness: 0.0416<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:120:&lt;h1&gt; --><h1 id="toc60"><a name="Jerome"></a><!-- ws:end:WikiTextHeadingRule:120 -->Jerome</h1> | ||
Jerome is related to <a class="wiki_link" href="/20ed5">Hieronymus' tuning</a>; the Hieronymus generator is 5^(1/20), or 139.316 cents. While the generator represents both 13/12 and 12/11, the POTE and Hieronymus generators are close to 13/12 in size.<br /> | Jerome is related to <a class="wiki_link" href="/20ed5">Hieronymus' tuning</a>; the Hieronymus generator is 5^(1/20), or 139.316 cents. While the generator represents both 13/12 and 12/11, the POTE and Hieronymus generators are close to 13/12 in size.<br /> | ||
<br /> | <br /> | ||
| Line 1,407: | Line 1,432: | ||
Badness: 0.1087<br /> | Badness: 0.1087<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:122:&lt;h2&gt; --><h2 id="toc61"><a name="Jerome-11-limit"></a><!-- ws:end:WikiTextHeadingRule:122 -->11-limit</h2> | ||
Commas: 81/80, 99/98, 864/847<br /> | Commas: 81/80, 99/98, 864/847<br /> | ||
<br /> | <br /> | ||
| Line 1,416: | Line 1,441: | ||
Badness: 0.0479<br /> | Badness: 0.0479<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:124:&lt;h2&gt; --><h2 id="toc62"><a name="Jerome-13-limit"></a><!-- ws:end:WikiTextHeadingRule:124 -->13-limit</h2> | ||
Commas: 77/78, 81/80, 99/98, 144/143<br /> | Commas: 77/78, 81/80, 99/98, 144/143<br /> | ||
<br /> | <br /> | ||
| Line 1,425: | Line 1,450: | ||
Badness: 0.0293<br /> | Badness: 0.0293<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:126:&lt;h2&gt; --><h2 id="toc63"><a name="Jerome-17-limit"></a><!-- ws:end:WikiTextHeadingRule:126 -->17-limit</h2> | ||
Commas: 78/77, 81/80, 99/98, 144/143, 189/187<br /> | Commas: 78/77, 81/80, 99/98, 144/143, 189/187<br /> | ||
<br /> | <br /> | ||
| Line 1,434: | Line 1,459: | ||
Badness: 0.0209<br /> | Badness: 0.0209<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:128:&lt;h1&gt; --><h1 id="toc64"><a name="Meanmag"></a><!-- ws:end:WikiTextHeadingRule:128 -->Meanmag</h1> | ||
Commas: 81/80, 3125/3072<br /> | Commas: 81/80, 3125/3072<br /> | ||
<br /> | <br /> | ||
POTE generator: ~8/7 = 238.396<br /> | POTE generator: ~8/7 = 238.396<br /> | ||
| Line 1,444: | Line 1,469: | ||
Badness: 0.0770<br /> | Badness: 0.0770<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:130:&lt;h1&gt; --><h1 id="toc65"><a name="Undevigintone"></a><!-- ws:end:WikiTextHeadingRule:130 -->Undevigintone</h1> | ||
Commas: 49/48, 81/80, 126/125<br /> | Commas: 49/48, 81/80, 126/125<br /> | ||
<br /> | <br /> | ||
| Line 1,451: | Line 1,476: | ||
Map: [&lt;19 30 44 53 0|, &lt;0 0 0 0 1|]<br /> | Map: [&lt;19 30 44 53 0|, &lt;0 0 0 0 1|]<br /> | ||
EDOs: 19, 38d<br /> | EDOs: 19, 38d<br /> | ||
Badness: 0.0364</body></html></pre></div> | Badness: 0.0364<br /> | ||
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 7822.5px; width: 1px;"><br /> | |||
<!-- ws:start:WikiTextHeadingRule:132:&lt;h2&gt; --><h2 id="toc66"><a name="Undevigintone-ese"></a><!-- ws:end:WikiTextHeadingRule:132 -->ese</h2> | |||
</span></body></html></pre></div> | |||