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List of edo-distinct 12f rank two temperaments

Revision as of 17:18, 17 May 2012 by Wikispaces>genewardsmith (**Imported revision 336799410 - Original comment: **)
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The original revision id was 336799410.
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Original Wikitext content:

The temperaments listed are 12edo-distinct, meaning that they are all different even if tuned in 12edo. The ordering is by increasing complexity of 3. The temperament of lowest TE complexity supported by the 12f val (<12 19 28 34 42 45|) was chosen as the representative for each class of edo-distinctness.

=5-limit temperaments= 
|| Number || Wedgie || Name || Complexity || Commas ||
|| 1 || <<1 4 4]] || Meantone || 1.231 || 81/80 ||
|| 2 || <<2 -4 -11]] || Srutal || 2.121 || 2048/2025 ||
|| 3 || <<3 0 -7]] || Augmented || 1.549 || 128/125 ||
|| 4 || <<4 4 -3]] || Diminished || 1.826 || 648/625 ||
|| 5 || <<5 8 1]] || Ripple || 2.702 || 6561/6250 ||
|| 6 || <<6 12 5]] || Wronecki || 3.781 || 531441/500000 ||

=7-limit temperaments= 
|| Number || Wedgie || Name || Complexity || Commas ||
|| 1 || <<1 4 -2 4 -6 -16]] || Dominant || 1.466 || 36/35 64/63 ||
|| 2 || <<2 -4 -4 -11 -12 2]] || Pajara || 1.953 || 50/49 64/63 ||
|| 3 || <<3 0 6 -7 1 14]] || August || 1.655 || 36/35 128/125 ||
|| 4 || <<4 4 4 -3 -5 -2]] || Diminished || 1.494 || 36/35 50/49 ||
|| 5 || <<5 8 2 1 -11 -18]] || Ripple || 2.454 || 36/35 2560/2401 ||
|| 6 || <<6 0 0 -14 -17 0]] || Hexe || 2.689 || 50/49 128/125 ||

=11-limit temperaments= 
|| Number || Wedgie || Name || Complexity || Commas ||
|| 1 || <<1 4 -2 6 4 -6 6 -16 0 24]] || