List of edo-distinct 27e rank two temperaments
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 2012-04-28 03:07:51 UTC.
- The original revision id was 326274606.
- 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:
The temperaments listed are 27edo-distinct, meaning that they are all different even if tuned in 27edo. The ordering is by increasing complexity of 3. The temperament of lowest TE complexity supported by the 27e val (<27 43 63 76 94 100|) was chosen as the representative for each class of edo-distinctness. =5-limit temperaments= || Rank || Wedgie || Name || Complexity || Commas || || 1 || <<1 9 12]] || Superpyth || 2.947 || 20480/19683 || || 2 || <<2 -9 -19]] || || 3.798 || 524288/492075 || || 3 || <<3 0 -7]] || Augmented || 1.549 || 128/125 || || 4 || <<4 9 5]] || Tetracot || 2.783 || 20000/19683 || || 5 || <<5 -9 -26]] || || 4.996 || 67108864/61509375 || || 6 || <<21 -27 -92]] || || 17.661 || |92 -27 -21> || || 7 || <<7 9 -2]] || Sensi || 3.407 || 78732/78125 || || 8 || <<8 -9 -33]] || || 6.348 || 8589934592/7688671875 || || 9 || <<9 -27 -64]] || || 12.515 || |64 -27 -9> || || 10 || <<10 9 -9]] || || 4.502 || 10077696/9765625 || || 11 || <<11 18 3]] || || 6.026 || 390625000/387420489 || || 12 || <<12 -27 -71]] || || 13.72 || |71 -27 -12> || || 13 || <<13 9 -16]] || || 5.808 || 1289945088/1220703125 || =7-limit temperaments= || Rank || Wedgie || Name || Complexity || Commas || || 1 || <<1 9 -2 12 -6 -30]] || Superpyth || 2.874 || 64/63 245/243 || || 2 || <<2 -9 -4 -19 -12 16]] || Beatles || 3.125 || 64/63 686/675 || || 3 || <<3 0 -6 -7 -18 -14]] || Augene || 2.336 || 64/63 126/125 || || 4 || <<4 9 19 5 19 19]] || Wollemia || 3.995 || 126/125 2240/2187 || || 5 || <<5 -9 -10 -26 -30 2]] || Fervor || 4.710 || 64/63 9604/9375 || || 6 || <<6 0 15 -14 7 35]] || Semiaug || 3.844 || 128/125 245/243 || || 7 || <<7 9 13 -2 1 5]] || Sensi || 3.080 || 126/125 245/243 || || 8 || <<8 18 11 10 -5 -25]] || Octacot || 4.551 || 245/243 2401/2400 || || 9 || <<9 0 9 -21 -11 21]] || Niner || 3.907 || 128/125 686/675 || || 10 || <<10 9 7 -9 -17 -9]] || Myna || 3.731 || 126/125 1728/1715 || || 11 || <<11 18 5 3 -23 -39]] || Quartonic || 5.395 || 1728/1715 4000/3969 || || 12 || <<12 0 3 -28 -29 7]] || Oodako || 5.164 || 128/125 2401/2400 || || 13 || <<13 9 1 -16 -35 -23]] || Kumonga || 5.411 || 126/125 12288/12005 || =11-limit temperaments= || Rank || Wedgie || Name || Complexity || Commas || || 1 || <<1 9 -2 16 12 -6 22 -30 6 52]] || Superpyth || 3.410 || 64/63 100/99 245/243 || || 2 || <<2 -9 -4 5 -19 -12 1 16 43 28]] || Ringo || 3.126 || 56/55 64/63 540/539 || || 3 || <<3 0 -6 -6 -7 -18 -20 -14 -14 4]] || Augene || 2.286 || 56/55 64/63 100/99 || || 4 || <<4 9 19 10 5 19 2 19 -8 -38]] || Wollemia || 3.472 || 56/55 100/99 243/242 || || 5 || <<5 -9 -10 -1 -26 -30 -19 2 29 32]] || Fervor || 4.112 || 56/55 64/63 1350/1331 || || 6 || <<6 0 15 15 -14 7 3 35 35 -10]] || Hemiaug || 3.575 || 56/55 128/125 245/243 || || 7 || <<7 9 13 4 -2 1 -18 5 -22 -34]] || Sensis || 2.980 || 56/55 100/99 245/243 || || 8 || <<8 18 11 20 10 -5 4 -25 -16 18]] || Octacot || 4.070 || 100/99 243/242 245/242 || || 9 || <<9 0 9 9 -21 -11 -17 21 21 -6]] || Niner || 3.394 || 56/55 128/125 540/539 || || 10 || <<10 9 7 -2 -9 -17 -38 -9 -36 -30]] || Coleto || 4.019 || 56/55 100/99 1728/1715 || || 11 || <<11 18 5 14 3 -23 -16 -39 -30 22]] || Quarto || 4.675 || 100/99 245/242 864/847 || || 12 || <<12 0 3 3 -28 -29 -37 7 7 -2]] || Oodako || 4.551 || 56/55 128/125 3773/3750 || || 13 || <<13 9 1 19 -16 -35 -15 -23 13 50]] || Kumonga || 4.924 || 126/125 176/175 864/847 || =13-limit temperaments= || Rank || Wedgie || Name || Complexity || Commas || || 1 || <<1 9 -2 16 13 12 -6 22 17 -30 6 -3 52 44 -14]] || Superpyth || 3.228 || 64/63 78/77 91/90 100/99 || || 2 || <<2 -9 -4 5 -1 -19 -12 1 -9 16 43 31 28 12 -22]] || Ringo || 2.798 || 56/55 64/63 78/77 91/90 || || 3 || <<3 0 -6 -6 12 -7 -18 -20 8 -14 -14 28 4 56 64]] || Ogene || 2.936 || 56/55 64/63 91/90 100/99 || || 4 || <<4 9 -8 10 -2 5 -24 2 -18 -44 -8 -38 56 24 -44]] || Modus || 3.607 || 64/63 78/77 100/99 144/143 || || 5 || <<5 -9 -10 -1 -16 -26 -30 -19 -44 2 29 -4 32 -8 -52]] || Fervor || 4.175 || 56/55 64/63 78/77 507/500 || || 6 || <<6 0 15 15 -3 -14 7 3 -27 35 35 -7 -10 -64 -66]] || Hemiaug || 3.785 || 56/55 91/90 128/125 245/243 || || 7 || <<7 9 13 4 10 -2 1 -18 -10 5 -22 -10 -34 -20 20]] || Sensis || 2.664 || 56/55 78/77 91/90 100/99 || || 8 || <<8 18 11 20 23 10 -5 4 7 -25 -16 -13 18 24 6]] || Octocat || 3.773 || 78/77 91/90 100/99 245/242 || || 9 || <<9 0 9 9 9 -21 -11 -17 -19 21 21 21 -6 -8 -2]] || Niner || 3.035 || 56/55 78/77 91/90 128/125 || || 10 || <<10 9 7 25 22 -9 -17 5 -2 -9 27 18 46 36 -16]] || Minah || 3.862 || 78/77 91/90 126/125 176/175 || || 11 || <<11 18 5 14 8 3 -23 -16 -28 -39 -30 -48 22 4 -24]] || Quarto || 4.328 || 78/77 100/99 144/143 245/242 || || 12 || <<12 0 3 3 -6 -28 -29 -37 -54 7 7 -14 -2 -28 -32]] || Oodako || 4.551 || 56/55 78/77 128/125 507/500 || || 13 || <<13 9 1 19 7 -16 -35 -15 -37 -23 13 -17 50 16 -46]] || Kumonga || 4.509 || 78/77 126/125 144/143 176/175 ||
Original HTML content:
<html><head><title>List of edo-distinct 27e rank two temperaments</title></head><body>The temperaments listed are 27edo-distinct, meaning that they are all different even if tuned in 27edo. The ordering is by increasing complexity of 3. The temperament of lowest TE complexity supported by the 27e val (<27 43 63 76 94 100|) 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>Rank<br />
</td>
<td>Wedgie<br />
</td>
<td>Name<br />
</td>
<td>Complexity<br />
</td>
<td>Commas<br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td><<1 9 12]]<br />
</td>
<td>Superpyth<br />
</td>
<td>2.947<br />
</td>
<td>20480/19683<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td><<2 -9 -19]]<br />
</td>
<td><br />
</td>
<td>3.798<br />
</td>
<td>524288/492075<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td><<3 0 -7]]<br />
</td>
<td>Augmented<br />
</td>
<td>1.549<br />
</td>
<td>128/125<br />
</td>
</tr>
<tr>
<td>4<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>5<br />
</td>
<td><<5 -9 -26]]<br />
</td>
<td><br />
</td>
<td>4.996<br />
</td>
<td>67108864/61509375<br />
</td>
<td><br />
</td>
<td>6<br />
</td>
<td><<21 -27 -92]]<br />
</td>
<td><br />
</td>
<td>17.661<br />
</td>
<td>|92 -27 -21><br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td><<7 9 -2]]<br />
</td>
<td>Sensi<br />
</td>
<td>3.407<br />
</td>
<td>78732/78125<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td><<8 -9 -33]]<br />
</td>
<td><br />
</td>
<td>6.348<br />
</td>
<td>8589934592/7688671875<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td><<9 -27 -64]]<br />
</td>
<td><br />
</td>
<td>12.515<br />
</td>
<td>|64 -27 -9><br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td><<10 9 -9]]<br />
</td>
<td><br />
</td>
<td>4.502<br />
</td>
<td>10077696/9765625<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td><<11 18 3]]<br />
</td>
<td><br />
</td>
<td>6.026<br />
</td>
<td>390625000/387420489<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td><<12 -27 -71]]<br />
</td>
<td><br />
</td>
<td>13.72<br />
</td>
<td>|71 -27 -12><br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td><<13 9 -16]]<br />
</td>
<td><br />
</td>
<td>5.808<br />
</td>
