List of edo-distinct 34d rank two temperaments
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The temperaments listed are 34edo-distinct, meaning that they are all different even if tuned in 34edo. The ordering is by increasing complexity of 5. The temperament of lowest TE complexity supported by the 34d val, <<34 54 79 96 118 126||, was chosen as the representative for each class of edo-distinctness. =5-limit temperaments= || Period generator || Wedgie || Name || Complexity || Commas || || 34 11 || <<8 1 -17]] || Würschmidt || 3.958 || 393216/390625 || || 17 6 || <<18 -2 -45]] || || 9.648 || 35184372088832/34332275390625 || || 34 15 || <<10 -3 -28]] || Mabila || 5.755 || 268435456/263671875 || || 17 3 || <<2 -4 -11]] || Srutal || 2.121 || 2048/2025 || || 34 9 || <<6 5 -6]] || Hanson || 2.685 || 15625/15552 || || 17 2 || <<14 6 -23]] || Vishnu || 6.423 || 6115295232/6103515625 || || 34 13 || <<12 -7 -39]] || || 7.718 || 549755813888/533935546875 || || 17 7 || <<30 8 -57]] || || 14.26 || 945539748965690376192/931322574615478515625 || || 34 5 || <<4 9 5]] || Tetracot || 2.783 || 20000/19683 || || 17 8 || <<22 24 -13]] || || 10.198 || 2384185791015625/2313662762852352 || || 34 1 || <<14 23 4]] || || 7.688 || 97656250000/94143178827 || || 17 1 || <<6 22 21]] || || 6.749 || 32768000000/31381059609 || || 34 7 || <<2 13 16]] || Immunity || 4.157 || 1638400/1594323 || || 17 4 || <<10 14 -1]] || Fifive || 5.041 || 9765625/9565938 || || 34 3 || <<16 19 -7]] || || 7.583 || 152587890625/148769467776 || || 17 5 || <<26 16 -35]] || Quatracot || 11.648 || 1490116119384765625/1479074071160291328 || || 2 1 || <<0 17 27]] || || 5.984 || 134217728/129140163 || =7-limit temperaments= || Period generator || Wedgie || Name || Complexity || Commas || || 34 11 || <<8 1 18 -17 6 39]] || Würschmidt || 4.578 || 225/224 8748/8575 || || 17 6 || <<16 2 2 -34 -42 -1]] || || 6.802 || 50/49 393216/390625 || || 34 15 || <<10 -3 14 -28 -6 41]] || Amavil || 5.254 || 225/224 17496/16807 || || 17 3 || <<2 -4 -4 -11 -12 2]] || Pajara || 1.953 || 50/49 64/63 || || 34 9 || <<6 5 22 -6 18 37]] || Catakleismic || 4.684 || 225/224 4375/4374 || || 17 2 || <<14 6 6 -23 -30 -3]] || || 5.385 || 50/49 110592/109375 || || 34 13 || <<12 -7 10 -39 -18 43]] || || 6.472 || 225/224 124416/117649 || || 17 7 || <<4 26 26 32 30 -13]] || || 7.556 || 50/49 1605632/1594323 || || 34 5 || <<4 9 -8 5 -24 -44]] || Modus || 4.203 || 50/49 1605632/1594323|| || 17 8 || <<12 10 10 -12 -18 -5]] || || 4.400 || 50/49 15625/15552 || || 34 1 || <<14 23 6 4 -30 -51]] || || 6.935 || 3200/3087 4375/4374 || || 17 1 || <<6 