List of edo-distinct 58et rank two temperaments
IMPORTED REVISION FROM WIKISPACES
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- The original revision id was 514265988.
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Original Wikitext content:
The temperaments listed are 58edo-distinct, meaning that they are all different even if tuned in 58edo. The ordering is by increasing complexity of 5. The temperament of lowest TE complexity supported by the patent val was chosen as the representative for each class of edo-distinctness. =5-limit temperaments= || Period generator || Wedgie || Name || Complexity || Commas || || 58 19 || <<14 1 -31]] || || 7.0510 || 6442450944/6103515625 || || 29 10 || <<30 -2 -73]] || || 15.837 || 9444732965739290427392/8381903171539306640625 || || 58 1 || <<16 -3 -42]] || || 8.828 || 4398046511104/4119873046875 || || 29 9 || <<2 -4 -11]] || || 2.121 || 2048/2025 || || 58 21 || <<12 5 -20]] || || 5.522 || 254803968/244140625 || || 29 1 || <<26 6 -51]] || || 12.488 || 1641562064176545792/1490116119384765625 || || 58 17 || <<18 -7 -53]] || || 10.731 || 9007199254740992/8342742919921875 || || 29 11 || <<54 8 -113]] || || 26.555 || [113 8 -54> || || 58 3 || <<10 9 -9]] || || 4.502 || 10077696/9765625 || || 29 8 || <<34 48 -3]] || || 17.206 || 638131544614980078906888/582076609134674072265625 || || 58 23 || <<20 -11 -64]] || || 12.703 || 18446744073709551616/16894054412841796875 || || 29 2 || <<6 46 59]] || || 14.875 || 9007199254740992000000/8862938119652501095929 || || 58 15 || <<8 13 2]] || || 4.363 || 1594323/1562500 || || 29 12 || <<22 14 -29]] || || 9.851 || 2567836929097728/2384185791015625 || || 58 5 || <<22 43 17]] || || 13.625 || 328256967394537077627/312500 || || 29 7 || <<50 16 -91]] || || 23.481 || [91 16 -50> || || 58 25 || <<6 17 13]] || || 5.177 || 129140163/128000000 || || 29 3 || <<38 40 -25]] || || 17.490 || 407943558924674501581996032/363797880709171295166015625 || || 58 13 || <<34 19 -49]] || || 15.323 || 654295038711035754184704/582076609134674072265625 || || 29 13 || <<10 38 37]] || || 11.672 || 1350851717672992089/1342177280000000000 || || 58 7 || <<4 21 24]] || || 6.600 || 10485760000/10460353203 || || 29 6 || <<18 22 -7]] || || 8.609 || 4016775629952/3814697265625 || || 58 27 || <<26 35 -5]] || || 12.886 || 1601009443167990624/1490116119384765625 || || 29 4 || <<46 24 -69]] || || 20.822 || [69 24 -46> || || 58 11 || <<2 25 35]] || || 8.326 || 858993459200/847288609443 || || 29 14 || <<42 32 -47]] || || 18.755 || 260789407250723664179754958848/227373675443232059478759765625 || || 58 9 || <<28 31 -16]] || || 13.029 || 40479843698864750592/37252902984619140625 || || 29 5 || <<14 30 15]] || || 9.338 || 205891132094649/200000000000000 || || 2 1 || <<0 29 46]] || || 10.202 || 70368744177664/68630377364883 || =7-limit temperaments= || Period generator || Wedgie || Name || Complexity || Commas || || 58 19 || <<14 1 33 -31 13 74]] || || 8.414 || 10976/10935 