<td>1289945088/1220703125<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>Rank<br />
</td>
<td>Wedgie<br />
</td>
<td>Name<br />
</td>
<td>Complexity<br />
</td>
<td>Commas<br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td><<1 9 -2 12 -6 -30]]<br />
</td>
<td>Superpyth<br />
</td>
<td>2.874<br />
</td>
<td>64/63 245/243<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td><<2 -9 -4 -19 -12 16]]<br />
</td>
<td>Beatles<br />
</td>
<td>3.125<br />
</td>
<td>64/63 686/675<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td><<3 0 -6 -7 -18 -14]]<br />
</td>
<td>Augene<br />
</td>
<td>2.336<br />
</td>
<td>64/63 126/125<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td><<4 9 19 5 19 19]]<br />
</td>
<td>Wollemia<br />
</td>
<td>3.995<br />
</td>
<td>126/125 2240/2187<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td><<5 -9 -10 -26 -30 2]]<br />
</td>
<td>Fervor<br />
</td>
<td>4.710<br />
</td>
<td>64/63 9604/9375<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td><<6 0 15 -14 7 35]]<br />
</td>
<td>Semiaug<br />
</td>
<td>3.844<br />
</td>
<td>128/125 245/243<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td><<7 9 13 -2 1 5]]<br />
</td>
<td>Sensi<br />
</td>
<td>3.080<br />
</td>
<td>126/125 245/243<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td><<8 18 11 10 -5 -25]]<br />
</td>
<td>Octacot<br />
</td>
<td>4.551<br />
</td>
<td>245/243 2401/2400<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td><<9 0 9 -21 -11 21]]<br />
</td>
<td>Niner<br />
</td>
<td>3.907<br />
</td>
<td>128/125 686/675<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td><<10 9 7 -9 -17 -9]]<br />
</td>
<td>Myna<br />
</td>
<td>3.731<br />
</td>
<td>126/125 1728/1715<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td><<11 18 5 3 -23 -39]]<br />
</td>
<td>Quartonic<br />
</td>
<td>5.395<br />
</td>
<td>1728/1715 4000/3969<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td><<12 0 3 -28 -29 7]]<br />
</td>
<td>Oodako<br />
</td>
<td>5.164<br />
</td>
<td>128/125 2401/2400<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td><<13 9 1 -16 -35 -23]]<br />
</td>
<td>Kumonga<br />
</td>
<td>5.411<br />
</td>
<td>126/125 12288/12005<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>Rank<br />
</td>
<td>Wedgie<br />
</td>
<td>Name<br />
</td>
<td>Complexity<br />
</td>
<td>Commas<br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td><<1 9 -2 16 12 -6 22 -30 6 52]]<br />
</td>
<td>Superpyth<br />
</td>
<td>3.410<br />
</td>
<td>64/63 100/99 245/243<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td><<2 -9 -4 5 -19 -12 1 16 43 28]]<br />
</td>
<td>Ringo<br />
</td>
<td>3.126<br />
</td>
<td>56/55 64/63 540/539<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td><<3 0 -6 -6 -7 -18 -20 -14 -14 4]]<br />
</td>
<td>Augene<br />
</td>
<td>2.286<br />
</td>
<td>56/55 64/63 100/99<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td><<4 9 19 10 5 19 2 19 -8 -38]]<br />
</td>
<td>Wollemia<br />
</td>
<td>3.472<br />
</td>
<td>56/55 100/99 243/242<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td><<5 -9 -10 -1 -26 -30 -19 2 29 32]]<br />
</td>
<td>Fervor<br />
</td>
<td>4.112<br />
</td>
<td>56/55 64/63 1350/1331<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td><<6 0 15 15 -14 7 3 35 35 -10]]<br />
</td>
<td>Hemiaug<br />
</td>
<td>3.575<br />
</td>
<td>56/55 128/125 245/243<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td><<7 9 13 4 -2 1 -18 5 -22 -34]]<br />
</td>
<td>Sensis<br />
</td>
<td>2.980<br />
</td>
<td>56/55 100/99 245/243<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td><<8 18 11 20 10 -5 4 -25 -16 18]]<br />
</td>
