List of edo-distinct 29et rank two temperaments
IMPORTED REVISION FROM WIKISPACES
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The temperaments listed are 29edo-distinct, meaning that they are all different even if tuned in 29edo. The ordering is by increasing complexity of 3. 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 || || 29 12 || <<1 -8 -15]] || Helmholtz || 3.103 || 32805/32768 || || 29 5 || <<2 13 16]] || Immunity || 4.157 || 1638400/1594323 || || 29 7 || <<3 5 1]] || Porcupine || 1.663 || 250/243 || || 29 10 || <<4 -3 -14]] || Negri || 2.739 || 16875/16384 || || 29 2 || <<5 18 17]] || || 5.519 || 409600000/387420489 || || 29 14 || <<6 -19 -44]] || || 8.646 || 18160335421875/17592186044416 || || 29 3 || <<7 2 -13]] || || 3.303 || 78125/73728 || || 29 9 || <<8 23 18]] || || 7.012 || 102400000000/94143178827 || || 29 8 || <<9 -14 -43]] || || 8.269 || 9341736328125/8796093022208 || || 29 4 || <<10 7 -12]] || || 4.455 || 9765625/8957952 || || 29 13 || <<11 -1 -27]] || || 5.836 || 146484375/134217728 || || 29 1 || <<17 9 -25]] || || 7.664 || 762939453125/660451885056 || || 29 11 || <<13 12 -11]] || || 5.857 || 1220703125/1088391168 || || 29 6 || <<15 -4 -41]] || || 8.498 || 2471923828125/2199023255552 || =7-limit temperaments= || Period generator || Wedgie || Name || Complexity || Commas || || 29 12 || <<1 -8 -14 -15 -25 -10]] || Garibaldi || 3.823 || 225/224 3125/3087 || || 29 5 || <<2 13 1 16 -4 -34]] || Immunity || 3.651 || 49/48 2240/2187 || || 29 7 || <<3 5 16 1 17 23]] || Porky || 3.362 || 225/224 250/243 || || 29 10 || <<4 -3 2 -14 -8 13]] || Negri || 2.245 || 49/48 225/224 || || 29 2 || <<5 18 17 17 13 -11]] || || 4.821 || 686/675 2240/2187 || || 29 14 || <<6 10 3 2 -12 -21]] || Nautilus || 2.943 || 49/48 250/243 || || 29 3 || <<7 2 18 -13 9 36]] || || 4.251 || 225/224 6125/5832 || || 29 9 || <<8 23 4 18 -16 -55]] || || 6.241 || 49/48 560000/531441 || || 29 8 || <<9 15 19 3 5 2]] || Ammonite || 4.506 || 250/243 686/675 || || 29 4 || <<10 7 5 -12 -20 -8]] || || 3.751 || 49/48 3125/3024 || || 29 13 || <<11 -1 20 -27 1 49]] || || 5.909 || 225/224 84035/78732 || || 29 1 || <<17 9 23 -25 -11 28]] || || 6.682 || 686/675 21875/20736 || || 29 11 || <<13 12 21 -11 -3 15]] || || 5.238 || 686/675 3125/3024 || || 29 6 || <<14 4 7 -26 -28 5]] || || 5.436 || 49/48 78125/73728 || =11-limit temperaments= || Period generator || Wedgie || Name || Complexity || Commas || || 29 12 || <<1 -8 -14 -18 -15 -25 -32 -10 -14 -2]] || Cassandra || 3.897 || 100/99 225/224 245/242 || || 29 5 || <<2 13 1 -7 16 -4 -18 -34 -61 -23]] || Immunity || 3.977 || 49/48 55/54 896/891 || || 29 7 || <<3 5 16 4 1 17 -4 23 -8 -44]] || Porky || 3.020 || 55/54 100/99 225/224 || || 29 10 || <<4 -3 2 15 -14 -8 10 13 45 35]] || Negroni || 3.110 || 49/48 55/54 225/224 || || 29 2 || <<5 -11 -12 -3 -29 -33 -22 3 31 33]] || Tritonic || 4.596 || 121/120 225/224 441/440 || || 29 14 || <<6 10 3 8 2 -12 -8 -21 -16 12]] || Nautilus || 2.548 || 49/48 55/54 245/242 || || 29 3 || <<7 2 18 19 -13 9 6 36 37 -9]] || || 4.023 || 55/54 225/224 245/242 || || 29 9 || <<8 -6 4 1 -28 -16 -26 26 23 -11]] || Wilsec || 3.911 || 49/48 121/120 225/224 || || 29 8 || <<9 15 19 12 3 5 -12 2 -24 -32]] || Ammonite || 3.980 || 55/54 100/99 686/675 || || 29 4 || <<10 7 5 23 -12 -20 2 -8 29 47]] || || 4.064 || 49/48 55/54 625/616 || || 29 13 || <<11 -1 20 5 -27 1 -30 49 15 -55]] || || 5.264 || 121/120 225/224 1225/1188 || || 29 1 || <<17 9 23 13 -25 -11 -38 28 -1 -43]] || || 5.913 || 121/120 625/616 686/675 || || 29 11 || <<13 12 21 27 -11 -3 -2 15 21 3]] || || 4.823 || 55/54 245/242 625/616 || || 29 6 || <<14 4 7 9 -26 -28 -34 5 7 1]] || || 4.725 || 49/48 121/120 625/616 || =13-limit temperaments= || Period generator || Wedgie || Name || Complexity || Commas || || 29 12 || <<1 -8 -14 -18 -21 -15 -25 -32 -37 -10 -14 -19 -2 -7 -6]] || Cassandra || 3.911 || 100/99 105/104 196/195 245/242 || || 29 5 || <<2 13 1 22 16 16 -4 28 18 -34 6 -11 58 41 -26]] || Impunity || 3.934 || 49/48 91/90 100/99 352/351 || || 29 7 || <<3 5 16 4 -5 1 17 -4 -19 23 -8 -30 -44 -73 -32]] || Porky || 3.380 || 55/54 65/64 91/90 100/99 || || 29 10 || <<4 -3 2 15 3 -14 -8 10 -10 13 45 18 35 1 -45]] || Negroni || 2.793 || 49/48 55/54 65/64 91/90 || || 29 2 || <<5 18 17 26 11 17 13 24 -1 -11 -2 -41 14 -32 -58]] || || 4.312 || 91/90 100/99 169/168 245/242 || || 29 14 || <<6 10 3 8 19 2 -12 -8 8 -21 -16 7 12 42 36]] || Nautilus || 2.806 || 49/48 55/54 91/90 100/99 || || 29 3 || <<7 2 -11 -10 -2 -13 -37 -40 -29 -31 -30 -12 10 35 30]] || Roman || 4.163 || 65/64 100/99 105/104 245/242 || || 29 9 || <<8 -6 4 1 6 -28 -16 -26 -20 26 23 36 -11 2 17]] || Wilsec || 3.527 || 49/48 65/64 91/90 121/120 || || 29 8 || <<9 15 19 12 14 3 5 -12 -11 2 -24 -23 -32 -31 4]] || Ammonite || 3.582 || 55/54 91/90 100/99 169/168 || || 29 4 || <<10 7 5 23 22 -12 -20 2 -2 -8 29 25 47 43 -9]] || || 3.888 || 49/48 55/54 91/90 847/845 || || 29 13 || <<11 -1 -9 5 1 -27 -45 -30 -39 -18 15 6 45 36 -15]] || || 4.743 || 65/64 121/120 169/168 275/273 || || 29 1 || <<12 20 6 16 9 4 -24 -16 -30 -42 -32 -53 24 3 -28]] || || 4.724 || 49/48 55/54 245/242 343/338 || || 29 11 || <<13 12 21 27 17 -11 -3 -2 -21 15 21 -5 3 -30 -41]] || || 4.362 || 55/54 91/90 169/168 245/242 || || 29 6 || <<14 4 7 9 25 -26 -28 -34 -12 5 7 43 1 44 53]] || || 4.713 || 49/48 91/90 121/120 625/616 ||
Original HTML content:
<html><head><title>List of edo-distinct 29et rank two temperaments</title></head><body>The temperaments listed are 29edo-distinct, meaning that they are all different even if tuned in 29edo. The ordering is by increasing complexity of 3. The temperament of lowest TE complexity supported by the patent val was chosen as the representative for each class of edo-distinctness.<br />
<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>29 12<br />
</td>
<td><<1 -8 -15]]<br />
</td>
<td>Helmholtz<br />
</td>
<td>3.103<br />
</td>
<td>32805/32768<br />
</td>
</tr>
