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Wikispaces>genewardsmith **Imported revision 299503926 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 299504200 - 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>2012-02-07 19: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-02-07 19:19:13 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>299504200</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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|| 65536/65219 || [[282edo]] || [[Porwell temperaments#Septisuperfourth|septisuperfourth]] || 540/539, 4000/3993, 5632/5625 || | || 65536/65219 || [[282edo]] || [[Porwell temperaments#Septisuperfourth|septisuperfourth]] || 540/539, 4000/3993, 5632/5625 || | ||
|| 243/242 || [[202edo]] || [[harry]] || 243/242, 441/440, 4000/3993 || | || 243/242 || [[202edo]] || [[harry]] || 243/242, 441/440, 4000/3993 || | ||
|| 3388/3375 || [[316edo]] || [[Ragismic microtemperaments#Semiparakleismic| | || 3388/3375 || [[316edo]] || [[Ragismic microtemperaments#Semiparakleismic|semiparakleismic]] || 3025/3024, 3136/3125, 4375/4374 || | ||
|| 385/384 || [[284edo]] || [[quadritikleismic]] || 385/384, 1375/1372, 6250/6237 || | || 385/384 || [[284edo]] || [[quadritikleismic]] || 385/384, 1375/1372, 6250/6237 || | ||
|| 441/400 || [[320edo]] || [[octowerck]] || 441/440, 8019/8000, 41503/41472 || | || 441/400 || [[320edo]] || [[octowerck]] || 441/440, 8019/8000, 41503/41472 || | ||
| Line 512: | Line 512: | ||
<td><a class="wiki_link" href="/316edo">316edo</a><br /> | <td><a class="wiki_link" href="/316edo">316edo</a><br /> | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/Ragismic%20microtemperaments#Semiparakleismic"> | <td><a class="wiki_link" href="/Ragismic%20microtemperaments#Semiparakleismic">semiparakleismic</a><br /> | ||
</td> | </td> | ||
<td>3025/3024, 3136/3125, 4375/4374<br /> | <td>3025/3024, 3136/3125, 4375/4374<br /> | ||
Revision as of 19:19, 7 February 2012
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 2012-02-07 19:19:13 UTC.
- The original revision id was 299504200.
- 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:
By an //associated temperament// to a p-limit comma is meant a p-limit temperament which shares the same [[optimal patent val]] as the [[Rank and codimension|codimension one]] temperament tempering out that comma. By definition, the optimal patent val defines the unique rank one associated temperament. For rank two temperaments, it is possible for more than one temperament to be associated, and some of these are listed below. The column headings are the comma being associated, the optimal patent val, the rank two temperament, and a comma basis for the rank two temperament. =7 limit= || Comma || OPV || Temperament || Basis || || 28/27 || [[15edo]] || [[blacksmith]] || 28/27, 49/48 || || 1029/1000 || [[55edo]] || [[liese]] || 81/80, 686/675 || || 36/35 || [[12edo]] || [[diminished]] || 36/35, 50/49 || || 36/35 || [[12edo]] || [[august]] || 36/35, 128/125 || || 36/35 || [[12edo]] || [[dominant]] || 36/35, 64/63 || || 525/512 || [[45edo]] || [[flattone]] || 81/80, 525/512 || || 49/48 || [[19edo]] || [[keemun]] || 49/48, 126/125 || || 49/48 || [[19edo]] || [[godzilla]] || 49/48, 81/80 || || 50/49 || [[48edo]] || [[doublewide]] || 50/49, 875/864 || || 64/63 || [[49edo]] || [[superpyth]] || 64/63, 245/243 || || 875/864 || [[41edo]] || [[magic]] || 225/224, 245/243 || || 3125/3087 || [[94edo]] || [[garibaldi]] || 225/224, 3125/3087 || || 2430/2401 || [[137edo]] || [[orwell]] || 225/224, 1728/1715 || || 245/243 || [[283edo]] || [[Escapade family#Escaped|escaped]] || 245/243, 65625/65536 || || 126/125 || [[185edo]] || [[valentine]] || 126/125, 1029/1024 || || 1728/1715 || [[111edo]] || [[Hemifamity temperaments#Buzzard|buzzard]] || 1728/1715, 5120/5103 || || 1728/1715 || [[111edo]] || [[semisept]] || 1728/1715, 3136/3125 || || 1029/1024 || [[190edo]] || [[unidec]] || 1029/1024, 4375/4374 || || 225/224 || [[197edo]] || [[catakleismic]] || 225/224, 4375/4374 || || 3136/3125 || [[446edo]] || [[Hemimean clan#Sengagen|sengagen]] || 3136/3125, 420175/419904 || || 5120/5103 || [[391edo]] || [[Hemifamity temperaments#Alphaquarter|alphaquarter]] || 5120/5103, 29360128/29296875 || || 5120/5103 || [[391edo]] || [[Hemifamity temperaments#Septiquarter|septiquarter]] || 5120/5103, 420175/419904 || || 6144/6125 || [[381edo]] || [[Porwell temperaments#Nessafof|nessafof]] || 6144/6125, 250047/250000 || || 65625/65536 || [[171edo]] || [[Breedsmic temperaments#Tertiaseptal|tertiaseptal]] || 2401/2400, 65625/65536 || || 703125/702464 || [[2185edo]] || [[Ragismic microtemperaments#Enneadecal|enneadecal]] || 4375/4374, 703125/702464 || || 4375/4374 || [[8419edo]] || [[Ragismic microtemperaments#Semidimi|semidimi]] || 4375/4374, 3955078125/3954653486 || || 250047/250000 || [[12555edo]] || || 250047/250000, 281484423828125/281474976710656 || =11 limit= || Comma || OPV || Temperament || Basis || || 33/32 || [[16edo]] || [[Pelogic family#Armodue|armodue]] || 33/32, 36/35, 45/44 || || 77/75 || [[39edo]] || [[triforce]] || 49/48, 56/55, 77/75 || || 352/343 || [[22edo]] || [[hedgehog]] || 50/49, 55/54, 99/98 || || 45/44 || [[45edo]] || [[flattone]] || 45/44, 81/80, 385/384 || || 55/54 || [[51edo]] || [[porky]] || 55/54, 100/99, 225/224 || || 56/55 || [[36edo]] || [[Pythagorean family#Catler temperament|catcall]] || 56/55, 81/80, 128/125 || || 245/242 || [[91edo]] || [[septimin]] || 225/224, 245/242, 385/384 || || 99/98 || [[127edo]] || [[Würschmidt family#Würschmidt|würschmidt]] || 99/98, 176/175, 243/242 || || 100/99 || [[104edo]] || [[magic]] || 100/99, 225/224, 245/243 || || 121/120 || [[99edo]] || [[hitchcock]] || 121/120, 176/175, 2200/2187 || || 176/175 || [[111edo]] || [[semisept]] || 176/175, 540/539, 1331/1323 || || 896/891 || [[208edo]] || [[Kleismic family#Metakleismic|metakleismic]] || 896/891, 2200/2187, 14700/14641 || || 65536/65219 || [[282edo]] || [[Porwell temperaments#Septisuperfourth|septisuperfourth]] || 540/539, 4000/3993, 5632/5625 || || 243/242 || [[202edo]] || [[harry]] || 243/242, 441/440, 4000/3993 || || 3388/3375 || [[316edo]] || [[Ragismic microtemperaments#Semiparakleismic|semiparakleismic]] || 3025/3024, 3136/3125, 4375/4374 || || 385/384 || [[284edo]] || [[quadritikleismic]] || 385/384, 1375/1372, 6250/6237 || || 441/400 || [[320edo]] || [[octowerck]] || 441/440, 8019/8000, 41503/41472 || || 540/539 || [[578edo]] || [[Schismatic family#Pogo|pogo]] || 540/539, 4000/3993, 32805/32768 ||
Original HTML content:
