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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>2010- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-12-11 01:40:29 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>187291107</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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">The 5-limit parent comma for the wuerschmidt family is 393216/390625, known as Wuerschmidt's comma. Its monzo is |17 1 -8>, and flipping that yields <<8 1 -17|| for the wedgie. This tells us the generator is a major third, and that to get to the interval class of fifths will require eight of these. In fact, (5/4)^8 * 393216/390625 = 6. 14/53 | <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;white-space: pre-wrap ! important" class="old-revision-html">The 5-limit parent comma for the wuerschmidt family is 393216/390625, known as Wuerschmidt's comma. Its monzo is |17 1 -8>, and flipping that yields <<8 1 -17|| for the wedgie. This tells us the generator is a major third, and that to get to the interval class of fifths will require eight of these. In fact, (5/4)^8 * 393216/390625 = 6. 14/53 or 21/65 are excellent generators, though 9/34 also makes sense and using 19edo is possible. Other tunings include 72edo, 87edo, 140edo and 164edo. Another tuning solution is to sharpen the major third by 1/8th of a Wuerschmift comma, which is to say by 1.43 cents, and thereby achieve pure fifths; this is the minimax tuning. Wuerschmidt is well-supplied with MOS scales, with 10, 13, 16, 19, 22, 25, 28 31 and 34 note MOS all possibilities. | ||
[[POTE tuning|POTE generator]]: 387.799 | |||
Map: [<1 7 3|, <0 -8 -1|] | |||
EDOs: 31, 34, 65, 164 | |||
==Seven limit children== | ==Seven limit children== | ||
| Line 13: | Line 19: | ||
===Wurschmidt=== | ===Wurschmidt=== | ||
Wurschmidt, aside from the commas listed above, also tempers out 225/224. [[31edo]] or [[127edo]] can be used as tunings. Wurschmidt has <<8 1 18 -17 6 39|| for a wedgie. It extends naturally to an 11-limit version <<8 1 18 20 ,,,|| which also tempers out 99/98, 176/175 and 243/242. [[127edo]] is again an excellent tuning for 11-limit wurschmidt, as well as for minerva, the 11-limit rank three temperament tempering out 99/98 and 176/175. | Wurschmidt, aside from the commas listed above, also tempers out 225/224. [[31edo]] or [[127edo]] can be used as tunings. Wurschmidt has <<8 1 18 -17 6 39|| for a wedgie. It extends naturally to an 11-limit version <<8 1 18 20 ,,,|| which also tempers out 99/98, 176/175 and 243/242. [[127edo]] is again an excellent tuning for 11-limit wurschmidt, as well as for minerva, the 11-limit rank three temperament tempering out 99/98 and 176/175. | ||
Commas: 225/224, 8748/8575 | |||
[[POTE tuning|POTE generator]]: 387.383 | |||
Map: [<1 7 3 15|, <0 -8 -1 -18|] | |||
EDOs: 31, 127 | |||
===Worschmidt=== | ===Worschmidt=== | ||
Worschmidt tempers out 126/125 rather than 225/224, and can use [[31edo]], [[34edo]], or [[127edo]] as a tuning. If 127 is used, note that the val is <127 201 295 356| and not <127 201 295 357| as with wurschmidt. The wedgie now is <<8 1 -13 -17 -43 -33|. In practice, of course, both mappings could be used ambiguously, which might be an interesting avenue for someone to explore. | Worschmidt tempers out 126/125 rather than 225/224, and can use [[31edo]], [[34edo]], or [[127edo]] as a tuning. If 127 is used, note that the val is <127 201 295 356| and not <127 201 295 357| as with wurschmidt. The wedgie now is <<8 1 -13 -17 -43 -33|. In practice, of course, both mappings could be used ambiguously, which might be an interesting avenue for someone to explore. | ||