22 22 21 18 -11]] || || 6.018 || 50/49 177147/175616 || || 34 7 || <<2 13 -4 16 -12 -46]] || Immunized || 4.300 || 64/63 8748/8575 || || 17 4 || <<10 14 14 -1 -6 -7]] || Crepuscular || 4.165 || 50/49 4375/4374 || || 34 3 || <<16 19 2 -7 -42 -49]] || || 7.287 || 3200/3087 15625/15309 || || 17 5 || <<8 18 18 10 6 -9]] || || 4.792 || 50/49 19683/19208 || || 2 1 || <<0 17 0 27 0 -48]] || || 5.191 || 64/63 17496/16807 || =11-limit temperaments= || Period generator || Wedgie || Name || Complexity || Commas || || 34 11 || <<8 1 18 20 -17 6 4 39 43 -6]] || Würschmidt || 4.344 || 99/98 176/175 243/242 || || 17 6 || <<16 2 2 6 -34 -42 -46 -1 7 10]] || || 5.940 || 50/49 176/175 1344/1331 || || 34 15 || <<10 -3 14 8 -28 -6 -22 41 29 -26]] || Amavil || 4.553 || 99/98 176/175 864/847 || || 17 3 || <<2 -4 -4 -12 -11 -12 -26 2 -14 -20]] || Pajara || 2.543 || 50/49 99/98 176/175 || || 34 9 || <<6 5 -12 -2 -6 -36 -24 -42 -22 36]] || || 4.331 || 64/63 100/99 1331/1323 || || 17 2 || <<14 6 6 18 -23 -30 -20 -3 21 30]] || || 4.804 || 50/49 176/175 1331/1323 || || 34 13 || <<12 -7 10 -4 -39 -18 -48 43 15 -46]] || || 5.960 || 50/49 176/175 1331/1323 || || 17 7 || <<4 -8 -8 10 -22 -24 2 4 51 56]] || || 4.167 || 50/49 64/63 243/242 || || 34 5 || <<4 9 -8 10 5 -24 2 -44 -8 56]] || Modus || 3.857 || 64/63 100/99 243/242 || || 17 8 || <<12 10 10 30 -12 -18 6 -5 35 50]] || || 4.879 || 50/49 176/175 243/242 || || 34 1 || <<14 23 6 18 4 -30 -20 -51 -38 30]] || || 6.007 || 100/99 352/343 864/847 || || 17 1 || <<6 -12 -12 -2 -33 -36 -24 6 37 36]] || || 5.104 || 50/49 64/63 1331/1323 || || 34 7 || <<2 13 -4 -12 16 -12 -26 -46 -73 -20]] || Immunized || 4.820 || 64/63 99/98 1944/1925 || || 17 4 || <<10 14 14 8 -1 -6 -22 -7 -30 -26]] || Crepuscular || 3.829 || 50/49 99/98 1944/1925 || || 34 3 || <<16 19 2 6 -7 -42 -46 -49 -52 10]] || || 6.595 || 100/99 352/343 1344/1331 || || 17 5 || <<8 18 18 20 10 6 4 -9 -16 -6]] || || 4.196 || 50/49 99/98 243/242 || || 2 1 || <<0 17 0 0 27 0 0 -48 -59 0]] || || 4.643 || 64/63 99/98 243/242 ||
Original HTML content:
<html><head><title>List of edo-distinct 34d rank two temperaments</title></head><body>The temperaments listed are 34edo-distinct, meaning that they are all different even if tuned in 34edo. The ordering is by increasing complexity of 5. The temperament of lowest TE complexity supported by the 34d val, <<34 54 79 96 118 126||, 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>34 11<br />
</td>
<td><<8 1 -17]]<br />
</td>
<td>Würschmidt<br />
</td>
<td>3.958<br />
</td>
<td>393216/390625<br />
</td>
</tr>
<tr>
<td>17 6<br />
</td>