<html><head><title>Associated rank two temperaments</title></head><body>By an <em>associated temperament</em> to a p-limit comma is meant a p-limit temperament which shares the same <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> as the <a class="wiki_link" href="/Rank%20and%20codimension">codimension one</a> temperament tempering out that comma. By definition, the optimal patent val defines the unique rank one associated temperament. For rank two temperaments, it is possible for more than one temperament to be associated, and some of these are listed below. The column headings are the comma being associated, the optimal patent val, the rank two temperament, and a comma basis for the rank two temperament.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="x7 limit"></a><!-- ws:end:WikiTextHeadingRule:0 -->7 limit</h1>
<table class="wiki_table">
<tr>
<td>Comma<br />
</td>
<td>OPV<br />
</td>
<td>Temperament<br />
</td>
<td>Basis<br />
</td>
</tr>
<tr>
<td>28/27<br />
</td>
<td><a class="wiki_link" href="/15edo">15edo</a><br />
</td>
<td><a class="wiki_link" href="/blacksmith">blacksmith</a><br />
</td>
<td>28/27, 49/48<br />
</td>
</tr>
<tr>
<td>1029/1000<br />
</td>
<td><a class="wiki_link" href="/55edo">55edo</a><br />
</td>
<td><a class="wiki_link" href="/liese">liese</a><br />
</td>
<td>81/80, 686/675<br />
</td>
</tr>
<tr>
<td>36/35<br />
</td>
<td><a class="wiki_link" href="/12edo">12edo</a><br />
</td>
<td><a class="wiki_link" href="/diminished">diminished</a><br />
</td>
<td>36/35, 50/49<br />
</td>
</tr>
<tr>
<td>36/35<br />
</td>
<td><a class="wiki_link" href="/12edo">12edo</a><br />
</td>
<td><a class="wiki_link" href="/august">august</a><br />
</td>
<td>36/35, 128/125<br />
</td>
</tr>
<tr>
<td>36/35<br />
</td>
<td><a class="wiki_link" href="/12edo">12edo</a><br />
</td>
<td><a class="wiki_link" href="/dominant">dominant</a><br />
</td>
<td>36/35, 64/63<br />
</td>
</tr>
<tr>
<td>525/512<br />
</td>
<td><a class="wiki_link" href="/45edo">45edo</a><br />
</td>
<td><a class="wiki_link" href="/flattone">flattone</a><br />
</td>
<td>81/80, 525/512<br />
</td>
</tr>
<tr>
<td>49/48<br />
</td>
<td><a class="wiki_link" href="/19edo">19edo</a><br />
</td>
<td><a class="wiki_link" href="/keemun">keemun</a><br />
</td>
<td>49/48, 126/125<br />
</td>
</tr>
<tr>
<td>49/48<br />
</td>
<td><a class="wiki_link" href="/19edo">19edo</a><br />
</td>
<td><a class="wiki_link" href="/godzilla">godzilla</a><br />
</td>
<td>49/48, 81/80<br />
</td>
</tr>
<tr>
<td>50/49<br />
</td>
<td><a class="wiki_link" href="/48edo">48edo</a><br />
</td>
<td><a class="wiki_link" href="/doublewide">doublewide</a><br />
</td>
<td>50/49, 875/864<br />
</td>
</tr>
<tr>
<td>64/63<br />
</td>
<td><a class="wiki_link" href="/49edo">49edo</a><br />
</td>
<td><a class="wiki_link" href="/superpyth">superpyth</a><br />
</td>
<td>64/63, 245/243<br />
</td>
</tr>
<tr>
<td>875/864<br />
</td>
<td><a class="wiki_link" href="/41edo">41edo</a><br />
</td>
<td><a class="wiki_link" href="/magic">magic</a><br />
</td>
<td>225/224, 245/243<br />
</td>
</tr>
<tr>
<td>3125/3087<br />
</td>
<td><a class="wiki_link" href="/94edo">94edo</a><br />
</td>
<td><a class="wiki_link" href="/garibaldi">garibaldi</a><br />
</td>
<td>225/224, 3125/3087<br />
</td>
</tr>
<tr>
<td>2430/2401<br />
</td>
<td><a class="wiki_link" href="/137edo">137edo</a><br />
</td>
<td><a class="wiki_link" href="/orwell">orwell</a><br />
</td>
<td>225/224, 1728/1715<br />
</td>
</tr>
<tr>
<td>245/243<br />
</td>
<td><a class="wiki_link" href="/283edo">283edo</a><br />
</td>
<td><a class="wiki_link" href="/Escapade%20family#Escaped">escaped</a><br />
</td>
<td>245/243, 65625/65536<br />
</td>
</tr>
<tr>
<td>126/125<br />
</td>
<td><a class="wiki_link" href="/185edo">185edo</a><br />
</td>
<td><a class="wiki_link" href="/valentine">valentine</a><br />
