Temperament orphanage: Difference between revisions
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Wikispaces>guest **Imported revision 235832416 - Original comment: ** |
Wikispaces>guest **Imported revision 235838744 - 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:guest|guest]] and made on <tt>2011-06-10 | : This revision was by author [[User:guest|guest]] and made on <tt>2011-06-10 16:06:14 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>235838744</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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3&8b temperament. It equates (5/4)^4 with 8/3. It is so named because the generator is a sharp major third. I don't think "smate" is actually a word, but it is now. | 3&8b temperament. It equates (5/4)^4 with 8/3. It is so named because the generator is a sharp major third. I don't think "smate" is actually a word, but it is now. | ||
POTE generator: ~5/4 = 420. | POTE generator: ~5/4 = 420.855 | ||
Map = [<1 2 3|, <0 -4 1|& | Map = [<1 2 3|, <0 -4 1|] | ||
==Enipucrop - 5-limit - tempers 1125/1024== | |||
6b&7 temperament. Its name is "porcupine" spelled backwards, because that's what this temperament is - it's porcupine, with the generator sharp of 2\7 such that the major and minor thirds switch places. The fifths are very flat, meaning that this is more of a melodic temperament than a harmonic one. | |||
POTE generator: ~16/15 = 173.101 | |||
Map = [<1 2 2|, <0 -3 2|] | |||
==Gravity - 5-limit - tempers 129140163/128000000== | ==Gravity - 5-limit - tempers 129140163/128000000== | ||
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3&amp;8b temperament. It equates (5/4)^4 with 8/3. It is so named because the generator is a sharp major third. I don't think &quot;smate&quot; is actually a word, but it is now.<br /> | 3&amp;8b temperament. It equates (5/4)^4 with 8/3. It is so named because the generator is a sharp major third. I don't think &quot;smate&quot; is actually a word, but it is now.<br /> | ||
<br /> | <br /> | ||
POTE generator: ~5/4 = 420. | POTE generator: ~5/4 = 420.855<br /> | ||
Map = [&lt;1 2 3|, &lt;0 -4 1|&gt;<br /> | Map = [&lt;1 2 3|, &lt;0 -4 1|]<br /> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Welcome to the Temperament Orphanage-Enipucrop - 5-limit - tempers 1125/1024"></a><!-- ws:end:WikiTextHeadingRule:8 -->Enipucrop - 5-limit - tempers 1125/1024</h2> | |||
6b&amp;7 temperament. Its name is &quot;porcupine&quot; spelled backwards, because that's what this temperament is - it's porcupine, with the generator sharp of 2\7 such that the major and minor thirds switch places. The fifths are very flat, meaning that this is more of a melodic temperament than a harmonic one.<br /> | |||
<br /> | |||
POTE generator: ~16/15 = 173.101<br /> | |||
Map = [&lt;1 2 2|, &lt;0 -3 2|]<br /> | |||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="Welcome to the Temperament Orphanage-Gravity - 5-limit - tempers 129140163/128000000"></a><!-- ws:end:WikiTextHeadingRule:10 -->Gravity - 5-limit - tempers 129140163/128000000</h2> | ||
5&amp;67 temperament. It equates (81/80)^4 with 25/24. It is so named because the generator is a &quot;Grave&quot; fifth (or 27/20). It is part of the Mavila -&gt; Dicot -&gt; Porcupine -&gt; Tetracot -&gt; Amity continuum, whereby (81/80)^n = 25/24.<br /> | 5&amp;67 temperament. It equates (81/80)^4 with 25/24. It is so named because the generator is a &quot;Grave&quot; fifth (or 27/20). It is part of the Mavila -&gt; Dicot -&gt; Porcupine -&gt; Tetracot -&gt; Amity continuum, whereby (81/80)^n = 25/24.<br /> | ||
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<a class="wiki_link_ext" href="http://x31eq.com/cgi-bin/rt.cgi?ets=65_7&amp;limit=5" rel="nofollow" target="_blank">http://x31eq.com/cgi-bin/rt. cgi?ets=65_7&amp;limit=5</a><br /> | <a class="wiki_link_ext" href="http://x31eq.com/cgi-bin/rt.cgi?ets=65_7&amp;limit=5" rel="nofollow" target="_blank">http://x31eq.com/cgi-bin/rt. cgi?ets=65_7&amp;limit=5</a><br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Welcome to the Temperament Orphanage-Absurdity - 5-limit - tempers 10460353203/10240000000"></a><!-- ws:end:WikiTextHeadingRule:12 -->Absurdity - 5-limit - tempers 10460353203/10240000000</h2> | ||
