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Wikispaces>genewardsmith **Imported revision 299529596 - 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 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-02-07 20:39:21 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>299529596</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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|| 441/400 || [[320edo]] || [[octowerck]] || 441/440, 8019/8000, 41503/41472 || | || 441/400 || [[320edo]] || [[octowerck]] || 441/440, 8019/8000, 41503/41472 || | ||
|| 540/539 || [[578edo]] || [[Schismatic family#Pogo|pogo]] || 540/539, 4000/3993, 32805/32768 || | || 540/539 || [[578edo]] || [[Schismatic family#Pogo|pogo]] || 540/539, 4000/3993, 32805/32768 || | ||
|| 4000/3993 || [[665edo]] || [[Ragismic microtemperaments#Brahmagupta|brahmagupta]] || 4000/3993, 4375/4374, 131072/130977 || | |||
| Line 545: | Line 546: | ||
</td> | </td> | ||
<td>540/539, 4000/3993, 32805/32768<br /> | <td>540/539, 4000/3993, 32805/32768<br /> | ||
</td> | |||
</tr> | |||
<tr> | |||
<td>4000/3993<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/665edo">665edo</a><br /> | |||
</td> | |||
<td><a class="wiki_link" href="/Ragismic%20microtemperaments#Brahmagupta">brahmagupta</a><br /> | |||
</td> | |||
<td>4000/3993, 4375/4374, 131072/130977<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
Revision as of 20:39, 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 20:39:21 UTC.
- The original revision id was 299529596.
- 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 || || 4000/3993 || [[665edo]] || [[Ragismic microtemperaments#Brahmagupta|brahmagupta]] || 4000/3993, 4375/4374, 131072/130977 ||
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>
<tr>
<td>4000/3993<br />
</td>
<td><a class="wiki_link" href="/665edo">665edo</a><br />
</td>
<td><a class="wiki_link" href="/Ragismic%20microtemperaments#Brahmagupta">brahmagupta</a><br />
</td>
<td>4000/3993, 4375/4374, 131072/130977<br />
</td>
</tr>
</table>
</body></html>