Meantone family: Difference between revisions

Wikispaces>genewardsmith
**Imported revision 204185074 - Original comment: **
Wikispaces>genewardsmith
**Imported revision 205324324 - 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>2011-02-22 21:01:45 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-02-26 21:39:15 UTC</tt>.<br>
: The original revision id was <tt>204185074</tt>.<br>
: The original revision id was <tt>205324324</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 36: Line 36:
Badness: 0.0137
Badness: 0.0137


==Unidecimal meantone==
==Unidecimal meantone aka Huygens==
Commas: 81/80, 126/125, 99/98
Commas: 81/80, 126/125, 99/98


Line 52: Line 52:
EDOs: 7, 12, 31, [[105edo|105]], [[198edo|198]]
EDOs: 7, 12, 31, [[105edo|105]], [[198edo|198]]
Badness: 0.0170
Badness: 0.0170
===Tridecimal meantone===
Commas: 66/65, 81/80, 99/98, 105/104
POTE generator: ~3/2 = 696.642
Map: Map: [&lt;1 0 -4 -13 -25 -20|, &lt;0 1 4 10 18 15|]
EDOs: 12, 19, 31, 267, 298
Badness: 0.0180


==Meanpop==
==Meanpop==
Line 70: Line 79:
Badness: 0.0215
Badness: 0.0215


===Tridecimal meantone===
===13-limit Meanpop===
Commas: 66/65, 81/80, 99/98, 105/104
Commas: 81/80, 105/104, 144/143, 196/195


POTE generator: ~3/2 = 696.642
POTE generator: ~3/2 = 696.211


Map: Map: [&lt;1 0 -4 -13 -25 -20|, &lt;0 1 4 10 18 15|]
Map: [&lt;1 0 -4 -13 24|, &lt;0 1 4 10 -13|]
EDOs: 12, 19, 31, 267, 298
EDOS: 7, 12, 19, 31, 50, 81, 131
Badness: 0.0180
Badness: 0.0209