5&amp;84 temperament. So named because this is just an absurd temperament. If you have a better name for it then it doesn't have to be absurdity anymore. The generator is 81/80 and the period is 800/729, which is (10/9) / (81/80). This is also a part of the syntonic-chromatic equivalence continuum, in this case where (81/80)^5 = 25/24.<br /> | 5&amp;84 temperament. So named because this is just an absurd temperament. If you have a better name for it then it doesn't have to be absurdity anymore. The generator is 81/80 and the period is 800/729, which is (10/9) / (81/80). This is also a part of the syntonic-chromatic equivalence continuum, in this case where (81/80)^5 = 25/24.<br /> | ||
<a class="wiki_link_ext" href="http://x31eq.com/cgi-bin/rt.cgi?ets=7_84&amp;limit=5" rel="nofollow" target="_blank">http://x31eq.com/cgi-bin/rt. cgi?ets=7_84&amp;limit=5</a><br /> | <a class="wiki_link_ext" href="http://x31eq.com/cgi-bin/rt.cgi?ets=7_84&amp;limit=5" rel="nofollow" target="_blank">http://x31eq.com/cgi-bin/rt. cgi?ets=7_84&amp;limit=5</a><br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="Welcome to the Temperament Orphanage-7&amp;49 - 5-limit - tempers 5000000/4782969"></a><!-- ws:end:WikiTextHeadingRule:14 --><strong>7&amp;49</strong> - 5-limit - tempers 5000000/4782969</h2> | ||
This is a fairly obvious temperament; it just equates 7 10/9's with a 2/1, hence the period is 10/9. One generator from 5\7 puts you at 3/2, two generators from 2\7 puts you at 5/4.<br /> | This is a fairly obvious temperament; it just equates 7 10/9's with a 2/1, hence the period is 10/9. One generator from 5\7 puts you at 3/2, two generators from 2\7 puts you at 5/4.<br /> | ||
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<a class="wiki_link_ext" href="http://x31eq.com/cgi-bin/rt.cgi?ets=7_49&amp;limit=5" rel="nofollow">http://x31eq.com/cgi-bin/rt.cgi?ets=7_49&amp;limit=5</a><br /> | <a class="wiki_link_ext" href="http://x31eq.com/cgi-bin/rt.cgi?ets=7_49&amp;limit=5" rel="nofollow">http://x31eq.com/cgi-bin/rt.cgi?ets=7_49&amp;limit=5</a><br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="Welcome to the Temperament Orphanage-7&amp;49c - 5-limit - tempers 78125/69984"></a><!-- ws:end:WikiTextHeadingRule:16 --><strong>7&amp;</strong>49c - 5-limit - tempers 78125/69984</h2> | ||
This is similar to the above, but provides a less complex avenue to 5, but this time at the sake of accuracy. One generator from 5\7 puts you at 3/2, and one generator from 2\7 puts you at 5/4.<br /> | This is similar to the above, but provides a less complex avenue to 5, but this time at the sake of accuracy. One generator from 5\7 puts you at 3/2, and one generator from 2\7 puts you at 5/4.<br /> | ||
<br /> | <br /> | ||
Revision as of 16:06, 10 June 2011
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author guest and made on 2011-06-10 16:06:14 UTC.
- The original revision id was 235838744.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
=__**Welcome to the Temperament Orphanage**__= ==These temperaments need to be adopted into a family== These are some temperaments that were found floating around. It isn't clear what family they belong to, so for now they're in the temperament orphanage. Should you know how to match these temperaments back up with their temperament family, feel free to remove them from the orphanage and put them on the right page. If a temperament listed doesn't have a name, give it a name. Please give a short description of whatever temperament you leave here so that someone can help to match this temperament back to its rightful progenitors. ==Smite - 5-limit - tempers 2916/3125== 7&18 temperament. It equates (6/5)^5 with 8/3. It is so named because the generator is a really sharp minor third, the contraction of which is "smite." POTE generator: ~6/5 = 338.365 Map = [<1 3 4|, <0 -5 -6|] EDOs: 7, 11, 18 ==Smate - 5-limit - tempers 2048/1875== 3&8b temperament. It equates (5/4)^4 with 8/3. It is so named because the generator is a sharp major third. I don't think "smate" is actually a word, but it is now. POTE generator: ~5/4 = 420.855 Map = [<1 2 3|, <0 -4 