Meantone family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 519225698 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 519231616 - 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:genewardsmith|genewardsmith]] and made on <tt>2014-08-21 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-08-21 18:13:51 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>519231616</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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==11-limit== | ==11-limit== | ||
Commas: 36/35, 64/63, 56/55 | Commas: 36/35, 64/63, 56/55 | ||
valid range: [700.000, 705.882] (12 to 17) | |||
nice range: [691.202, 715.587] | |||
strict range: [700.000, 705.882] | |||
POTE generator: ~3/2 = 703.254 | POTE generator: ~3/2 = 703.254 | ||
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==13-limit== | ==13-limit== | ||
Commas: 36/35, 56/55, 64/63, 66/65 | Commas: 36/35, 56/55, 64/63, 66/65 | ||
valid range: 705.882 (17) | |||
nice range: [691.202, 715.587] | |||
strict range:705.882 | |||
POTE generator: ~3/2 = 703.636 | POTE generator: ~3/2 = 703.636 | ||
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[[http://tech.groups.yahoo.com/group/tuning-math/message/3091|Origin of the name]] | [[http://tech.groups.yahoo.com/group/tuning-math/message/3091|Origin of the name]] | ||
valid range: [685.714, 700.000] (14c to 12) | |||
nice range: [688.957, 701.955] | |||
strict range: [688.957, 700.000] | |||
[[POTE tuning|POTE generator]]: 694.375 | [[POTE tuning|POTE generator]]: 694.375 | ||
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==11-limit== | ==11-limit== | ||
Commas: 45/44, 50/49, 81/80 | Commas: 45/44, 50/49, 81/80 | ||
valid range: [685.714, 700.000] (14c to 12) | |||
nice range: [682.458, 701.955] | |||
strict range: [685.714, 700.000] | |||
POTE generator: ~3/2 = 692.840 | POTE generator: ~3/2 = 692.840 | ||
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==13-limit== | ==13-limit== | ||
Commas: 45/44, 50/49, 81/80, 78/77 | Commas: 45/44, 50/49, 81/80, 78/77 | ||
valid range: 692.308 (26) | |||
nice range: [682.458, 701.955] | |||
strict range: 692.308 (26) | |||
POTE generator: ~3/2 = 692.673 | POTE generator: ~3/2 = 692.673 | ||
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Godzilla has wedgie <<2 8 1 8 -4 -20||, and tempers out 49/48, equating 8/7 with 7/6. Two of the step-and-a-quarter intervals these represent give a fourth, and so step-and-a-quarter generators generate godzilla. [[19edo]] is the perfect godzilla tuning, so much so that's there's not much point in looking elsewhere. Hence it can be more or less equated with taking 4\19 as a generator. MOS are of 5, 9, or 14 notes. | Godzilla has wedgie <<2 8 1 8 -4 -20||, and tempers out 49/48, equating 8/7 with 7/6. Two of the step-and-a-quarter intervals these represent give a fourth, and so step-and-a-quarter generators generate godzilla. [[19edo]] is the perfect godzilla tuning, so much so that's there's not much point in looking elsewhere. Hence it can be more or less equated with taking 4\19 as a generator. MOS are of 5, 9, or 14 notes. | ||
valid range: [240.000, 257.143] (5 to 14c) | |||
nice range: [231.174, 266.871] | |||
strict range: [240.000, 257.143] | |||