<td>Octacot<br />
</td>
<td>4.070<br />
</td>
<td>100/99 243/242 245/242<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td><<9 0 9 9 -21 -11 -17 21 21 -6]]<br />
</td>
<td>Niner<br />
</td>
<td>3.394<br />
</td>
<td>56/55 128/125 540/539<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td><<10 9 7 -2 -9 -17 -38 -9 -36 -30]]<br />
</td>
<td>Coleto<br />
</td>
<td>4.019<br />
</td>
<td>56/55 100/99 1728/1715<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td><<11 18 5 14 3 -23 -16 -39 -30 22]]<br />
</td>
<td>Quarto<br />
</td>
<td>4.675<br />
</td>
<td>100/99 245/242 864/847<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td><<12 0 3 3 -28 -29 -37 7 7 -2]]<br />
</td>
<td>Oodako<br />
</td>
<td>4.551<br />
</td>
<td>56/55 128/125 3773/3750<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td><<13 9 1 19 -16 -35 -15 -23 13 50]]<br />
</td>
<td>Kumonga<br />
</td>
<td>4.924<br />
</td>
<td>126/125 176/175 864/847<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>Rank<br />
</td>
<td>Wedgie<br />
</td>
<td>Name<br />
</td>
<td>Complexity<br />
</td>
<td>Commas<br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td><<1 9 -2 16 13 12 -6 22 17 -30 6 -3 52 44 -14]]<br />
</td>
<td>Superpyth<br />
</td>
<td>3.228<br />
</td>
<td>64/63 78/77 91/90 100/99<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td><<2 -9 -4 5 -1 -19 -12 1 -9 16 43 31 28 12 -22]]<br />
</td>
<td>Ringo<br />
</td>
<td>2.798<br />
</td>
<td>56/55 64/63 78/77 91/90<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td><<3 0 -6 -6 12 -7 -18 -20 8 -14 -14 28 4 56 64]]<br />
</td>
<td>Ogene<br />
</td>
<td>2.936<br />
</td>
<td>56/55 64/63 91/90 100/99<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td><<4 9 -8 10 -2 5 -24 2 -18 -44 -8 -38 56 24 -44]]<br />
</td>
<td>Modus<br />
</td>
<td>3.607<br />
</td>
<td>64/63 78/77 100/99 144/143<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td><<5 -9 -10 -1 -16 -26 -30 -19 -44 2 29 -4 32 -8 -52]]<br />
</td>
<td>Fervor<br />
</td>
<td>4.175<br />
</td>
<td>56/55 64/63 78/77 507/500<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td><<6 0 15 15 -3 -14 7 3 -27 35 35 -7 -10 -64 -66]]<br />
</td>
<td>Hemiaug<br />
</td>
<td>3.785<br />
</td>
<td>56/55 91/90 128/125 245/243<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td><<7 9 13 4 10 -2 1 -18 -10 5 -22 -10 -34 -20 20]]<br />
</td>
<td>Sensis<br />
</td>
<td>2.664<br />
</td>
<td>56/55 78/77 91/90 100/99<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td><<8 18 11 20 23 10 -5 4 7 -25 -16 -13 18 24 6]]<br />
</td>
<td>Octocat<br />
</td>
<td>3.773<br />
</td>
<td>78/77 91/90 100/99 245/242<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td><<9 0 9 9 9 -21 -11 -17 -19 21 21 21 -6 -8 -2]]<br />
</td>
<td>Niner<br />
</td>
<td>3.035<br />
</td>
<td>56/55 78/77 91/90 128/125<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td><<10 9 7 25 22 -9 -17 5 -2 -9 27 18 46 36 -16]]<br />
</td>
<td>Minah<br />
</td>
<td>3.862<br />
</td>
<td>78/77 91/90 126/125 176/175<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td><<11 18 5 14 8 3 -23 -16 -28 -39 -30 -48 22 4 -24]]<br />
</td>
<td>Quarto<br />
</td>
<td>4.328<br />
</td>
<td>78/77 100/99 144/143 245/242<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td><<12 0 3 3 -6 -28 -29 -37 -54 7 7 -14 -2 -28 -32]]<br />
</td>
<td>Oodako<br />
</td>
<td>4.551<br />
</td>
<td>56/55 78/77 128/125 507/500<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td><<13 9 1 19 7 -16 -35 -15 -37 -23 13 -17 50 16 -46]]<br />
</td>
<td>Kumonga<br />
</td>
<td>4.509<br />
</td>
<td>78/77 126/125 144/143 176/175<br />
</td>
</tr>
</table>
</body></html>