Commas: 126/125, 33075/32768 | |||
[[POTE tuning|POTE generator]]: 387.392 | |||
Map: [<1 7 3 -6|, <0 -8 -1 13|] | |||
EDOs: 31, 127 | |||
===Whirrschmidt=== | ===Whirrschmidt=== | ||
[[99edo]] is such a good tuning for whirrschimdt that we hardly need look any farther. Unfortunately, the temperament while accurate is complex, with <<8 1 52 -17 60 118|| for a wedgie. | [[99edo]] is such a good tuning for whirrschimdt that we hardly need look any farther. Unfortunately, the temperament while accurate is complex, with <<8 1 52 -17 60 118|| for a wedgie. | ||
Commas: 4375/4374, 393216/390625 | |||
[[POTE tuning|POTE generator]]: 387.881 | |||
Map: [<1 7 3 38|, <0 -8 -1 -52|] | |||
EDOs: 31, 34, 99 | |||
===Hemiwuerschmift=== | ===Hemiwuerschmift=== | ||
Hemiwuerschmidt, which splits the major third in two and uses that for a generator, is the most important of these temperaments even with the rather large complexity for the fifth. It tempers out 3136/3125, 6144/6125 and 2401/2400. [[68edo]], [[99edo]] and [[130edo]] can all be used as tunings, but 130 is not only the most accurate, it shows how hemiwuerschmidt extends to a higher limit temperament, <<16 2 5 40 -39 -49 -48 28...</pre></div> | Hemiwuerschmidt, which splits the major third in two and uses that for a generator, is the most important of these temperaments even with the rather large complexity for the fifth. It tempers out 3136/3125, 6144/6125 and 2401/2400. [[68edo]], [[99edo]] and [[130edo]] can all be used as tunings, but 130 is not only the most accurate, it shows how hemiwuerschmidt extends to a higher limit temperament, <<16 2 5 40 -39 -49 -48 28... | ||
Commas: 2401/2400, 3136/3125 | |||
[[POTE tuning|POTE generator]]: 193.898 | |||
Map: [<1 15 4 7|, <0 -16 -2 -5|] | |||
EDOs: 31, 99, 229</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>Würschmidt family</title></head><body>The 5-limit parent comma for the wuerschmidt family is 393216/390625, known as Wuerschmidt's comma. Its monzo is |17 1 -8&gt;, and flipping that yields &lt;&lt;8 1 -17|| for the wedgie. This tells us the generator is a major third, and that to get to the interval class of fifths will require eight of these. In fact, (5/4)^8 * 393216/390625 = 6. 14/53 | <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>Würschmidt family</title></head><body>The 5-limit parent comma for the wuerschmidt family is 393216/390625, known as Wuerschmidt's comma. Its monzo is |17 1 -8&gt;, and flipping that yields &lt;&lt;8 1 -17|| for the wedgie. This tells us the generator is a major third, and that to get to the interval class of fifths will require eight of these. In fact, (5/4)^8 * 393216/390625 = 6. 14/53 or 21/65 are excellent generators, though 9/34 also makes sense and using 19edo is possible. Other tunings include 72edo, 87edo, 140edo and 164edo. Another tuning solution is to sharpen the major third by 1/8th of a Wuerschmift comma, which is to say by 1.43 cents, and thereby achieve pure fifths; this is the minimax tuning. Wuerschmidt is well-supplied with MOS scales, with 10, 13, 16, 19, 22, 25, 28 31 and 34 note MOS all possibilities.<br /> | ||