[[POTE tuning|POTE generator]]: ~8/7 = 252.635 | [[POTE tuning|POTE generator]]: ~8/7 = 252.635 | ||
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==11-limit== | ==11-limit== | ||
Commas: 45/44, 49/48, 81/80 | Commas: 45/44, 49/48, 81/80 | ||
valid range: [252.632, 257.143] (19 to 14c) | |||
nice range: [231.174, 266.871] | |||
strict range: [252.632, 257.143] | |||
POTE generator: ~8/7 = 254.027 | POTE generator: ~8/7 = 254.027 | ||
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==13-limit== | ==13-limit== | ||
Commas: 45/44, 49/48, 78/77, 81/80 | Commas: 45/44, 49/48, 78/77, 81/80 | ||
valid range: 694.737 (19) | |||
nice range: [621.581, 737.652] | |||
strict range: 694.737 | |||
POTE generator: ~8/7 = 253.603 | POTE generator: ~8/7 = 253.603 | ||
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<!-- ws:start:WikiTextHeadingRule:44:&lt;h2&gt; --><h2 id="toc22"><a name="Dominant-11-limit"></a><!-- ws:end:WikiTextHeadingRule:44 -->11-limit</h2> | <!-- ws:start:WikiTextHeadingRule:44:&lt;h2&gt; --><h2 id="toc22"><a name="Dominant-11-limit"></a><!-- ws:end:WikiTextHeadingRule:44 -->11-limit</h2> | ||
Commas: 36/35, 64/63, 56/55<br /> | Commas: 36/35, 64/63, 56/55<br /> | ||
<br /> | |||
valid range: [700.000, 705.882] (12 to 17)<br /> | |||
nice range: [691.202, 715.587]<br /> | |||
strict range: [700.000, 705.882]<br /> | |||
<br /> | <br /> | ||
POTE generator: ~3/2 = 703.254<br /> | POTE generator: ~3/2 = 703.254<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:46:&lt;h2&gt; --><h2 id="toc23"><a name="Dominant-13-limit"></a><!-- ws:end:WikiTextHeadingRule:46 -->13-limit</h2> | <!-- ws:start:WikiTextHeadingRule:46:&lt;h2&gt; --><h2 id="toc23"><a name="Dominant-13-limit"></a><!-- ws:end:WikiTextHeadingRule:46 -->13-limit</h2> | ||
Commas: 36/35, 56/55, 64/63, 66/65<br /> | Commas: 36/35, 56/55, 64/63, 66/65<br /> | ||
<br /> | |||
valid range: 705.882 (17)<br /> | |||
nice range: [691.202, 715.587]<br /> | |||
strict range:705.882 <br /> | |||
<br /> | <br /> | ||
POTE generator: ~3/2 = 703.636<br /> | POTE generator: ~3/2 = 703.636<br /> | ||
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<br /> | <br /> | ||
<a class="wiki_link_ext" href="http://tech.groups.yahoo.com/group/tuning-math/message/3091" rel="nofollow">Origin of the name</a><br /> | <a class="wiki_link_ext" href="http://tech.groups.yahoo.com/group/tuning-math/message/3091" rel="nofollow">Origin of the name</a><br /> | ||
<br /> | |||
valid range: [685.714, 700.000] (14c to 12)<br /> | |||
nice range: [688.957, 701.955]<br /> | |||
strict range: [688.957, 700.000]<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 694.375<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 694.375<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:78:&lt;h2&gt; --><h2 id="toc39"><a name="Injera-11-limit"></a><!-- ws:end:WikiTextHeadingRule:78 -->11-limit</h2> | <!-- ws:start:WikiTextHeadingRule:78:&lt;h2&gt; --><h2 id="toc39"><a name="Injera-11-limit"></a><!-- ws:end:WikiTextHeadingRule:78 -->11-limit</h2> | ||
Commas: 45/44, 50/49, 81/80<br /> | Commas: 45/44, 50/49, 81/80<br /> | ||
<br /> | |||
valid range: [685.714, 700.000] (14c to 12)<br /> | |||
nice range: [682.458, 701.955]<br /> | |||
strict range: [685.714, 700.000] <br /> | |||
<br /> | <br /> | ||