==Meanenneadecal==
==Meanenneadecal==
Line 312: Line 321:
Badness: 0.0137&lt;br /&gt;
Badness: 0.0137&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x-Unidecimal meantone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Unidecimal meantone&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x-Unidecimal meantone aka Huygens"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Unidecimal meantone aka Huygens&lt;/h2&gt;
Commas: 81/80, 126/125, 99/98&lt;br /&gt;
Commas: 81/80, 126/125, 99/98&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 329: Line 338:
Badness: 0.0170&lt;br /&gt;
Badness: 0.0170&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x-Meanpop"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Meanpop&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="x-Unidecimal meantone aka Huygens-Tridecimal meantone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Tridecimal meantone&lt;/h3&gt;
Commas: 66/65, 81/80, 99/98, 105/104&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~3/2 = 696.642&lt;br /&gt;
&lt;br /&gt;
Map: Map: [&amp;lt;1 0 -4 -13 -25 -20|, &amp;lt;0 1 4 10 18 15|]&lt;br /&gt;
EDOs: 12, 19, 31, 267, 298&lt;br /&gt;
Badness: 0.0180&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="x-Meanpop"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Meanpop&lt;/h2&gt;
Commas: 81/80, 126/125, 385/384&lt;br /&gt;
Commas: 81/80, 126/125, 385/384&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 346: Line 364:
Badness: 0.0215&lt;br /&gt;
Badness: 0.0215&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc4"&gt;&lt;a name="x-Meanpop-Tridecimal meantone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Tridecimal meantone&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc5"&gt;&lt;a name="x-Meanpop-13-limit Meanpop"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;13-limit Meanpop&lt;/h3&gt;
Commas: 66/65, 81/80, 99/98, 105/104&lt;br /&gt;
Commas: 81/80, 105/104, 144/143, 196/195&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~3/2 = 696.642&lt;br /&gt;
POTE generator: ~3/2 = 696.211&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: Map: [&amp;lt;1 0 -4 -13 -25 -20|, &amp;lt;0 1 4 10 18 15|]&lt;br /&gt;
Map: [&amp;lt;1 0 -4 -13 24|, &amp;lt;0 1 4 10 -13|]&lt;br /&gt;
EDOs: 12, 19, 31, 267, 298&lt;br /&gt;
EDOS: 7, 12, 19, 31, 50, 81, 131&lt;br /&gt;
Badness: 0.0180&lt;br /&gt;
Badness: 0.0209&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="x-Meanenneadecal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Meanenneadecal&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="x-Meanenneadecal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Meanenneadecal&lt;/h2&gt;
Commas: 45/44, 56/55, 81/80&lt;br /&gt;
Commas: 45/44, 56/55, 81/80&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 364: Line 382:
Badness: 0.0214&lt;br /&gt;
Badness: 0.0214&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc6"&gt;&lt;a name="x-Meanenneadecal-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;13-limit&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc7"&gt;&lt;a name="x-Meanenneadecal-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;13-limit&lt;/h3&gt;
Commas: 45/44, 56/55, 78/77, 81/80&lt;br /&gt;
Commas: 45/44, 56/55, 78/77, 81/80&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 373: Line 391:
Badness: 0.0212&lt;br /&gt;
Badness: 0.0212&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="x-Flattone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Flattone&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="x-Flattone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Flattone&lt;/h2&gt;
Commas: 81/80, 525/512&lt;br /&gt;
Commas: 81/80, 525/512&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 398: Line 416:
Badness: 0.0386&lt;br /&gt;
Badness: 0.0386&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="x-Dominant"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Dominant&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="x-Dominant"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Dominant&lt;/h2&gt;
Commas: 36/35, 64/63&lt;br /&gt;
Commas: 36/35, 64/63&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 410: Line 428:
Badness: 0.0207&lt;br /&gt;
Badness: 0.0207&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="x-Sharptone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Sharptone&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="x-Sharptone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Sharptone&lt;/h2&gt;
Commas: 21/20, 28/27&lt;br /&gt;
Commas: 21/20, 28/27&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 422: Line 440:
Badness: 0.0248&lt;br /&gt;
Badness: 0.0248&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="x-Injera"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Injera&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc11"&gt;&lt;a name="x-Injera"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Injera&lt;/h2&gt;
Commas: 50/49, 81/80&lt;br /&gt;
Commas: 50/49, 81/80&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 434: Line 452:
Badness: 0.0311&lt;br /&gt;
Badness: 0.0311&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc11"&gt;&lt;a name="x-Godzilla"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Godzilla&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc12"&gt;&lt;a name="x-Godzilla"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Godzilla&lt;/h2&gt;
Commas: 49/48, 81/80&lt;br /&gt;
Commas: 49/48, 81/80&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 446: Line 464:
Badness: 0.0267&lt;br /&gt;
Badness: 0.0267&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc12"&gt;&lt;a name="x-Mohajira"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Mohajira&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="x-Mohajira"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;Mohajira&lt;/h2&gt;
Commas: 81/80, 6144/6125&lt;br /&gt;
Commas: 81/80, 6144/6125&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 465: Line 483:
Badness: 0.0557&lt;br /&gt;
Badness: 0.0557&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc13"&gt;&lt;a name="x-Mohajira-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;11-limit&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc14"&gt;&lt;a name="x-Mohajira-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;11-limit&lt;/h3&gt;
Commas: 81/80, 121/120, 176/175&lt;br /&gt;
Commas: 81/80, 121/120, 176/175&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 480: Line 498:
Badness: 0.0261&lt;br /&gt;
Badness: 0.0261&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc14"&gt;&lt;a name="x-Mothra"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;Mothra&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc15"&gt;&lt;a name="x-Mothra"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;Mothra&lt;/h2&gt;
Commas: 81/80, 1029/1024&lt;br /&gt;
Commas: 81/80, 1029/1024&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 499: Line 517:
Badness: 0.0371&lt;br /&gt;
Badness: 0.0371&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc15"&gt;&lt;a name="x-Mothra-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;11-limit&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc16"&gt;&lt;a name="x-Mothra-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;11-limit&lt;/h3&gt;
Commas: 81/80, 99/98, 385/384&lt;br /&gt;
Commas: 81/80, 99/98, 385/384&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 508: Line 526:
Badness: 0.0256&lt;br /&gt;
Badness: 0.0256&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc16"&gt;&lt;a name="x-Squares"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;Squares&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc17"&gt;&lt;a name="x-Squares"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;Squares&lt;/h2&gt;
Commas: 81/80, 2401/2400&lt;br /&gt;
Commas: 81/80, 2401/2400&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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Music:&lt;br /&gt;
Music:&lt;br /&gt;
By Chris Vaisvil&lt;br /&gt;
By Chris Vaisvil&lt;br /&gt;
&lt;!-- ws:start:WikiTextUrlRule:349:http://tinyurl.com/25kv7cq --&gt;&lt;a class="wiki_link_ext" href="http://tinyurl.com/25kv7cq" rel="nofollow"&gt;http://tinyurl.com/25kv7cq&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:349 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextUrlRule:359:http://tinyurl.com/25kv7cq --&gt;&lt;a class="wiki_link_ext" href="http://tinyurl.com/25kv7cq" rel="nofollow"&gt;http://tinyurl.com/25kv7cq&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:359 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextUrlRule:350:http://tinyurl.com/24cbxse --&gt;&lt;a class="wiki_link_ext" href="http://tinyurl.com/24cbxse" rel="nofollow"&gt;http://tinyurl.com/24cbxse&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:350 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextUrlRule:360:http://tinyurl.com/24cbxse --&gt;&lt;a class="wiki_link_ext" href="http://tinyurl.com/24cbxse" rel="nofollow"&gt;http://tinyurl.com/24cbxse&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:360 --&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc17"&gt;&lt;a name="x-Squares-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;11-limit&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc18"&gt;&lt;a name="x-Squares-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;11-limit&lt;/h3&gt;
Commas: 81/80, 385/384, 1375/1372&lt;br /&gt;
Commas: 81/80, 385/384, 1375/1372&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 540: Line 558:
Badness: 0.0568&lt;br /&gt;
Badness: 0.0568&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc18"&gt;&lt;a name="x-Liese"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;Liese&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc19"&gt;&lt;a name="x-Liese"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;Liese&lt;/h2&gt;
Commas: 81/80, 686/675&lt;br /&gt;
Commas: 81/80, 686/675&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;