Table of rank-3 temperament lattice bases
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Original Wikitext content:
Below are tabulated bases (temperamental Minkowski bases) of minimal temperamental complexity for the pitch classes of various regular temperaments. =Rank Three= ==Seven limit== || Comma || Name || Gen 1 || Length || Gen 2 || Length || Angle || || 686/675 || Keema || 15/14 || 0.6977 || 3/2 || 1.4208 || 103.732 || || 64/63 || Archytas || 3/2 || 1.0508 || 5/4 || 2.3219 || 90.000 || || 875/864 || Keema || 6/5 || 0.8879 || 3/2 || 1.3391 || 77.834 || || 81/80 || Didymus || 3/2 || 0.5451 || 8/7 || 2.8074 || 90.000 || || 3125/3087 || Gariboh || 25/21 || 0.5928 || 21/20 || 1.2018 || 80.810 || || 2430/2401 || Nuwell || 7/6 || 0.6247 || 9/7 || 1.1894 || 94.044 || || 50421/50000 || Trimyna || 7/5 || 0.3158 || 5/4 || 1.7938 || 94.101 || || 245/243 || Sensamagic || 3/2 || 0.9644 || 9/7 || 1.0807 || 96.914 || || 126/125 || Starling || 6/5 || 1.068 || 5/4 || 1.206 || 100.364 || || 4000/3969 || Octagar || 63/50 || 0.8966 || 21/20 || 1.0605 || 97.743 || || 1728/1715 || Orwellisma || 7/6 || 0.7526 || 3/2 || 1.3931 || 97.508 || || 1029/1024 || Gamelisma || 8/7 || 0.5192 || 5/4 || 2.3219 || 90.000 || || 225/224 || Marvel || 16/15 || 1.256 || 3/2 || 1.369 || 106.958 || || 3136/3125 || Hemimean || 28/25 || 0.5055 || 3/2 || 1.5849 || 90.000 || || 5120/5103 || Hemifamity || 3/2 || 0.5670 || 10/9 || 1.8063 || 82.112 || || 6144/6125 || Porwell || 35/32 || 0.9584 || 35/24 || 1.1877 || 92.681 || || 65625/65536 || Horwell || 5/4 || 0.6213 || 16/15 || 1.3863 || 64.638 || || 703125/702464 || Meter || 75/56 || 0.7305 || 375/224 || 0.7675 || 97.289 || || 420175 / 419904 || Wizma || 245/216 || 0.5541 || 324/245 || 0.9731 || 79.663 || || 2401/2400 || Breedsma || 49/40 || 0.7858 || 8/7 || 1.1241 || 107.367 || || 4375/4374 || Ragisma || 10/9 || 0.7890 || 6/5 || 0.9208 || 105.299 || ==Eleven limit== || Commas || Name || Gen 1 || Length || Gen 2 || Length || Angle || || 225/224&385/384 || Marvel || 16/15 || 1.0364 || 5/4 || 1.0759 || 104.028 || || 225/224&441/400 || Prodigy || 16/15 || 0.9111 || 3/2 || 0.9477 || 65.933 || || 99/98&176/175 || Minerva || 16/15 || 0.8997 || 5/4 || 1.0457 || 98.604 ||
Original HTML content:
<html><head><title>Temperament lattice bases</title></head><body>Below are tabulated bases (temperamental Minkowski bases) of minimal temperamental complexity for the pitch classes of various regular temperaments.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Rank Three"></a><!-- ws:end:WikiTextHeadingRule:0 -->Rank Three</h1>
<br />
<!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="Rank Three-Seven limit"></a><!-- ws:end:WikiTextHeadingRule:2 -->Seven limit</h2>
<table class="wiki_table">
<tr>
<td>Comma<br />
</td>
<td>Name<br />
</td>
<td>Gen 1<br />
</td>
<td>Length<br />
</td>
<td>Gen 2<br />
</td>
<td>Length<br />
</td>
<td>Angle<br />
</td>
</tr>
<tr>
<td>686/675<br />
</td>
<td>Keema<br />
</td>
<td>15/14<br />
</td>
<td>0.6977<br />
</td>
<td>3/2<br />
</td>
<td>1.4208<br />
</td>
<td>103.732<br />
</td>
</tr>
<tr>
<td>64/63<br />
</td>
<td>Archytas<br />
</td>
<td>3/2<br />
</td>
<td>1.0508<br />
</td>
<td>5/4<br />
</td>
<td>2.3219<br />
</td>
<td>90.000<br />
</td>
</tr>
<tr>
<td>875/864<br />
</td>
<td>Keema<br />
</td>
<td>6/5<br />
</td>
<td>0.8879<br />
</td>
<td>3/2<br />
</td>
<td>1.3391<br />
</td>
<td>77.834<br />
</td>
</tr>
<tr>
<td>81/80<br />
</td>
<td>Didymus<br />
</td>
<td>3/2<br />
</td>
<td>0.5451<br />
</td>
<td>8/7<br />
</td>
<td>2.8074<br />
</td>
<td>90.000<br />
</td>
</tr>
<tr>
<td>3125/3087<br />
</td>
<td>Gariboh<br />
</td>
<td>25/21<br />
</td>
<td>0.5928<br />
</td>
<td>21/20<br />
</td>
<td>1.2018<br />
</td>
<td>80.810<br />
</td>
</tr>
<tr>
<td>2430/2401<br />
</td>
<td>Nuwell<br />
</td>
<td>7/6<br />
</td>
<td>0.6247<br />
</td>
<td>9/7<br />
</td>
<td>1.1894<br />
</td>
<td>94.044<br />
</td>
</tr>
<tr>
<td>50421/50000<br />
</td>
<td>Trimyna<br />
</td>
<td>7/5<br />
</td>
<td>0.3158<br />
</td>
<td>5/4<br />
</td>
<td>1.7938<br />
</td>
<td>94.101<br />
</td>
</tr>
<tr>
<td>245/243<br />
</td>
<td>Sensamagic<br />
</td>
<td>3/2<br />
</td>
<td>0.9644<br />
</td>
<td>9/7<br />
</td>
<td>1.0807<br />
</td>
<td>96.914<br />
</td>
</tr>
<tr>
<td>126/125<br />
</td>
<td>Starling<br />
</td>
<td>6/5<br />
</td>
<td>1.068<br />
</td>
<td>5/4<br />
</td>
<td>1.206<br />
</td>
<td>100.364<br />
</td>
</tr>
<tr>
<td>4000/3969<br />
</td>
<td>Octagar<br />
</td>
<td>63/50<br />
</td>
<td>0.8966<br />
</td>
<td>21/20<br />
</td>
<td>1.0605<br />
</td>
<td>97.743<br />
</td>
</tr>
<tr>
<td>1728/1715<br />
</td>
<td>Orwellisma<br />
</td>
<td>7/6<br />
</td>
<td>0.7526<br />
</td>
<td>3/2<br />
</td>
<td>1.3931<br />
</td>
<td>97.508<br />
</td>
</tr>
<tr>
<td>1029/1024<br />
</td>
<td>Gamelisma<br />
</td>
<td>8/7<br />
</td>
<td>0.5192<br />
</td>
<td>5/4<br />
</td>
<td>2.3219<br />
</td>
<td>90.000<br />
</td>
</tr>
<tr>
<td>225/224<br />
</td>
<td>Marvel<br />
</td>
<td>16/15<br />
</td>
<td>1.256<br />
</td>
<td>3/2<br />
</td>
<td>1.369<br />
</td>
<td>106.958<br />
</td>
</tr>
<tr>
<td>3136/3125<br />
</td>
<td>Hemimean<br />
</td>
<td>28/25<br />
</td>
<td>0.5055<br />
</td>
<td>3/2<br />
</td>
<td>1.5849<br />
</td>
<td>90.000<br />
</td>
</tr>
<tr>
<td>5120/5103<br />
</td>
<td>Hemifamity<br />
</td>
<td>3/2<br />
</td>
<td>0.5670<br />
</td>
<td>10/9<br />
</td>
<td>1.8063<br />
</td>
<td>82.112<br />
</td>
</tr>
<tr>
<td>6144/6125<br />
</td>
<td>Porwell<br />
</td>
<td>35/32<br />
</td>
<td>0.9584<br />
</td>
<td>35/24<br />
</td>
<td>1.1877<br />
</td>
<td>92.681<br />
</td>
</tr>
<tr>
<td>65625/65536<br />
</td>
<td>Horwell<br />
</td>
<td>5/4<br />
</td>
<td>0.6213<br />
</td>
<td>16/15<br />
</td>
<td>1.3863<br />
</td>
<td>64.638<br />
</td>
</tr>
<tr>
<td>703125/702464<br />
</td>
<td>Meter<br />
</td>
<td>75/56<br />
</td>
<td>0.7305<br />
</td>
<td>375/224<br />
</td>
<td>0.7675<br />
</td>
<td>97.289<br />
</td>
</tr>
<tr>
<td>420175 / 419904<br />
</td>
<td>Wizma<br />
</td>
<td>245/216<br />
</td>
<td>0.5541<br />
</td>
<td>324/245<br />
</td>
<td>0.9731<br />
</td>
<td>79.663<br />
</td>
</tr>
<tr>
<td>2401/2400<br />
</td>
<td>Breedsma<br />
</td>
<td>49/40<br />
</td>
<td>0.7858<br />
</td>
<td>8/7<br />
</td>
<td>1.1241<br />
</td>
<td>107.367<br />
</td>
</tr>
<tr>
<td>4375/4374<br />
</td>
<td>Ragisma<br />
</td>
<td>10/9<br />
</td>
<td>0.7890<br />
</td>
<td>6/5<br />
</td>
<td>0.9208<br />
</td>
<td>105.299<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="Rank Three-Eleven limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->Eleven limit</h2>
<table class="wiki_table">
<tr>
<td>Commas<br />
</td>
<td>Name<br />
</td>
<td>Gen 1<br />
</td>
<td>Length<br />
</td>
<td>Gen 2<br />
</td>
<td>Length<br />
</td>
<td>Angle<br />
</td>
</tr>
<tr>
<td>225/224&385/384<br />
</td>
<td>Marvel<br />
</td>
<td>16/15<br />
</td>
<td>1.0364<br />
</td>
<td>5/4<br />
</td>
<td>1.0759<br />
</td>
<td>104.028<br />
</td>
</tr>
<tr>
<td>225/224&441/400<br />
</td>
<td>Prodigy<br />
</td>
<td>16/15<br />
</td>
<td>0.9111<br />
</td>
<td>3/2<br />
</td>
<td>0.9477<br />
</td>
<td>65.933<br />
</td>
</tr>
</table>
|| 99/98&176/175 || Minerva || 16/15 || 0.8997 || 5/4 || 1.0457 || 98.604 ||</body></html>