POTE generator: ~3/2 = 692.840<br /> | POTE generator: ~3/2 = 692.840<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:80:&lt;h2&gt; --><h2 id="toc40"><a name="Injera-13-limit"></a><!-- ws:end:WikiTextHeadingRule:80 -->13-limit</h2> | <!-- ws:start:WikiTextHeadingRule:80:&lt;h2&gt; --><h2 id="toc40"><a name="Injera-13-limit"></a><!-- ws:end:WikiTextHeadingRule:80 -->13-limit</h2> | ||
Commas: 45/44, 50/49, 81/80, 78/77<br /> | Commas: 45/44, 50/49, 81/80, 78/77<br /> | ||
<br /> | |||
valid range: 692.308 (26)<br /> | |||
nice range: [682.458, 701.955]<br /> | |||
strict range: 692.308 (26)<br /> | |||
<br /> | <br /> | ||
POTE generator: ~3/2 = 692.673<br /> | POTE generator: ~3/2 = 692.673<br /> | ||
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<br /> | <br /> | ||
Godzilla has wedgie &lt;&lt;2 8 1 8 -4 -20||, and tempers out 49/48, equating 8/7 with 7/6. Two of the step-and-a-quarter intervals these represent give a fourth, and so step-and-a-quarter generators generate godzilla. <a class="wiki_link" href="/19edo">19edo</a> is the perfect godzilla tuning, so much so that's there's not much point in looking elsewhere. Hence it can be more or less equated with taking 4\19 as a generator. MOS are of 5, 9, or 14 notes.<br /> | Godzilla has wedgie &lt;&lt;2 8 1 8 -4 -20||, and tempers out 49/48, equating 8/7 with 7/6. Two of the step-and-a-quarter intervals these represent give a fourth, and so step-and-a-quarter generators generate godzilla. <a class="wiki_link" href="/19edo">19edo</a> is the perfect godzilla tuning, so much so that's there's not much point in looking elsewhere. Hence it can be more or less equated with taking 4\19 as a generator. MOS are of 5, 9, or 14 notes.<br /> | ||
<br /> | |||
valid range: [240.000, 257.143] (5 to 14c)<br /> | |||
nice range: [231.174, 266.871]<br /> | |||
strict range: [240.000, 257.143]<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~8/7 = 252.635<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~8/7 = 252.635<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:90:&lt;h2&gt; --><h2 id="toc45"><a name="Godzilla-11-limit"></a><!-- ws:end:WikiTextHeadingRule:90 -->11-limit</h2> | <!-- ws:start:WikiTextHeadingRule:90:&lt;h2&gt; --><h2 id="toc45"><a name="Godzilla-11-limit"></a><!-- ws:end:WikiTextHeadingRule:90 -->11-limit</h2> | ||
Commas: 45/44, 49/48, 81/80<br /> | Commas: 45/44, 49/48, 81/80<br /> | ||
<br /> | |||
valid range: [252.632, 257.143] (19 to 14c)<br /> | |||
nice range: [231.174, 266.871]<br /> | |||
strict range: [252.632, 257.143]<br /> | |||
<br /> | <br /> | ||
POTE generator: ~8/7 = 254.027<br /> | POTE generator: ~8/7 = 254.027<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:92:&lt;h2&gt; --><h2 id="toc46"><a name="Godzilla-13-limit"></a><!-- ws:end:WikiTextHeadingRule:92 -->13-limit</h2> | <!-- ws:start:WikiTextHeadingRule:92:&lt;h2&gt; --><h2 id="toc46"><a name="Godzilla-13-limit"></a><!-- ws:end:WikiTextHeadingRule:92 -->13-limit</h2> | ||
Commas: 45/44, 49/48, 78/77, 81/80<br /> | Commas: 45/44, 49/48, 78/77, 81/80<br /> | ||
<br /> | |||
valid range: 694.737 (19)<br /> | |||
nice range: [621.581, 737.652]<br /> | |||
strict range: 694.737<br /> | |||
<br /> | <br /> | ||
POTE generator: ~8/7 = 253.603<br /> | POTE generator: ~8/7 = 253.603<br /> | ||