<br /> | |||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 387.799<br /> | |||
<br /> | |||
Map: [&lt;1 7 3|, &lt;0 -8 -1|]<br /> | |||
<br /> | |||
EDOs: 31, 34, 65, 164<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Seven limit children"></a><!-- ws:end:WikiTextHeadingRule:0 -->Seven limit children</h2> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Seven limit children"></a><!-- ws:end:WikiTextHeadingRule:0 -->Seven limit children</h2> | ||
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<!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x-Seven limit children-Wurschmidt"></a><!-- ws:end:WikiTextHeadingRule:2 -->Wurschmidt</h3> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x-Seven limit children-Wurschmidt"></a><!-- ws:end:WikiTextHeadingRule:2 -->Wurschmidt</h3> | ||
Wurschmidt, aside from the commas listed above, also tempers out 225/224. <a class="wiki_link" href="/31edo">31edo</a> or <a class="wiki_link" href="/127edo">127edo</a> can be used as tunings. Wurschmidt has &lt;&lt;8 1 18 -17 6 39|| for a wedgie. It extends naturally to an 11-limit version &lt;&lt;8 1 18 20 ,,,|| which also tempers out 99/98, 176/175 and 243/242. <a class="wiki_link" href="/127edo">127edo</a> is again an excellent tuning for 11-limit wurschmidt, as well as for minerva, the 11-limit rank three temperament tempering out 99/98 and 176/175.<br /> | Wurschmidt, aside from the commas listed above, also tempers out 225/224. <a class="wiki_link" href="/31edo">31edo</a> or <a class="wiki_link" href="/127edo">127edo</a> can be used as tunings. Wurschmidt has &lt;&lt;8 1 18 -17 6 39|| for a wedgie. It extends naturally to an 11-limit version &lt;&lt;8 1 18 20 ,,,|| which also tempers out 99/98, 176/175 and 243/242. <a class="wiki_link" href="/127edo">127edo</a> is again an excellent tuning for 11-limit wurschmidt, as well as for minerva, the 11-limit rank three temperament tempering out 99/98 and 176/175.<br /> | ||
<br /> | |||
Commas: 225/224, 8748/8575<br /> | |||
<br /> | |||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 387.383<br /> | |||
<br /> | |||
Map: [&lt;1 7 3 15|, &lt;0 -8 -1 -18|]<br /> | |||
<br /> | |||
EDOs: 31, 127<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x-Seven limit children-Worschmidt"></a><!-- ws:end:WikiTextHeadingRule:4 -->Worschmidt</h3> | <!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x-Seven limit children-Worschmidt"></a><!-- ws:end:WikiTextHeadingRule:4 -->Worschmidt</h3> | ||
Worschmidt tempers out 126/125 rather than 225/224, and can use <a class="wiki_link" href="/31edo">31edo</a>, <a class="wiki_link" href="/34edo">34edo</a>, or <a class="wiki_link" href="/127edo">127edo</a> as a tuning. If 127 is used, note that the val is &lt;127 201 295 356| and not &lt;127 201 295 357| as with wurschmidt. The wedgie now is &lt;&lt;8 1 -13 -17 -43 -33|. In practice, of course, both mappings could be used ambiguously, which might be an interesting avenue for someone to explore. <br /> | Worschmidt tempers out 126/125 rather than 225/224, and can use <a class="wiki_link" href="/31edo">31edo</a>, <a class="wiki_link" href="/34edo">34edo</a>, or <a class="wiki_link" href="/127edo">127edo</a> as a tuning. If 127 is used, note that the val is &lt;127 201 295 356| and not &lt;127 201 295 357| as with wurschmidt. The wedgie now is &lt;&lt;8 1 -13 -17 -43 -33|. In practice, of course, both mappings could be used ambiguously, which might be an interesting avenue for someone to explore. <br /> | ||