1|] ==Enipucrop - 5-limit - tempers 1125/1024== 6b&7 temperament. Its name is "porcupine" spelled backwards, because that's what this temperament is - it's porcupine, with the generator sharp of 2\7 such that the major and minor thirds switch places. The fifths are very flat, meaning that this is more of a melodic temperament than a harmonic one. POTE generator: ~16/15 = 173.101 Map = [<1 2 2|, <0 -3 2|] ==Gravity - 5-limit - tempers 129140163/128000000== 5&67 temperament. It equates (81/80)^4 with 25/24. It is so named because the generator is a "Grave" fifth (or 27/20). It is part of the Mavila -> Dicot -> Porcupine -> Tetracot -> Amity continuum, whereby (81/80)^n = 25/24. POTE generator: ~27/20 = 516.844 cents Map: [<1 5 12|, <0 -6 -17|] EDOs: 7, 58, 65, 137, 202, 267, 469 Tempering out 65625/65536 does little damage to tuning accuracy but results in a very complex temperament. [[@http://x31eq.com/cgi-bin/rt.cgi?ets=65_7&limit=5|http://x31eq.com/cgi-bin/rt. cgi?ets=65_7&limit=5]] ==Absurdity - 5-limit - tempers 10460353203/10240000000== 5&84 temperament. So named because this is just an absurd temperament. If you have a better name for it then it doesn't have to be absurdity anymore. The generator is 81/80 and the period is 800/729, which is (10/9) / (81/80). This is also a part of the syntonic-chromatic equivalence continuum, in this case where (81/80)^5 = 25/24. [[@http://x31eq.com/cgi-bin/rt.cgi?ets=7_84&limit=5|http://x31eq.com/cgi-bin/rt. cgi?ets=7_84&limit=5]] ==**7&49** - 5-limit - tempers 5000000/4782969== This is a fairly obvious temperament; it just equates 7 10/9's with a 2/1, hence the period is 10/9. One generator from 5\7 puts you at 3/2, two generators from 2\7 puts you at 5/4. POTE generator: ~3/2 = 706.288 cents Map: [<7 0 -6|, <0 1 2|] EDOs: 7, 42, 49, 56, 119 Adding 875/864 to the commas extends this to the 7-limit: POTE generator: ~3/2 = 705.613 cents Map: [<7 0 -6 53|, <0 1 2 -3|] EDOs: 7, 56, 63, 119 [[http://x31eq.com/cgi-bin/rt.cgi?ets=7_49&limit=5]] ==**7&**49c - 5-limit - tempers 78125/69984== This is similar to the above, but provides a less complex avenue to 5, but this time at the sake of accuracy. One generator from 5\7 puts you at 3/2, and one generator from 2\7 puts you at 5/4. Comma: 78125/69984 POTE generator: ~3/2 = 706.410 cents Map: [<7 0 5|, <0 1 1|] EDOs: 7, 56 [[http://x31eq.com/cgi-bin/rt.cgi?ets=7_49c&limit=5]]
Original HTML content:
<html><head><title>TemperamentOrphanage</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Welcome to the Temperament Orphanage"></a><!-- ws:end:WikiTextHeadingRule:0 --><u><strong>Welcome to the Temperament Orphanage</strong></u></h1> <!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="Welcome to the Temperament Orphanage-These temperaments need to be adopted into a family"></a><!-- ws:end:WikiTextHeadingRule:2 -->These temperaments need to be adopted into a family</h2> <br /> These are some temperaments that were found floating around. It isn't clear what family they belong to, so for now they're in the temperament orphanage. Should you know how to match these temperaments back up with their temperament family, feel free to remove them from the orphanage and put them on the right page. If a temperament listed doesn't have a name, give it a name.<br /> <br /> Please give a short description of whatever temperament you leave here so that someone can help to match this temperament back to its rightful progenitors.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="Welcome to the Temperament Orphanage-Smite - 5-limit - tempers 2916/3125"></a><!-- ws:end:WikiTextHeadingRule:4 -->Smite - 5-limit - tempers 2916/3125</h2> 7&18 temperament. It equates (6/5)^5 with 8/3. It is so named because the generator is a really sharp minor third, the contraction of which is "smite."<br /> <br /> POTE generator: ~6/5 = 338.365<br /> <br /> Map = [<1 3 4|, <0 -5 -6|]<br /> EDOs: 7, 11, 18<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="Welcome to the Temperament Orphanage-Smate - 5-limit - tempers 2048/1875"></a><!-- ws:end:WikiTextHeadingRule:6 -->Smate - 5-limit - tempers 2048/1875</h2> 3&8b temperament. It equates (5/4)^4 with 8/3. It is so named because the generator is a sharp major third. I don't think "smate" is actually a word, but it is now.