28672/28125 || || 29 10 || <<28 2 8 -62 -66 13]] || || 11.753 || 2401/2400 401408/390625 || || 58 1 || <<16 -3 17 -42 -18 48]] || || 7.540 || 1728/1715 28672/28125 || || 29 9 || <<2 -4 -16 -11 -31 -26]] || || 4.290 || 126/125 2048/2025 || || 58 21 || <<12 5 -9 -20 -48 -35]] || || 6.416 || 126/125 65536/64827 || || 29 1 || <<26 6 24 -51 -35 39]] || || 10.316 || 1728/1715 401408/390625 || || 58 17 || <<18 -7 1 -53 -49 22]] || || 8.928 || 2401/2400 28672/28125 || || 29 11 || <<4 -8 26 -22 30 83]] || || 7.609 || 2048/2025 19683/19600 || || 58 3 || <<10 9 7 -9 -17 -9]] || || 3.731 || 126/125 1728/1715 || || 29 8 || <<24 10 40 -40 -4 65]] || || 10.561 || 31104/30625 118098/117649 || || 58 23 || <<20 -11 -15 -64 -80 -4]] || || 11.806 || 28672/28125 50421/50000 || || 29 2 || <<6 -12 10 -33 -1 57]] || || 5.925 || 1728/1715 2048/2025 || || 58 15 || <<8 13 23 2 14 17]] || || 4.847 || 126/125 10976/10935 || || 29 12 || <<22 14 -2 -29 -65 -44]] || || 9.579 || 126/125 4194304/4117715 || || 58 5 || <<22 43 27 17 -19 -58]] || || 11.157 || 2401/2400 177147/175000 || || 29 7 || <<8 -16 -6 -44 -32 31]] || || 7.010 || 2048/2025 2401/2400 || || 58 25 || <<6 17 39 13 45 43]] || || 8.359 || 126/125 1605632/1594323 || || 29 3 || <<38 40 44 -25 -37 -10]] || || 14.346 || 126/125 97955205120/96889010407 || || 58 13 || <<24 39 11 6 -50 -84]] || || 11.703 || 1728/1715 1594323/1562500 || || 29 13 || <<10 -20 -22 -55 -63 5]] || || 9.999 || 2048/2025 50421/50000 || || 58 7 || <<4 21 -3 24 -16 -66]] || || 6.420 || 1728/1715 5120/5103 || || 29 6 || <<18 22 30 -7 -3 8]] || || 7.511 || 126/125 118098/117649 || || 58 27 || <<26 35 53 -5 11 25]] || || 12.079 || 126/125 645700815/645657712 || || 29 4 || <<12 34 20 26 -2 -49]] || || 8.457 || 2401/2400 19683/19600 || || 58 11 || <<2 25 13 35 15 -40]] || || 6.812 || 2401/2400 5120/5103 || || 29 14 || <<16 26 -12 4 -64 -101]] || || 10.753 || 31104/30625 65536/64827 || || 58 9 || <<28 31 37 -16 -20 -1]] || || 10.826 || 126/125 204073344/201768035 || || 29 5 || <<14 30 4 15 -33 -75]] || || 8.670 || 1728/1715 177147/175000 || || 2 1 || <<0 29 29 46 46 -14]] || || 9.402 || 5120/5103 50421/50000 ||
Original HTML content:
<html><head><title>List of edo-distinct 58et rank two temperaments</title></head><body>The temperaments listed are 58edo-distinct, meaning that they are all different even if tuned in 58edo. The ordering is by increasing complexity of 5. The temperament of lowest TE complexity supported by the patent val was chosen as the representative for each class of edo-distinctness.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="x5-limit temperaments"></a><!-- ws:end:WikiTextHeadingRule:0 -->5-limit temperaments</h1>
<table class="wiki_table">
<tr>
<td>Period generator<br />
</td>
<td>Wedgie<br />
</td>
<td>Name<br />
</td>
<td>Complexity<br />
</td>
<td>Commas<br />
</td>
</tr>
<tr>
<td>58 19<br />
</td>
<td><<14 1 -31]]<br />
</td>
<td><br />
</td>
<td>7.0510<br />
</td>
<td>6442450944/6103515625<br />
