List of 12et rank two temperaments by complexity
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author phylingual and made on 2012-04-23 21:43:24 UTC.
- The original revision id was 324425526.
- 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:
Below are listed rank-two temperaments supported by the [[12edo]] patent val, below the indicated cutoff in TE badness. =5-limit temperaments with badness below 0.1= Listed is the wedgie and the TE complexity for six temperaments with badness less than 0.1. || Rank || Wedgie || Name || Complexity || Commas || || 1 || <<1 4 4]] || Meantone || 1.523 || 81/80 || || 2 || <<3 0 -7]] || Augmented || 1.549 || 128/125 || || 3 || <<12 -84 -161]] || Diminished || 1.826 || 648/625 || || 4 || <<2 -4 -11]] || Srutal || 2.121 || 2048/2025 || || 5 || <<1 -8 -15]] || Helmholtz || 3.103 || 32805/32768 || || 6 || <<4 4 -3]] || Atomic || 33.065 || |161 -84 -12> || =7-limit temperaments with badness below 0.06= Listed is the wedgie and the TE complexity for 18 temperaments with badness less than 0.06. || <span style="font-family: Arial,sans-serif; font-size: 10pt;">Rank</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">Wedgie</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">Name</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">Complexity</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">Commas</span> || || <span style="font-family: Arial,sans-serif; font-size: 10pt;">1</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;"><<1 4 -2 4 -6 -16]]</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">Dominant</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">1.466</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">36/35 64/63</span> || || <span style="font-family: Arial,sans-serif; font-size: 10pt;">2</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;"><<4 4 4 -3 -5 -2]]</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">Diminished</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">1.494</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">36/35 50/49</span> || || <span style="font-family: Arial,sans-serif; font-size: 10pt;">3</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;"><<3 0 6 -7 1 14]]</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">August</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">1.655</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">36/35 128/125</span> || || <span style="font-family: Arial,sans-serif; font-size: 10pt;">4</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;"><<2 -4 -4 -11 -12 2]]</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">Pajara</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">1.953</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">50/49 64/63</span> || || <span style="font-family: Arial,sans-serif; font-size: 10pt;">5</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;"><<1 4 10 4 13 12]]</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">Meantone</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">2.204</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">81/80 126/125</span> || || <span style="font-family: Arial,sans-serif; font-size: 10pt;">6</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;"><<2 8 8 8 7 -4]]</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">Injera</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">2.205</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">50/49 81/80</span> || || <span style="font-family: Arial,sans-serif; font-size: 10pt;">7</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;"><<3 0 -6 -7 -18 -14]]</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">Augene</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">2.336</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">64/63 126/125</span> || || <span style="font-family: Arial,sans-serif; font-size: 10pt;">8</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;"><<5 8 2 1 -11 -18]]</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">Ripple</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">2.454</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">36/35 2560/2401</span> || || <span style="font-family: Arial,sans-serif; font-size: 10pt;">9</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;"><<1 -8 -2 -15 -6 18]]</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">Schism</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">2.544</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">64/63 360/343</span> || || <span style="font-family: Arial,sans-serif; font-size: 10pt;">10</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;"><<6 0 0 -14 -17 0]]</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">Hexe</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">2.689</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">50/49 128/125</span> || || <span style="font-family: Arial,sans-serif; font-size: 10pt;">11</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;"><<0 0 12 0 19 28]]</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">Catler</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">3.026</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">81/80 128/125</span> || || <span style="font-family: Arial,sans-serif; font-size: 10pt;">12</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;"><<3 -12 -30 -26 -56 -36]]</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">Misty</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">3.656</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">3136/3125 5120/5103</span> || || <span style="font-family: Arial,sans-serif; font-size: 10pt;">13</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;"><<1 -8 -14 -15 -25 -10]]</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">Garibaldi</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">3.823</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">225/224 3125/3087</span> || || <span style="font-family: Arial,sans-serif; font-size: 10pt;">14</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;"><<2 -4 -16 -11 -31 -26]]</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">Diaschismic</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">4.290</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">126/125 2048/2025</span> || || <span style="font-family: Arial,sans-serif; font-size: 10pt;">15</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;"><<0 12 24 19 38 22]]</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">Compton/Waage</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">5.927</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">225/224 250047/250000</span> || || <span style="font-family: Arial,sans-serif; font-size: 10pt;">16</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;"><<4 -8 -20 -22 -43 -24]]</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">Bidia</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">5.940</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">2048/2025 3136/3125</span> || || <span style="font-family: Arial,sans-serif; font-size: 10pt;">17</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;"><<2 -16 -40 -30 -69 -48]]</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">Bischismic</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">10.110</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">3136/3125 32805/32768</span> || || <span style="font-family: Arial,sans-serif; font-size: 10pt;">18</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;"><<3 -24 -54 -45 -94 -58]]</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">Term</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">13.877</span> || <span style="font-family: Arial,sans-serif; font-size: 10pt;">32805/32768 250047/250000</span> || =11-limit temperaments with badness below 0.05= Listed is the wedgie and the TE complexity for 40 temperaments with badness less than 0.05.