<td><<18 -2 -45]]<br />
</td>
<td><br />
</td>
<td>9.648<br />
</td>
<td>35184372088832/34332275390625<br />
</td>
</tr>
<tr>
<td>34 15<br />
</td>
<td><<10 -3 -28]]<br />
</td>
<td>Mabila<br />
</td>
<td>5.755<br />
</td>
<td>268435456/263671875<br />
</td>
</tr>
<tr>
<td>17 3<br />
</td>
<td><<2 -4 -11]]<br />
</td>
<td>Srutal<br />
</td>
<td>2.121<br />
</td>
<td>2048/2025<br />
</td>
</tr>
<tr>
<td>34 9<br />
</td>
<td><<6 5 -6]]<br />
</td>
<td>Hanson<br />
</td>
<td>2.685<br />
</td>
<td>15625/15552<br />
</td>
</tr>
<tr>
<td>17 2<br />
</td>
<td><<14 6 -23]]<br />
</td>
<td>Vishnu<br />
</td>
<td>6.423<br />
</td>
<td>6115295232/6103515625<br />
</td>
</tr>
<tr>
<td>34 13<br />
</td>
<td><<12 -7 -39]]<br />
</td>
<td><br />
</td>
<td>7.718<br />
</td>
<td>549755813888/533935546875<br />
</td>
</tr>
<tr>
<td>17 7<br />
</td>
<td><<30 8 -57]]<br />
</td>
<td><br />
</td>
<td>14.26<br />
</td>
<td>945539748965690376192/931322574615478515625<br />
</td>
</tr>
<tr>
<td>34 5<br />
</td>
<td><<4 9 5]]<br />
</td>
<td>Tetracot<br />
</td>
<td>2.783<br />
</td>
<td>20000/19683<br />
</td>
</tr>
<tr>
<td>17 8<br />
</td>
<td><<22 24 -13]]<br />
</td>
<td><br />
</td>
<td>10.198<br />
</td>
<td>2384185791015625/2313662762852352<br />
</td>
</tr>
<tr>
<td>34 1<br />
</td>
<td><<14 23 4]]<br />
</td>
<td><br />
</td>
<td>7.688<br />
</td>
<td>97656250000/94143178827<br />
</td>
</tr>
<tr>
<td>17 1<br />
</td>
<td><<6 22 21]]<br />
</td>
<td><br />
</td>
<td>6.749<br />
</td>
<td>32768000000/31381059609<br />
</td>
</tr>
<tr>
<td>34 7<br />
</td>
<td><<2 13 16]]<br />
</td>
<td>Immunity<br />
</td>
<td>4.157<br />
</td>
<td>1638400/1594323<br />
</td>
</tr>
<tr>
<td>17 4<br />
</td>
<td><<10 14 -1]]<br />
</td>
<td>Fifive<br />
</td>
<td>5.041<br />
</td>
<td>9765625/9565938<br />
</td>
</tr>
<tr>
<td>34 3<br />
</td>
<td><<16 19 -7]]<br />
</td>
<td><br />
</td>
<td>7.583<br />
</td>
<td>152587890625/148769467776<br />
</td>
</tr>
<tr>
<td>17 5<br />
</td>
<td><<26 16 -35]]<br />
</td>
<td>Quatracot<br />
</td>
<td>11.648<br />
</td>
<td>1490116119384765625/1479074071160291328<br />
</td>
</tr>
<tr>
<td>2 1<br />
</td>
<td><<0 17 27]]<br />
</td>
<td><br />
</td>
<td>5.984<br />
</td>
<td>134217728/129140163<br />
</td>
</tr>
</table>
<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>34 11<br />
</td>
<td><<8 1 18 -17 6 39]]<br />
</td>
<td>Würschmidt<br />
</td>
<td>4.578<br />
</td>
<td>225/224 8748/8575<br />
</td>
</tr>
<tr>
<td>17 6<br />
</td>
<td><<16 2 2 -34 -42 -1]]<br />
</td>
<td><br />
</td>
<td>6.802<br />
</td>
<td>50/49 393216/390625<br />