</td>
</tr>
<tr>
<td>29 10<br />
</td>
<td><<30 -2 -73]]<br />
</td>
<td><br />
</td>
<td>15.837<br />
</td>
<td>9444732965739290427392/8381903171539306640625<br />
</td>
</tr>
<tr>
<td>58 1<br />
</td>
<td><<16 -3 -42]]<br />
</td>
<td><br />
</td>
<td>8.828<br />
</td>
<td>4398046511104/4119873046875<br />
</td>
</tr>
<tr>
<td>29 9<br />
</td>
<td><<2 -4 -11]]<br />
</td>
<td><br />
</td>
<td>2.121<br />
</td>
<td>2048/2025<br />
</td>
</tr>
<tr>
<td>58 21<br />
</td>
<td><<12 5 -20]]<br />
</td>
<td><br />
</td>
<td>5.522<br />
</td>
<td>254803968/244140625<br />
</td>
</tr>
<tr>
<td>29 1<br />
</td>
<td><<26 6 -51]]<br />
</td>
<td><br />
</td>
<td>12.488<br />
</td>
<td>1641562064176545792/1490116119384765625<br />
</td>
</tr>
<tr>
<td>58 17<br />
</td>
<td><<18 -7 -53]]<br />
</td>
<td><br />
</td>
<td>10.731<br />
</td>
<td>9007199254740992/8342742919921875<br />
</td>
</tr>
<tr>
<td>29 11<br />
</td>
<td><<54 8 -113]]<br />
</td>
<td><br />
</td>
<td>26.555<br />
</td>
<td>[113 8 -54><br />
</td>
</tr>
<tr>
<td>58 3<br />
</td>
<td><<10 9 -9]]<br />
</td>
<td><br />
</td>
<td>4.502<br />
</td>
<td>10077696/9765625<br />
</td>
</tr>
<tr>
<td>29 8<br />
</td>
<td><<34 48 -3]]<br />
</td>
<td><br />
</td>
<td>17.206<br />
</td>
<td>638131544614980078906888/582076609134674072265625<br />
</td>
</tr>
<tr>
<td>58 23<br />
</td>
<td><<20 -11 -64]]<br />
</td>
<td><br />
</td>
<td>12.703<br />
</td>
<td>18446744073709551616/16894054412841796875<br />
</td>
</tr>
<tr>
<td>29 2<br />
</td>
<td><<6 46 59]]<br />
</td>
<td><br />
</td>
<td>14.875<br />
</td>
<td>9007199254740992000000/8862938119652501095929<br />
</td>
</tr>
<tr>
<td>58 15<br />
</td>
<td><<8 13 2]]<br />
</td>
<td><br />
</td>
<td>4.363<br />
</td>
<td>1594323/1562500<br />
</td>
</tr>
<tr>
<td>29 12<br />
</td>
<td><<22 14 -29]]<br />
</td>
<td><br />
</td>
<td>9.851<br />
</td>
<td>2567836929097728/2384185791015625<br />
</td>
</tr>
<tr>
<td>58 5<br />
</td>
<td><<22 43 17]]<br />
</td>
<td><br />
</td>
<td>13.625<br />
</td>
<td>328256967394537077627/312500<br />
</td>
</tr>
<tr>
<td>29 7<br />
</td>
<td><<50 16 -91]]<br />
</td>
<td><br />
</td>
<td>23.481<br />
</td>
<td>[91 16 -50><br />
</td>
</tr>
<tr>
<td>58 25<br />
</td>
<td><<6 17 13]]<br />
</td>
<td><br />
</td>
<td>5.177<br />
</td>
<td>129140163/128000000<br />
</td>
</tr>
<tr>
<td>29 3<br />
</td>
<td><<38 40 -25]]<br />
</td>
<td><br />
</td>
<td>17.490<br />
</td>
<td>407943558924674501581996032/363797880709171295166015625<br />
</td>
</tr>
<tr>
<td>58 13<br />
</td>
<td><<34 19 -49]]<br />
</td>
<td><br />
</td>
<td>15.323<br />
</td>
<td>654295038711035754184704/582076609134674072265625<br />
</td>
</tr>
<tr>
<td>29 13<br />
</td>
<td><<10 38 37]]<br />
</td>
<td><br />
</td>
<td>11.672<br />
</td>
<td>1350851717672992089/1342177280000000000<br />
</td>
</tr>
<tr>
<td>58 7<br />
</td>
<td><<4 21 24]]<br />
</td>
<td><br />
</td>
<td>6.600<br />
</td>
<td>10485760000/10460353203<br />