<tr>
<td>29 5<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>29 7<br />
</td>
<td><<3 5 1]]<br />
</td>
<td>Porcupine<br />
</td>
<td>1.663<br />
</td>
<td>250/243<br />
</td>
</tr>
<tr>
<td>29 10<br />
</td>
<td><<4 -3 -14]]<br />
</td>
<td>Negri<br />
</td>
<td>2.739<br />
</td>
<td>16875/16384<br />
</td>
</tr>
<tr>
<td>29 2<br />
</td>
<td><<5 18 17]]<br />
</td>
<td><br />
</td>
<td>5.519<br />
</td>
<td>409600000/387420489<br />
</td>
</tr>
<tr>
<td>29 14<br />
</td>
<td><<6 -19 -44]]<br />
</td>
<td><br />
</td>
<td>8.646<br />
</td>
<td>18160335421875/17592186044416<br />
</td>
</tr>
<tr>
<td>29 3<br />
</td>
<td><<7 2 -13]]<br />
</td>
<td><br />
</td>
<td>3.303<br />
</td>
<td>78125/73728<br />
</td>
</tr>
<tr>
<td>29 9<br />
</td>
<td><<8 23 18]]<br />
</td>
<td><br />
</td>
<td>7.012<br />
</td>
<td>102400000000/94143178827<br />
</td>
</tr>
<tr>
<td>29 8<br />
</td>
<td><<9 -14 -43]]<br />
</td>
<td><br />
</td>
<td>8.269<br />
</td>
<td>9341736328125/8796093022208<br />
</td>
</tr>
<tr>
<td>29 4<br />
</td>
<td><<10 7 -12]]<br />
</td>
<td><br />
</td>
<td>4.455<br />
</td>
<td>9765625/8957952<br />
</td>
</tr>
<tr>
<td>29 13<br />
</td>
<td><<11 -1 -27]]<br />
</td>
<td><br />
</td>
<td>5.836<br />
</td>
<td>146484375/134217728<br />
</td>
</tr>
<tr>
<td>29 1<br />
</td>
<td><<17 9 -25]]<br />
</td>
<td><br />
</td>
<td>7.664<br />
</td>
<td>762939453125/660451885056<br />
</td>
</tr>
<tr>
<td>29 11<br />
</td>
<td><<13 12 -11]]<br />
</td>
<td><br />
</td>
<td>5.857<br />
</td>
<td>1220703125/1088391168<br />
</td>
</tr>
<tr>
<td>29 6<br />
</td>
<td><<15 -4 -41]]<br />
</td>
<td><br />
</td>
<td>8.498<br />
</td>
<td>2471923828125/2199023255552<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>29 12<br />
</td>
<td><<1 -8 -14 -15 -25 -10]]<br />
</td>
<td>Garibaldi<br />
</td>
<td>3.823<br />
</td>
<td>225/224 3125/3087<br />
</td>
</tr>
<tr>
<td>29 5<br />
</td>
<td><<2 13 1 16 -4 -34]]<br />
</td>
<td>Immunity<br />
</td>
<td>3.651<br />
</td>
<td>49/48 2240/2187<br />
</td>
</tr>
<tr>
<td>29 7<br />
</td>
<td><<3 5 16 1 17 23]]<br />
</td>
<td>Porky<br />
</td>
<td>3.362<br />
</td>
<td>225/224 250/243<br />
</td>
</tr>
<tr>
<td>29 10<br />
</td>
<td><<4 -3 2 -14 -8 13]]<br />
</td>
<td>Negri<br />
</td>
<td>2.245<br />
</td>
<td>49/48 225/224<br />
</td>
</tr>
<tr>
<td>29 2<br />
</td>
<td><<5 18 17 17 13 -11]]<br />
</td>
<td><br />
</td>
<td>4.821<br />
</td>
<td>686/675 2240/2187<br />
</td>
</tr>
<tr>
<td>29 14<br />
</td>
<td><<6 10 3 2 -12 -21]]<br />
</td>
<td>Nautilus<br />
</td>
<td>2.943<br />
</td>
<td>49/48 250/243<br />
</td>
</tr>
<tr>
<td>29 3<br />
</td>
<td><<7 2 18 -13 9 36]]<br />
</td>
<td><br />
</td>
<td>4.251<br />
</td>
<td>225/224 6125/5832<br />
</td>
</tr>
<tr>
<td>29 9<br />
</td>
<td><<8 23 4 18 -16 -55]]<br />
</td>
<td><br />
</td>
<td>6.241<br />
</td>
<td>49/48 560000/531441<br />
</td>
</tr>
<tr>
<td>29 8<br />
</td>
<td><<9 15 19 3 5 2]]<br />