</td>
</tr>
<tr>
<td>34 15<br />
</td>
<td><<10 -3 14 -28 -6 41]]<br />
</td>
<td>Amavil<br />
</td>
<td>5.254<br />
</td>
<td>225/224 17496/16807<br />
</td>
</tr>
<tr>
<td>17 3<br />
</td>
<td><<2 -4 -4 -11 -12 2]]<br />
</td>
<td>Pajara<br />
</td>
<td>1.953<br />
</td>
<td>50/49 64/63<br />
</td>
</tr>
<tr>
<td>34 9<br />
</td>
<td><<6 5 22 -6 18 37]]<br />
</td>
<td>Catakleismic<br />
</td>
<td>4.684<br />
</td>
<td>225/224 4375/4374<br />
</td>
</tr>
<tr>
<td>17 2<br />
</td>
<td><<14 6 6 -23 -30 -3]]<br />
</td>
<td><br />
</td>
<td>5.385<br />
</td>
<td>50/49 110592/109375<br />
</td>
</tr>
<tr>
<td>34 13<br />
</td>
<td><<12 -7 10 -39 -18 43]]<br />
</td>
<td><br />
</td>
<td>6.472<br />
</td>
<td>225/224 124416/117649<br />
</td>
</tr>
<tr>
<td>17 7<br />
</td>
<td><<4 26 26 32 30 -13]]<br />
</td>
<td><br />
</td>
<td>7.556<br />
</td>
<td>50/49 1605632/1594323<br />
</td>
</tr>
<tr>
<td>34 5<br />
</td>
<td><<4 9 -8 5 -24 -44]]<br />
</td>
<td>Modus<br />
</td>
<td>4.203<br />
</td>
<td>50/49 1605632/1594323<br />
</td>
</tr>
<tr>
<td>17 8<br />
</td>
<td><<12 10 10 -12 -18 -5]]<br />
</td>
<td><br />
</td>
<td>4.400<br />
</td>
<td>50/49 15625/15552<br />
</td>
</tr>
<tr>
<td>34 1<br />
</td>
<td><<14 23 6 4 -30 -51]]<br />
</td>
<td><br />
</td>
<td>6.935<br />
</td>
<td>3200/3087 4375/4374<br />
</td>
</tr>
<tr>
<td>17 1<br />
</td>
<td><<6 22 22 21 18 -11]]<br />
</td>
<td><br />
</td>
<td>6.018<br />
</td>
<td>50/49 177147/175616<br />
</td>
</tr>
<tr>
<td>34 7<br />
</td>
<td><<2 13 -4 16 -12 -46]]<br />
</td>
<td>Immunized<br />
</td>
<td>4.300<br />
</td>
<td>64/63 8748/8575<br />
</td>
</tr>
<tr>
<td>17 4<br />
</td>
<td><<10 14 14 -1 -6 -7]]<br />
</td>
<td>Crepuscular<br />
</td>
<td>4.165<br />
</td>
<td>50/49 4375/4374<br />
</td>
</tr>
<tr>
<td>34 3<br />
</td>
<td><<16 19 2 -7 -42 -49]]<br />
</td>
<td><br />
</td>
<td>7.287<br />
</td>
<td>3200/3087 15625/15309<br />
</td>
</tr>
<tr>
<td>17 5<br />
</td>
<td><<8 18 18 10 6 -9]]<br />
</td>
<td><br />
</td>
<td>4.792<br />
</td>
<td>50/49 19683/19208<br />
</td>
</tr>
<tr>
<td>2 1<br />
</td>
<td><<0 17 0 27 0 -48]]<br />
</td>
<td><br />
</td>
<td>5.191<br />
</td>
<td>64/63 17496/16807<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:4:<h1> --><h1 id="toc2"><a name="x11-limit temperaments"></a><!-- ws:end:WikiTextHeadingRule:4 -->11-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>34 11<br />
</td>
<td><<8 1 18 20 -17 6 4 39 43 -6]]<br />
</td>
<td>Würschmidt<br />
</td>
<td>4.344<br />
</td>
<td>99/98 176/175 243/242<br />
</td>
</tr>
<tr>
<td>17 6<br />
</td>