</td>
</tr>
<tr>
<td>29 6<br />
</td>
<td><<18 22 -7]]<br />
</td>
<td><br />
</td>
<td>8.609<br />
</td>
<td>4016775629952/3814697265625<br />
</td>
</tr>
<tr>
<td>58 27<br />
</td>
<td><<26 35 -5]]<br />
</td>
<td><br />
</td>
<td>12.886<br />
</td>
<td>1601009443167990624/1490116119384765625<br />
</td>
</tr>
<tr>
<td>29 4<br />
</td>
<td><<46 24 -69]]<br />
</td>
<td><br />
</td>
<td>20.822<br />
</td>
<td>[69 24 -46><br />
</td>
</tr>
<tr>
<td>58 11<br />
</td>
<td><<2 25 35]]<br />
</td>
<td><br />
</td>
<td>8.326<br />
</td>
<td>858993459200/847288609443<br />
</td>
</tr>
<tr>
<td>29 14<br />
</td>
<td><<42 32 -47]]<br />
</td>
<td><br />
</td>
<td>18.755<br />
</td>
<td>260789407250723664179754958848/227373675443232059478759765625<br />
</td>
</tr>
<tr>
<td>58 9<br />
</td>
<td><<28 31 -16]]<br />
</td>
<td><br />
</td>
<td>13.029<br />
</td>
<td>40479843698864750592/37252902984619140625<br />
</td>
</tr>
<tr>
<td>29 5<br />
</td>
<td><<14 30 15]]<br />
</td>
<td><br />
</td>
<td>9.338<br />
</td>
<td>205891132094649/200000000000000<br />
</td>
</tr>
<tr>
<td>2 1<br />
</td>
<td><<0 29 46]]<br />
</td>
<td><br />
</td>
<td>10.202<br />
</td>
<td>70368744177664/68630377364883<br />
</td>
</tr>
</table>
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="x7-limit temperaments"></a><!-- ws:end:WikiTextHeadingRule:2 -->7-limit temperaments</h1>
<table class="wiki_table">
<tr>
<td>Period generator<br />
</td>
<td>Wedgie<br />
</td>
<td>Name<br />
</td>
<td>Complexity<br />
</td>
<td>Commas<br />
</td>
</tr>
<tr>
<td>58 19<br />
</td>
<td><<14 1 33 -31 13 74]]<br />
</td>
<td><br />
</td>
<td>8.414<br />
</td>
<td>10976/10935 28672/28125<br />
</td>
</tr>
<tr>
<td>29 10<br />
</td>
<td><<28 2 8 -62 -66 13]]<br />
</td>
<td><br />
</td>
<td>11.753<br />
</td>
<td>2401/2400 401408/390625<br />
</td>
</tr>
<tr>
<td>58 1<br />
</td>
<td><<16 -3 17 -42 -18 48]]<br />
</td>
<td><br />
</td>
<td>7.540<br />
</td>
<td>1728/1715 28672/28125<br />
</td>
</tr>
<tr>
<td>29 9<br />
</td>
<td><<2 -4 -16 -11 -31 -26]]<br />
</td>
<td><br />
</td>
<td>4.290<br />
</td>
<td>126/125 2048/2025<br />
</td>
</tr>
<tr>
<td>58 21<br />
</td>
<td><<12 5 -9 -20 -48 -35]]<br />
</td>
<td><br />
</td>
<td>6.416<br />
</td>
<td>126/125 65536/64827<br />
</td>
</tr>
<tr>
<td>29 1<br />
</td>
<td><<26 6 24 -51 -35 39]]<br />
</td>
<td><br />
</td>
<td>10.316<br />
</td>
<td>1728/1715 401408/390625<br />
</td>
</tr>
<tr>
<td>58 17<br />
</td>
<td><<18 -7 1 -53 -49 22]]<br />
</td>
<td><br />
</td>
<td>8.928<br />
</td>
<td>2401/2400 28672/28125<br />
</td>
</tr>
<tr>
<td>29 11<br />
</td>
<td><<4 -8 26 -22 30 83]]<br />
</td>
<td><br />
</td>
<td>7.609<br />
</td>
<td>2048/2025 19683/19600<br />
</td>
</tr>
<tr>
<td>58 3<br />
</td>
<td><<10 9 7 -9 -17 -9]]<br />
</td>
<td><br />
</td>
<td>3.731<br />
</td>
<td>126/125 1728/1715<br />
</td>
</tr>
<tr>
<td>29 8<br />
</td>
<td><<24 10 40 -40 -4 65]]<br />
</td>
<td><br />