<br /> | |||
Commas: 126/125, 33075/32768<br /> | |||
<br /> | |||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 387.392<br /> | |||
<br /> | |||
Map: [&lt;1 7 3 -6|, &lt;0 -8 -1 13|]<br /> | |||
<br /> | |||
EDOs: 31, 127<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc3"><a name="x-Seven limit children-Whirrschmidt"></a><!-- ws:end:WikiTextHeadingRule:6 -->Whirrschmidt</h3> | <!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc3"><a name="x-Seven limit children-Whirrschmidt"></a><!-- ws:end:WikiTextHeadingRule:6 -->Whirrschmidt</h3> | ||
<a class="wiki_link" href="/99edo">99edo</a> is such a good tuning for whirrschimdt that we hardly need look any farther. Unfortunately, the temperament while accurate is complex, with &lt;&lt;8 1 52 -17 60 118|| for a wedgie.<br /> | <a class="wiki_link" href="/99edo">99edo</a> is such a good tuning for whirrschimdt that we hardly need look any farther. Unfortunately, the temperament while accurate is complex, with &lt;&lt;8 1 52 -17 60 118|| for a wedgie.<br /> | ||
<br /> | |||
Commas: 4375/4374, 393216/390625<br /> | |||
<br /> | |||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 387.881<br /> | |||
<br /> | |||
Map: [&lt;1 7 3 38|, &lt;0 -8 -1 -52|]<br /> | |||
<br /> | |||
EDOs: 31, 34, 99<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><a name="x-Seven limit children-Hemiwuerschmift"></a><!-- ws:end:WikiTextHeadingRule:8 -->Hemiwuerschmift</h3> | <!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><a name="x-Seven limit children-Hemiwuerschmift"></a><!-- ws:end:WikiTextHeadingRule:8 -->Hemiwuerschmift</h3> | ||
Hemiwuerschmidt, which splits the major third in two and uses that for a generator, is the most important of these temperaments even with the rather large complexity for the fifth. It tempers out 3136/3125, 6144/6125 and 2401/2400. <a class="wiki_link" href="/68edo">68edo</a>, <a class="wiki_link" href="/99edo">99edo</a> and <a class="wiki_link" href="/130edo">130edo</a> can all be used as tunings, but 130 is not only the most accurate, it shows how hemiwuerschmidt extends to a higher limit temperament, &lt;&lt;16 2 5 40 -39 -49 -48 28...</body></html></pre></div> | Hemiwuerschmidt, which splits the major third in two and uses that for a generator, is the most important of these temperaments even with the rather large complexity for the fifth. It tempers out 3136/3125, 6144/6125 and 2401/2400. <a class="wiki_link" href="/68edo">68edo</a>, <a class="wiki_link" href="/99edo">99edo</a> and <a class="wiki_link" href="/130edo">130edo</a> can all be used as tunings, but 130 is not only the most accurate, it shows how hemiwuerschmidt extends to a higher limit temperament, &lt;&lt;16 2 5 40 -39 -49 -48 28...<br /> | ||
<br /> | |||
Commas: 2401/2400, 3136/3125<br /> | |||
<br /> | |||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 193.898<br /> | |||
<br /> | |||
Map: [&lt;1 15 4 7|, &lt;0 -16 -2 -5|]<br /> | |||
<br /> | |||
EDOs: 31, 99, 229</body></html></pre></div> | |||
Revision as of 01:40, 11 December 2010
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author genewardsmith and made on 2010-12-11 01:40:29 UTC.
- The original revision id was 187291107.