<td><<16 2 2 6 -34 -42 -46 -1 7 10]]<br />
</td>
<td><br />
</td>
<td>5.940<br />
</td>
<td>50/49 176/175 1344/1331<br />
</td>
</tr>
<tr>
<td>34 15<br />
</td>
<td><<10 -3 14 8 -28 -6 -22 41 29 -26]]<br />
</td>
<td>Amavil<br />
</td>
<td>4.553<br />
</td>
<td>99/98 176/175 864/847<br />
</td>
</tr>
<tr>
<td>17 3<br />
</td>
<td><<2 -4 -4 -12 -11 -12 -26 2 -14 -20]]<br />
</td>
<td>Pajara<br />
</td>
<td>2.543<br />
</td>
<td>50/49 99/98 176/175<br />
</td>
</tr>
<tr>
<td>34 9<br />
</td>
<td><<6 5 -12 -2 -6 -36 -24 -42 -22 36]]<br />
</td>
<td><br />
</td>
<td>4.331<br />
</td>
<td>64/63 100/99 1331/1323<br />
</td>
</tr>
<tr>
<td>17 2<br />
</td>
<td><<14 6 6 18 -23 -30 -20 -3 21 30]]<br />
</td>
<td><br />
</td>
<td>4.804<br />
</td>
<td>50/49 176/175 1331/1323<br />
</td>
</tr>
<tr>
<td>34 13<br />
</td>
<td><<12 -7 10 -4 -39 -18 -48 43 15 -46]]<br />
</td>
<td><br />
</td>
<td>5.960<br />
</td>
<td>50/49 176/175 1331/1323<br />
</td>
</tr>
<tr>
<td>17 7<br />
</td>
<td><<4 -8 -8 10 -22 -24 2 4 51 56]]<br />
</td>
<td><br />
</td>
<td>4.167<br />
</td>
<td>50/49 64/63 243/242<br />
</td>
</tr>
<tr>
<td>34 5<br />
</td>
<td><<4 9 -8 10 5 -24 2 -44 -8 56]]<br />
</td>
<td>Modus<br />
</td>
<td>3.857<br />
</td>
<td>64/63 100/99 243/242<br />
</td>
</tr>
<tr>
<td>17 8<br />
</td>
<td><<12 10 10 30 -12 -18 6 -5 35 50]]<br />
</td>
<td><br />
</td>
<td>4.879<br />
</td>
<td>50/49 176/175 243/242<br />
</td>
</tr>
<tr>
<td>34 1<br />
</td>
<td><<14 23 6 18 4 -30 -20 -51 -38 30]]<br />
</td>
<td><br />
</td>
<td>6.007<br />
</td>
<td>100/99 352/343 864/847<br />
</td>
</tr>
<tr>
<td>17 1<br />
</td>
<td><<6 -12 -12 -2 -33 -36 -24 6 37 36]]<br />
</td>
<td><br />
</td>
<td>5.104<br />
</td>
<td>50/49 64/63 1331/1323<br />
</td>
</tr>
<tr>
<td>34 7<br />
</td>
<td><<2 13 -4 -12 16 -12 -26 -46 -73 -20]]<br />
</td>
<td>Immunized<br />
</td>
<td>4.820<br />
</td>
<td>64/63 99/98 1944/1925<br />
</td>
</tr>
<tr>
<td>17 4<br />
</td>
<td><<10 14 14 8 -1 -6 -22 -7 -30 -26]]<br />
</td>
<td>Crepuscular<br />
</td>
<td>3.829<br />
</td>
<td>50/49 99/98 1944/1925<br />
</td>
</tr>
<tr>
<td>34 3<br />
</td>
<td><<16 19 2 6 -7 -42 -46 -49 -52 10]]<br />
</td>
<td><br />
</td>
<td>6.595<br />
</td>
<td>100/99 352/343 1344/1331<br />
</td>
</tr>
<tr>
<td>17 5<br />
</td>
<td><<8 18 18 20 10 6 4 -9 -16 -6]]<br />
</td>
<td><br />
</td>
<td>4.196<br />
</td>
<td>50/49 99/98 243/242<br />
</td>
</tr>
<tr>
<td>2 1<br />
</td>
<td><<0 17 0 0 27 0 0 -48 -59 0]]<br />
</td>
<td><br />
</td>
<td>4.643<br />
</td>
<td>64/63 99/98 243/242<br />
</td>
</tr>
</table>
</body></html>