</td>
<td>10.561<br />
</td>
<td>31104/30625 118098/117649<br />
</td>
</tr>
<tr>
<td>58 23<br />
</td>
<td><<20 -11 -15 -64 -80 -4]]<br />
</td>
<td><br />
</td>
<td>11.806<br />
</td>
<td>28672/28125 50421/50000<br />
</td>
</tr>
<tr>
<td>29 2<br />
</td>
<td><<6 -12 10 -33 -1 57]]<br />
</td>
<td><br />
</td>
<td>5.925<br />
</td>
<td>1728/1715 2048/2025<br />
</td>
</tr>
<tr>
<td>58 15<br />
</td>
<td><<8 13 23 2 14 17]]<br />
</td>
<td><br />
</td>
<td>4.847<br />
</td>
<td>126/125 10976/10935<br />
</td>
</tr>
<tr>
<td>29 12<br />
</td>
<td><<22 14 -2 -29 -65 -44]]<br />
</td>
<td><br />
</td>
<td>9.579<br />
</td>
<td>126/125 4194304/4117715<br />
</td>
</tr>
<tr>
<td>58 5<br />
</td>
<td><<22 43 27 17 -19 -58]]<br />
</td>
<td><br />
</td>
<td>11.157<br />
</td>
<td>2401/2400 177147/175000<br />
</td>
</tr>
<tr>
<td>29 7<br />
</td>
<td><<8 -16 -6 -44 -32 31]]<br />
</td>
<td><br />
</td>
<td>7.010<br />
</td>
<td>2048/2025 2401/2400<br />
</td>
</tr>
<tr>
<td>58 25<br />
</td>
<td><<6 17 39 13 45 43]]<br />
</td>
<td><br />
</td>
<td>8.359<br />
</td>
<td>126/125 1605632/1594323<br />
</td>
</tr>
<tr>
<td>29 3<br />
</td>
<td><<38 40 44 -25 -37 -10]]<br />
</td>
<td><br />
</td>
<td>14.346<br />
</td>
<td>126/125 97955205120/96889010407<br />
</td>
</tr>
<tr>
<td>58 13<br />
</td>
<td><<24 39 11 6 -50 -84]]<br />
</td>
<td><br />
</td>
<td>11.703<br />
</td>
<td>1728/1715 1594323/1562500<br />
</td>
</tr>
<tr>
<td>29 13<br />
</td>
<td><<10 -20 -22 -55 -63 5]]<br />
</td>
<td><br />
</td>
<td>9.999<br />
</td>
<td>2048/2025 50421/50000<br />
</td>
</tr>
<tr>
<td>58 7<br />
</td>
<td><<4 21 -3 24 -16 -66]]<br />
</td>
<td><br />
</td>
<td>6.420<br />
</td>
<td>1728/1715 5120/5103<br />
</td>
</tr>
<tr>
<td>29 6<br />
</td>
<td><<18 22 30 -7 -3 8]]<br />
</td>
<td><br />
</td>
<td>7.511<br />
</td>
<td>126/125 118098/117649<br />
</td>
</tr>
<tr>
<td>58 27<br />
</td>
<td><<26 35 53 -5 11 25]]<br />
</td>
<td><br />
</td>
<td>12.079<br />
</td>
<td>126/125 645700815/645657712<br />
</td>
</tr>
<tr>
<td>29 4<br />
</td>
<td><<12 34 20 26 -2 -49]]<br />
</td>
<td><br />
</td>
<td>8.457<br />
</td>
<td>2401/2400 19683/19600<br />
</td>
</tr>
<tr>
<td>58 11<br />
</td>
<td><<2 25 13 35 15 -40]]<br />
</td>
<td><br />
</td>
<td>6.812<br />
</td>
<td>2401/2400 5120/5103<br />
</td>
</tr>
<tr>
<td>29 14<br />
</td>
<td><<16 26 -12 4 -64 -101]]<br />
</td>
<td><br />
</td>
<td>10.753<br />
</td>
<td>31104/30625 65536/64827<br />
</td>
</tr>
<tr>
<td>58 9<br />
</td>
<td><<28 31 37 -16 -20 -1]]<br />
</td>
<td><br />
</td>
<td>10.826<br />
</td>
<td>126/125 204073344/201768035<br />
</td>
</tr>
<tr>
<td>29 5<br />
</td>
<td><<14 30 4 15 -33 -75]]<br />
</td>
<td><br />
</td>
<td>8.670<br />
</td>
<td>1728/1715 177147/175000<br />
</td>
</tr>
<tr>
<td>2 1<br />
</td>
<td><<0 29 29 46 46 -14]]<br />
</td>
<td><br />
</td>
<td>9.402<br />
</td>
<td>5120/5103 50421/50000<br />
</td>
</tr>
</table>
</body></html>