</td>
<td>126/125, 1029/1024<br />
</td>
</tr>
<tr>
<td>1728/1715<br />
</td>
<td><a class="wiki_link" href="/111edo">111edo</a><br />
</td>
<td><a class="wiki_link" href="/Hemifamity%20temperaments#Buzzard">buzzard</a><br />
</td>
<td>1728/1715, 5120/5103<br />
</td>
</tr>
<tr>
<td>1728/1715<br />
</td>
<td><a class="wiki_link" href="/111edo">111edo</a><br />
</td>
<td><a class="wiki_link" href="/semisept">semisept</a><br />
</td>
<td>1728/1715, 3136/3125<br />
</td>
</tr>
<tr>
<td>1029/1024<br />
</td>
<td><a class="wiki_link" href="/190edo">190edo</a><br />
</td>
<td><a class="wiki_link" href="/unidec">unidec</a><br />
</td>
<td>1029/1024, 4375/4374<br />
</td>
</tr>
<tr>
<td>225/224<br />
</td>
<td><a class="wiki_link" href="/197edo">197edo</a><br />
</td>
<td><a class="wiki_link" href="/catakleismic">catakleismic</a><br />
</td>
<td>225/224, 4375/4374<br />
</td>
</tr>
<tr>
<td>3136/3125<br />
</td>
<td><a class="wiki_link" href="/446edo">446edo</a><br />
</td>
<td><a class="wiki_link" href="/Hemimean%20clan#Sengagen">sengagen</a><br />
</td>
<td>3136/3125, 420175/419904<br />
</td>
</tr>
<tr>
<td>5120/5103<br />
</td>
<td><a class="wiki_link" href="/391edo">391edo</a><br />
</td>
<td><a class="wiki_link" href="/Hemifamity%20temperaments#Alphaquarter">alphaquarter</a><br />
</td>
<td>5120/5103, 29360128/29296875<br />
</td>
</tr>
<tr>
<td>5120/5103<br />
</td>
<td><a class="wiki_link" href="/391edo">391edo</a><br />
</td>
<td><a class="wiki_link" href="/Hemifamity%20temperaments#Septiquarter">septiquarter</a><br />
</td>
<td>5120/5103, 420175/419904<br />
</td>
</tr>
<tr>
<td>6144/6125<br />
</td>
<td><a class="wiki_link" href="/381edo">381edo</a><br />
</td>
<td><a class="wiki_link" href="/Porwell%20temperaments#Nessafof">nessafof</a><br />
</td>
<td>6144/6125, 250047/250000<br />
</td>
</tr>
<tr>
<td>65625/65536<br />
</td>
<td><a class="wiki_link" href="/171edo">171edo</a><br />
</td>
<td><a class="wiki_link" href="/Breedsmic%20temperaments#Tertiaseptal">tertiaseptal</a><br />
</td>
<td>2401/2400, 65625/65536<br />
</td>
</tr>
<tr>
<td>703125/702464<br />
</td>
<td><a class="wiki_link" href="/2185edo">2185edo</a><br />
</td>
<td><a class="wiki_link" href="/Ragismic%20microtemperaments#Enneadecal">enneadecal</a><br />
</td>
<td>4375/4374, 703125/702464<br />
</td>
</tr>
<tr>
<td>4375/4374<br />
</td>
<td><a class="wiki_link" href="/8419edo">8419edo</a><br />
</td>
<td><a class="wiki_link" href="/Ragismic%20microtemperaments#Semidimi">semidimi</a><br />
</td>
<td>4375/4374, 3955078125/3954653486<br />
</td>
</tr>
<tr>
<td>250047/250000<br />
</td>
<td><a class="wiki_link" href="/12555edo">12555edo</a><br />
</td>
<td><br />
</td>
<td>250047/250000, 281484423828125/281474976710656<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="x11 limit"></a><!-- ws:end:WikiTextHeadingRule:2 -->11 limit</h1>
<table class="wiki_table">
<tr>
<td>Comma<br />
</td>
<td>OPV<br />
</td>
<td>Temperament<br />
</td>
<td>Basis<br />
</td>
</tr>
<tr>
<td>33/32<br />
</td>
<td><a class="wiki_link" href="/16edo">16edo</a><br />
</td>
<td><a class="wiki_link" href="/Pelogic%20family#Armodue">armodue</a><br />
</td>
<td>33/32, 36/35, 45/44<br />
</td>
</tr>
<tr>
<td>77/75<br />
</td>
<td><a class="wiki_link" href="/39edo">39edo</a><br />
</td>
<td><a class="wiki_link" href="/triforce">triforce</a><br />
</td>
<td>49/48, 56/55, 77/75<br />
</td>
</tr>
<tr>
<td>352/343<br />
</td>
<td><a class="wiki_link" href="/22edo">22edo</a><br />