</td>
<td>Ammonite<br />
</td>
<td>4.506<br />
</td>
<td>250/243 686/675<br />
</td>
</tr>
<tr>
<td>29 4<br />
</td>
<td><<10 7 5 -12 -20 -8]]<br />
</td>
<td><br />
</td>
<td>3.751<br />
</td>
<td>49/48 3125/3024<br />
</td>
</tr>
<tr>
<td>29 13<br />
</td>
<td><<11 -1 20 -27 1 49]]<br />
</td>
<td><br />
</td>
<td>5.909<br />
</td>
<td>225/224 84035/78732<br />
</td>
</tr>
<tr>
<td>29 1<br />
</td>
<td><<17 9 23 -25 -11 28]]<br />
</td>
<td><br />
</td>
<td>6.682<br />
</td>
<td>686/675 21875/20736<br />
</td>
</tr>
<tr>
<td>29 11<br />
</td>
<td><<13 12 21 -11 -3 15]]<br />
</td>
<td><br />
</td>
<td>5.238<br />
</td>
<td>686/675 3125/3024<br />
</td>
</tr>
<tr>
<td>29 6<br />
</td>
<td><<14 4 7 -26 -28 5]]<br />
</td>
<td><br />
</td>
<td>5.436<br />
</td>
<td>49/48 78125/73728<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>29 12<br />
</td>
<td><<1 -8 -14 -18 -15 -25 -32 -10 -14 -2]]<br />
</td>
<td>Cassandra<br />
</td>
<td>3.897<br />
</td>
<td>100/99 225/224 245/242<br />
</td>
</tr>
<tr>
<td>29 5<br />
</td>
<td><<2 13 1 -7 16 -4 -18 -34 -61 -23]]<br />
</td>
<td>Immunity<br />
</td>
<td>3.977<br />
</td>
<td>49/48 55/54 896/891<br />
</td>
</tr>
<tr>
<td>29 7<br />
</td>
<td><<3 5 16 4 1 17 -4 23 -8 -44]]<br />
</td>
<td>Porky<br />
</td>
<td>3.020<br />
</td>
<td>55/54 100/99 225/224<br />
</td>
</tr>
<tr>
<td>29 10<br />
</td>
<td><<4 -3 2 15 -14 -8 10 13 45 35]]<br />
</td>
<td>Negroni<br />
</td>
<td>3.110<br />
</td>
<td>49/48 55/54 225/224<br />
</td>
</tr>
<tr>
<td>29 2<br />
</td>
<td><<5 -11 -12 -3 -29 -33 -22 3 31 33]]<br />
</td>
<td>Tritonic<br />
</td>
<td>4.596<br />
</td>
<td>121/120 225/224 441/440<br />
</td>
</tr>
<tr>
<td>29 14<br />
</td>
<td><<6 10 3 8 2 -12 -8 -21 -16 12]]<br />
</td>
<td>Nautilus<br />
</td>
<td>2.548<br />
</td>
<td>49/48 55/54 245/242<br />
</td>
</tr>
<tr>
<td>29 3<br />
</td>
<td><<7 2 18 19 -13 9 6 36 37 -9]]<br />
</td>
<td><br />
</td>
<td>4.023<br />
</td>
<td>55/54 225/224 245/242<br />
</td>
</tr>
<tr>
<td>29 9<br />
</td>
<td><<8 -6 4 1 -28 -16 -26 26 23 -11]]<br />
</td>
<td>Wilsec<br />
</td>
<td>3.911<br />
</td>
<td>49/48 121/120 225/224<br />
</td>
</tr>
<tr>
<td>29 8<br />
</td>
<td><<9 15 19 12 3 5 -12 2 -24 -32]]<br />
</td>
<td>Ammonite<br />
</td>
<td>3.980<br />
</td>
<td>55/54 100/99 686/675<br />
</td>
</tr>
<tr>
<td>29 4<br />
</td>
<td><<10 7 5 23 -12 -20 2 -8 29 47]]<br />
</td>
<td><br />
</td>
<td>4.064<br />
</td>
<td>49/48 55/54 625/616<br />
</td>
</tr>
<tr>
<td>29 13<br />
</td>
<td><<11 -1 20 5 -27 1 -30 49 15 -55]]<br />
</td>
<td><br />
</td>
<td>5.264<br />
</td>
<td>121/120 225/224 1225/1188<br />
</td>
</tr>
<tr>
<td>29 1<br />
</td>
<td><<17 9 23 13 -25 -11 -38 28 -1 -43]]<br />
</td>
<td><br />
</td>
<td>5.913<br />
</td>
<td>121/120 625/616 686/675<br />
</td>
</tr>
<tr>
<td>29 11<br />
</td>
<td><<13 12 21 27 -11 -3 -2 15 21 3]]<br />
</td>
<td><br />
</td>
<td>4.823<br />
</td>
<td>55/54 245/242 625/616<br />
</td>