- 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:
The 5-limit parent comma for the wuerschmidt family is 393216/390625, known as Wuerschmidt's comma. Its monzo is |17 1 -8>, and flipping that yields <<8 1 -17|| for the wedgie. This tells us the generator is a major third, and that to get to the interval class of fifths will require eight of these. In fact, (5/4)^8 * 393216/390625 = 6. 14/53 or 21/65 are excellent generators, though 9/34 also makes sense and using 19edo is possible. Other tunings include 72edo, 87edo, 140edo and 164edo. Another tuning solution is to sharpen the major third by 1/8th of a Wuerschmift comma, which is to say by 1.43 cents, and thereby achieve pure fifths; this is the minimax tuning. Wuerschmidt is well-supplied with MOS scales, with 10, 13, 16, 19, 22, 25, 28 31 and 34 note MOS all possibilities. [[POTE tuning|POTE generator]]: 387.799 Map: [<1 7 3|, <0 -8 -1|] EDOs: 31, 34, 65, 164 ==Seven limit children== The second comma of the [[Normal lists|normal comma list]] defines which 7-limit family member we are looking at. Wurschmidt adds |12 3 -6 -1>, worschmidt adds 65625/65536 = |-16 1 5 1>, whirrschmidt adds 4375/4374 = |-1 -7 4 1> and hemiwuerschmidt adds 6144/6125 = |11 1 -3 -2>. ===Wurschmidt=== Wurschmidt, aside from the commas listed above, also tempers out 225/224. [[31edo]] or [[127edo]] can be used as tunings. Wurschmidt has <<8 1 18 -17 6 39|| for a wedgie. It extends naturally to an 11-limit version <<8 1 18 20 ,,,|| which also tempers out 99/98, 176/175 and 243/242. [[127edo]] is again an excellent tuning for 11-limit wurschmidt, as well as for minerva, the 11-limit rank three temperament tempering out 99/98 and 176/175. Commas: 225/224, 8748/8575 [[POTE tuning|POTE generator]]: 387.383 Map: [<1 7 3 15|, <0 -8 -1 -18|] EDOs: 31, 127 ===Worschmidt=== Worschmidt tempers out 126/125 rather than 225/224, and can use [[31edo]], [[34edo]], or [[127edo]] as a tuning. If 127 is used, note that the val is <127 201 295 356| and not <127 201 295 357| as with wurschmidt. The wedgie now is <<8 1 -13 -17 -43 -33|. In practice, of course, both mappings could be used ambiguously, which might be an interesting avenue for someone to explore. Commas: 126/125, 33075/32768 [[POTE tuning|POTE generator]]: 387.392 Map: [<1 7 3 -6|, <0 -8 -1 13|] EDOs: 31, 127 ===Whirrschmidt=== [[99edo]] is such a good tuning for whirrschimdt that we hardly need look any farther. Unfortunately, the temperament while accurate is complex, with <<8 1 52 -17 60 118|| for a wedgie. Commas: 4375/4374, 393216/390625 [[POTE tuning|POTE generator]]: 387.881 Map: [<1 7 3 38|, <0 -8 -1 -52|] EDOs: 31, 34, 99 ===Hemiwuerschmift=== Hemiwuerschmidt, which splits the major third in two and uses that for a generator, is the most important of these temperaments even with the rather large complexity for the fifth. It tempers out 3136/3125, 6144/6125 and 2401/2400. [[68edo]], [[99edo]] and [[130edo]] can all be used as tunings, but 130 is not only the most accurate, it shows how hemiwuerschmidt extends to a higher limit temperament, <<16 2 5 40 -39 -49 -48 28... Commas: 2401/2400, 3136/3125 [[POTE tuning|POTE generator]]: 193.898 Map: [<1 15 4 7|, <0 -16 -2 -5|] EDOs: 31, 99, 229
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<html><head><title>Würschmidt family</title></head><body>The 5-limit parent comma for the wuerschmidt family is 393216/390625, known as Wuerschmidt's comma. Its monzo is |17 1 -8>, and flipping that yields <<8 1 -17|| for the wedgie. This tells us the generator is a major third, and that to get to the interval class of fifths will require eight of these. In fact, (5/4)^8 * 393216/390625 = 6. 14/53 or 21/65 are excellent generators, though 9/34 also makes sense and using 19edo is possible. Other tunings include 72edo, 87edo, 140edo and 164edo. Another tuning solution is to sharpen the major third by 1/8th of a Wuerschmift comma, which is to say by 1.43 cents, and thereby achieve pure fifths; this is the minimax tuning. Wuerschmidt is well-supplied with MOS scales, with 10, 13, 16, 19, 22, 25, 28 31 and 34 note MOS all possibilities.