</td>
<td><a class="wiki_link" href="/hedgehog">hedgehog</a><br />
</td>
<td>50/49, 55/54, 99/98<br />
</td>
</tr>
<tr>
<td>45/44<br />
</td>
<td><a class="wiki_link" href="/45edo">45edo</a><br />
</td>
<td><a class="wiki_link" href="/flattone">flattone</a><br />
</td>
<td>45/44, 81/80, 385/384<br />
</td>
</tr>
<tr>
<td>55/54<br />
</td>
<td><a class="wiki_link" href="/51edo">51edo</a><br />
</td>
<td><a class="wiki_link" href="/porky">porky</a><br />
</td>
<td>55/54, 100/99, 225/224<br />
</td>
</tr>
<tr>
<td>56/55<br />
</td>
<td><a class="wiki_link" href="/36edo">36edo</a><br />
</td>
<td><a class="wiki_link" href="/Pythagorean%20family#Catler temperament">catcall</a><br />
</td>
<td>56/55, 81/80, 128/125<br />
</td>
</tr>
<tr>
<td>245/242<br />
</td>
<td><a class="wiki_link" href="/91edo">91edo</a><br />
</td>
<td><a class="wiki_link" href="/septimin">septimin</a><br />
</td>
<td>225/224, 245/242, 385/384<br />
</td>
</tr>
<tr>
<td>99/98<br />
</td>
<td><a class="wiki_link" href="/127edo">127edo</a><br />
</td>
<td><a class="wiki_link" href="/W%C3%BCrschmidt%20family#Würschmidt">würschmidt</a><br />
</td>
<td>99/98, 176/175, 243/242<br />
</td>
</tr>
<tr>
<td>100/99<br />
</td>
<td><a class="wiki_link" href="/104edo">104edo</a><br />
</td>
<td><a class="wiki_link" href="/magic">magic</a><br />
</td>
<td>100/99, 225/224, 245/243<br />
</td>
</tr>
<tr>
<td>121/120<br />
</td>
<td><a class="wiki_link" href="/99edo">99edo</a><br />
</td>
<td><a class="wiki_link" href="/hitchcock">hitchcock</a><br />
</td>
<td>121/120, 176/175, 2200/2187<br />
</td>
</tr>
<tr>
<td>176/175<br />
</td>
<td><a class="wiki_link" href="/111edo">111edo</a><br />
</td>
<td><a class="wiki_link" href="/semisept">semisept</a><br />
</td>
<td>176/175, 540/539, 1331/1323<br />
</td>
</tr>
<tr>
<td>896/891<br />
</td>
<td><a class="wiki_link" href="/208edo">208edo</a><br />
</td>
<td><a class="wiki_link" href="/Kleismic%20family#Metakleismic">metakleismic</a><br />
</td>
<td>896/891, 2200/2187, 14700/14641<br />
</td>
</tr>
<tr>
<td>65536/65219<br />
</td>
<td><a class="wiki_link" href="/282edo">282edo</a><br />
</td>
<td><a class="wiki_link" href="/Porwell%20temperaments#Septisuperfourth">septisuperfourth</a><br />
</td>
<td>540/539, 4000/3993, 5632/5625<br />
</td>
</tr>
<tr>
<td>243/242<br />
</td>
<td><a class="wiki_link" href="/202edo">202edo</a><br />
</td>
<td><a class="wiki_link" href="/harry">harry</a><br />
</td>
<td>243/242, 441/440, 4000/3993<br />
</td>
</tr>
<tr>
<td>3388/3375<br />
</td>
<td><a class="wiki_link" href="/316edo">316edo</a><br />
</td>
<td><a class="wiki_link" href="/Ragismic%20microtemperaments#Semiparakleismic">semiparakleismic</a><br />
</td>
<td>3025/3024, 3136/3125, 4375/4374<br />
</td>
</tr>
<tr>
<td>385/384<br />
</td>
<td><a class="wiki_link" href="/284edo">284edo</a><br />
</td>
<td><a class="wiki_link" href="/quadritikleismic">quadritikleismic</a><br />
</td>
<td>385/384, 1375/1372, 6250/6237<br />
</td>
</tr>
<tr>
<td>441/400<br />
</td>
<td><a class="wiki_link" href="/320edo">320edo</a><br />
</td>
<td><a class="wiki_link" href="/octowerck">octowerck</a><br />
</td>
<td>441/440, 8019/8000, 41503/41472<br />
</td>
</tr>
<tr>
<td>540/539<br />
</td>
<td><a class="wiki_link" href="/578edo">578edo</a><br />
</td>
<td><a class="wiki_link" href="/Schismatic%20family#Pogo">pogo</a><br />
</td>
<td>540/539, 4000/3993, 32805/32768<br />
</td>
</tr>
</table>
</body></html>