</tr>
<tr>
<td>29 6<br />
</td>
<td><<14 4 7 9 -26 -28 -34 5 7 1]]<br />
</td>
<td><br />
</td>
<td>4.725<br />
</td>
<td>49/48 121/120 625/616<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:6:<h1> --><h1 id="toc3"><a name="x13-limit temperaments"></a><!-- ws:end:WikiTextHeadingRule:6 -->13-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>29 12<br />
</td>
<td><<1 -8 -14 -18 -21 -15 -25 -32 -37 -10 -14 -19 -2 -7 -6]]<br />
</td>
<td>Cassandra<br />
</td>
<td>3.911<br />
</td>
<td>100/99 105/104 196/195 245/242<br />
</td>
</tr>
<tr>
<td>29 5<br />
</td>
<td><<2 13 1 22 16 16 -4 28 18 -34 6 -11 58 41 -26]]<br />
</td>
<td>Impunity<br />
</td>
<td>3.934<br />
</td>
<td>49/48 91/90 100/99 352/351<br />
</td>
</tr>
<tr>
<td>29 7<br />
</td>
<td><<3 5 16 4 -5 1 17 -4 -19 23 -8 -30 -44 -73 -32]]<br />
</td>
<td>Porky<br />
</td>
<td>3.380<br />
</td>
<td>55/54 65/64 91/90 100/99<br />
</td>
</tr>
<tr>
<td>29 10<br />
</td>
<td><<4 -3 2 15 3 -14 -8 10 -10 13 45 18 35 1 -45]]<br />
</td>
<td>Negroni<br />
</td>
<td>2.793<br />
</td>
<td>49/48 55/54 65/64 91/90<br />
</td>
</tr>
<tr>
<td>29 2<br />
</td>
<td><<5 18 17 26 11 17 13 24 -1 -11 -2 -41 14 -32 -58]]<br />
</td>
<td><br />
</td>
<td>4.312<br />
</td>
<td>91/90 100/99 169/168 245/242<br />
</td>
</tr>
<tr>
<td>29 14<br />
</td>
<td><<6 10 3 8 19 2 -12 -8 8 -21 -16 7 12 42 36]]<br />
</td>
<td>Nautilus<br />
</td>
<td>2.806<br />
</td>
<td>49/48 55/54 91/90 100/99<br />
</td>
</tr>
<tr>
<td>29 3<br />
</td>
<td><<7 2 -11 -10 -2 -13 -37 -40 -29 -31 -30 -12 10 35 30]]<br />
</td>
<td>Roman<br />
</td>
<td>4.163<br />
</td>
<td>65/64 100/99 105/104 245/242<br />
</td>
</tr>
<tr>
<td>29 9<br />
</td>
<td><<8 -6 4 1 6 -28 -16 -26 -20 26 23 36 -11 2 17]]<br />
</td>
<td>Wilsec<br />
</td>
<td>3.527<br />
</td>
<td>49/48 65/64 91/90 121/120<br />
</td>
</tr>
<tr>
<td>29 8<br />
</td>
<td><<9 15 19 12 14 3 5 -12 -11 2 -24 -23 -32 -31 4]]<br />
</td>
<td>Ammonite<br />
</td>
<td>3.582<br />
</td>
<td>55/54 91/90 100/99 169/168<br />
</td>
</tr>
<tr>
<td>29 4<br />
</td>
<td><<10 7 5 23 22 -12 -20 2 -2 -8 29 25 47 43 -9]]<br />
</td>
<td><br />
</td>
<td>3.888<br />
</td>
<td>49/48 55/54 91/90 847/845<br />
</td>
</tr>
<tr>
<td>29 13<br />
</td>
<td><<11 -1 -9 5 1 -27 -45 -30 -39 -18 15 6 45 36 -15]]<br />
</td>
<td><br />
</td>
<td>4.743<br />
</td>
<td>65/64 121/120 169/168 275/273<br />
</td>
</tr>
<tr>
<td>29 1<br />
</td>
<td><<12 20 6 16 9 4 -24 -16 -30 -42 -32 -53 24 3 -28]]<br />
</td>
<td><br />
</td>
<td>4.724<br />
</td>
<td>49/48 55/54 245/242 343/338<br />
</td>
</tr>
<tr>
<td>29 11<br />
</td>
<td><<13 12 21 27 17 -11 -3 -2 -21 15 21 -5 3 -30 -41]]<br />
</td>
<td><br />
</td>
<td>4.362<br />
</td>
<td>55/54 91/90 169/168 245/242<br />
</td>
</tr>
<tr>
<td>29 6<br />
</td>
<td><<14 4 7 9 25 -26 -28 -34 -12 5 7 43 1 44 53]]<br />
</td>
<td><br />
</td>
<td>4.713<br />
</td>
<td>49/48 91/90 121/120 625/616<br />
</td>
</tr>
</table>
</body></html>