<br /> <br /> POTE generator: ~5/4 = 420.855<br /> Map = [<1 2 3|, <0 -4 1|]<br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h2> --><h2 id="toc4"><a name="Welcome to the Temperament Orphanage-Enipucrop - 5-limit - tempers 1125/1024"></a><!-- ws:end:WikiTextHeadingRule:8 -->Enipucrop - 5-limit - tempers 1125/1024</h2> 6b&7 temperament. Its name is "porcupine" spelled backwards, because that's what this temperament is - it's porcupine, with the generator sharp of 2\7 such that the major and minor thirds switch places. The fifths are very flat, meaning that this is more of a melodic temperament than a harmonic one.<br /> <br /> POTE generator: ~16/15 = 173.101<br /> Map = [<1 2 2|, <0 -3 2|]<br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h2> --><h2 id="toc5"><a name="Welcome to the Temperament Orphanage-Gravity - 5-limit - tempers 129140163/128000000"></a><!-- ws:end:WikiTextHeadingRule:10 -->Gravity - 5-limit - tempers 129140163/128000000</h2> 5&67 temperament. It equates (81/80)^4 with 25/24. It is so named because the generator is a "Grave" fifth (or 27/20). It is part of the Mavila -> Dicot -> Porcupine -> Tetracot -> Amity continuum, whereby (81/80)^n = 25/24.<br /> <br /> POTE generator: ~27/20 = 516.844 cents<br /> <br /> Map: [<1 5 12|, <0 -6 -17|]<br /> EDOs: 7, 58, 65, 137, 202, 267, 469<br /> <br /> Tempering out 65625/65536 does little damage to tuning accuracy but results in a very complex temperament.<br /> <br /> <a class="wiki_link_ext" href="http://x31eq.com/cgi-bin/rt.cgi?ets=65_7&limit=5" rel="nofollow" target="_blank">http://x31eq.com/cgi-bin/rt. cgi?ets=65_7&limit=5</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h2> --><h2 id="toc6"><a name="Welcome to the Temperament Orphanage-Absurdity - 5-limit - tempers 10460353203/10240000000"></a><!-- ws:end:WikiTextHeadingRule:12 -->Absurdity - 5-limit - tempers 10460353203/10240000000</h2> 5&84 temperament. So named because this is just an absurd temperament. If you have a better name for it then it doesn't have to be absurdity anymore. The generator is 81/80 and the period is 800/729, which is (10/9) / (81/80). This is also a part of the syntonic-chromatic equivalence continuum, in this case where (81/80)^5 = 25/24.<br /> <a class="wiki_link_ext" href="http://x31eq.com/cgi-bin/rt.cgi?ets=7_84&limit=5" rel="nofollow" target="_blank">http://x31eq.com/cgi-bin/rt. cgi?ets=7_84&limit=5</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:14:<h2> --><h2 id="toc7"><a name="Welcome to the Temperament Orphanage-7&49 - 5-limit - tempers 5000000/4782969"></a><!-- ws:end:WikiTextHeadingRule:14 --><strong>7&49</strong> - 5-limit - tempers 5000000/4782969</h2> This is a fairly obvious temperament; it just equates 7 10/9's with a 2/1, hence the period is 10/9. One generator from 5\7 puts you at 3/2, two generators from 2\7 puts you at 5/4.<br /> <br /> POTE generator: ~3/2 = 706.288 cents<br /> <br /> Map: [<7 0 -6|, <0 1 2|]<br /> EDOs: 7, 42, 49, 56, 119<br /> <br /> Adding 875/864 to the commas extends this to the 7-limit:<br /> <br /> POTE generator: ~3/2 = 705.613 cents<br /> <br /> Map: [<7 0 -6 53|, <0 1 2 -3|]<br /> EDOs: 7, 56, 63, 119<br /> <br /> <a class="wiki_link_ext" href="http://x31eq.com/cgi-bin/rt.cgi?ets=7_49&limit=5" rel="nofollow">http://x31eq.com/cgi-bin/rt.cgi?ets=7_49&limit=5</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:16:<h2> --><h2 id="toc8"><a name="Welcome to the Temperament Orphanage-7&49c - 5-limit - tempers 78125/69984"></a><!-- ws:end:WikiTextHeadingRule:16 --><strong>7&</strong>49c - 5-limit - tempers 78125/69984</h2> This is similar to the above, but provides a less complex avenue to 5, but this time at the sake of accuracy. One generator from 5\7 puts you at 3/2, and one generator from 2\7 puts you at 5/4.<br /> <br /> Comma: 78125/69984<br /> <br /> POTE generator: ~3/2 = 706.410 cents<br /> <br /> Map: [<7 0 5|, <0 1 1|]<br /> EDOs: 7, 56<br /> <br /> <a class="wiki_link_ext" href="http://x31eq.com/cgi-bin/rt.cgi?ets=7_49c&limit=5" rel="nofollow">http://x31eq.com/cgi-bin/rt.cgi?ets=7_49c&limit=5</a></body></html>