Original HTML content:
<html><head><title>List of 12et rank two temperaments by complexity</title></head><body>Below are listed rank-two temperaments supported by the <a class="wiki_link" href="/12edo">12edo</a> patent val, below the indicated cutoff in TE badness.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="x5-limit temperaments with badness below 0.1"></a><!-- ws:end:WikiTextHeadingRule:0 -->5-limit temperaments with badness below 0.1</h1>
Listed is the wedgie and the TE complexity for six temperaments with badness less than 0.1.<br />
<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 4 4]]<br />
</td>
<td>Meantone<br />
</td>
<td>1.523<br />
</td>
<td>81/80<br />
</td>
</tr>
<tr>
<td>2<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>3<br />
</td>
<td><<12 -84 -161]]<br />
</td>
<td>Diminished<br />
</td>
<td>1.826<br />
</td>
<td>648/625<br />
</td>
</tr>
<tr>
<td>4<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>5<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>6<br />
</td>
<td><<4 4 -3]]<br />
</td>
<td>Atomic<br />
</td>
<td>33.065<br />
</td>
<td>|161 -84 -12><br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="x7-limit temperaments with badness below 0.06"></a><!-- ws:end:WikiTextHeadingRule:2 -->7-limit temperaments with badness below 0.06</h1>
Listed is the wedgie and the TE complexity for 18 temperaments with badness less than 0.06.<br />
<table class="wiki_table">
<tr>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">Rank</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">Wedgie</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">Name</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">Complexity</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">Commas</span><br />
</td>
</tr>
<tr>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">1</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;"><<1 4 -2 4 -6 -16]]</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">Dominant</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">1.466</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">36/35 64/63</span><br />
</td>
</tr>
<tr>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">2</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;"><<4 4 4 -3 -5 -2]]</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">Diminished</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">1.494</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">36/35 50/49</span><br />
</td>
</tr>
<tr>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">3</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;"><<3 0 6 -7 1 14]]</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">August</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">1.655</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">36/35 128/125</span><br />
</td>
</tr>
<tr>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">4</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;"><<2 -4 -4 -11 -12 2]]</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">Pajara</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">1.953</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">50/49 64/63</span><br />
</td>
</tr>
<tr>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">5</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;"><<1 4 10 4 13 12]]</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">Meantone</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">2.204</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">81/80 126/125</span><br />
</td>
</tr>
<tr>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">6</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;"><<2 8 8 8 7 -4]]</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">Injera</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">2.205</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">50/49 81/80</span><br />
</td>
</tr>
<tr>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">7</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;"><<3 0 -6 -7 -18 -14]]</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">Augene</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">2.336</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">64/63 126/125</span><br />
</td>
</tr>
<tr>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">8</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;"><<5 8 2 1 -11 -18]]</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">Ripple</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">2.454</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">36/35 2560/2401</span><br />
</td>
</tr>
<tr>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">9</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;"><<1 -8 -2 -15 -6 18]]</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">Schism</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">2.544</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">64/63 360/343</span><br />
</td>
</tr>
<tr>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">10</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;"><<6 0 0 -14 -17 0]]</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">Hexe</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">2.689</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">50/49 128/125</span><br />
</td>
</tr>
<tr>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">11</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;"><<0 0 12 0 19 28]]</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">Catler</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">3.026</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">81/80 128/125</span><br />
</td>
</tr>
<tr>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">12</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;"><<3 -12 -30 -26 -56 -36]]</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">Misty</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">3.656</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">3136/3125 5120/5103</span><br />
</td>
</tr>
<tr>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">13</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;"><<1 -8 -14 -15 -25 -10]]</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">Garibaldi</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">3.823</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">225/224 3125/3087</span><br />
</td>
</tr>
<tr>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">14</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;"><<2 -4 -16 -11 -31 -26]]</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">Diaschismic</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">4.290</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">126/125 2048/2025</span><br />
</td>
</tr>
<tr>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">15</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;"><<0 12 24 19 38 22]]</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">Compton/Waage</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">5.927</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">225/224 250047/250000</span><br />
</td>
</tr>
<tr>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">16</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;"><<4 -8 -20 -22 -43 -24]]</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">Bidia</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">5.940</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">2048/2025 3136/3125</span><br />
</td>
</tr>
<tr>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">17</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;"><<2 -16 -40 -30 -69 -48]]</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">Bischismic</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">10.110</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">3136/3125 32805/32768</span><br />
</td>
</tr>
<tr>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">18</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;"><<3 -24 -54 -45 -94 -58]]</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">Term</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">13.877</span><br />
</td>
<td><span style="font-family: Arial,sans-serif; font-size: 10pt;">32805/32768 250047/250000</span><br />
</td>
</tr>
</table>
<!-- ws:start:WikiTextHeadingRule:4:<h1> --><h1 id="toc2"><a name="x11-limit temperaments with badness below 0.05"></a><!-- ws:end:WikiTextHeadingRule:4 -->11-limit temperaments with badness below 0.05</h1>
Listed is the wedgie and the TE complexity for 40 temperaments with badness less than 0.05.</body></html>