<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 387.799<br /> <br /> Map: [<1 7 3|, <0 -8 -1|]<br /> <br /> EDOs: 31, 34, 65, 164<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h2> --><h2 id="toc0"><a name="x-Seven limit children"></a><!-- ws:end:WikiTextHeadingRule:0 -->Seven limit children</h2> The second comma of the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> defines which 7-limit family member we are looking at. Wurschmidt adds |12 3 -6 -1>, worschmidt adds 65625/65536 = |-16 1 5 1>, whirrschmidt adds 4375/4374 = |-1 -7 4 1> and hemiwuerschmidt adds 6144/6125 = |11 1 -3 -2>.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h3> --><h3 id="toc1"><a name="x-Seven limit children-Wurschmidt"></a><!-- ws:end:WikiTextHeadingRule:2 -->Wurschmidt</h3> Wurschmidt, aside from the commas listed above, also tempers out 225/224. <a class="wiki_link" href="/31edo">31edo</a> or <a class="wiki_link" href="/127edo">127edo</a> can be used as tunings. Wurschmidt has <<8 1 18 -17 6 39|| for a wedgie. It extends naturally to an 11-limit version <<8 1 18 20 ,,,|| which also tempers out 99/98, 176/175 and 243/242. <a class="wiki_link" href="/127edo">127edo</a> is again an excellent tuning for 11-limit wurschmidt, as well as for minerva, the 11-limit rank three temperament tempering out 99/98 and 176/175.<br /> <br /> Commas: 225/224, 8748/8575<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 387.383<br /> <br /> Map: [<1 7 3 15|, <0 -8 -1 -18|]<br /> <br /> EDOs: 31, 127<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h3> --><h3 id="toc2"><a name="x-Seven limit children-Worschmidt"></a><!-- ws:end:WikiTextHeadingRule:4 -->Worschmidt</h3> Worschmidt tempers out 126/125 rather than 225/224, and can use <a class="wiki_link" href="/31edo">31edo</a>, <a class="wiki_link" href="/34edo">34edo</a>, or <a class="wiki_link" href="/127edo">127edo</a> as a tuning. If 127 is used, note that the val is <127 201 295 356| and not <127 201 295 357| as with wurschmidt. The wedgie now is <<8 1 -13 -17 -43 -33|. In practice, of course, both mappings could be used ambiguously, which might be an interesting avenue for someone to explore. <br /> <br /> Commas: 126/125, 33075/32768<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 387.392<br /> <br /> Map: [<1 7 3 -6|, <0 -8 -1 13|]<br /> <br /> EDOs: 31, 127<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h3> --><h3 id="toc3"><a name="x-Seven limit children-Whirrschmidt"></a><!-- ws:end:WikiTextHeadingRule:6 -->Whirrschmidt</h3> <a class="wiki_link" href="/99edo">99edo</a> is such a good tuning for whirrschimdt that we hardly need look any farther. Unfortunately, the temperament while accurate is complex, with <<8 1 52 -17 60 118|| for a wedgie.<br /> <br /> Commas: 4375/4374, 393216/390625<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 387.881<br /> <br /> Map: [<1 7 3 38|, <0 -8 -1 -52|]<br /> <br /> EDOs: 31, 34, 99<br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h3> --><h3 id="toc4"><a name="x-Seven limit children-Hemiwuerschmift"></a><!-- ws:end:WikiTextHeadingRule:8 -->Hemiwuerschmift</h3> Hemiwuerschmidt, which splits the major third in two and uses that for a generator, is the most important of these temperaments even with the rather large complexity for the fifth. It tempers out 3136/3125, 6144/6125 and 2401/2400. <a class="wiki_link" href="/68edo">68edo</a>, <a class="wiki_link" href="/99edo">99edo</a> and <a class="wiki_link" href="/130edo">130edo</a> can all be used as tunings, but 130 is not only the most accurate, it shows how hemiwuerschmidt extends to a higher limit temperament, <<16 2 5 40 -39 -49 -48 28...<br /> <br /> Commas: 2401/2400, 3136/3125<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 193.898<br /> <br /> Map: [<1 15 4 7|, <0 -16 -2 -5|]<br /> <br /> EDOs: 31, 99, 229</body></html>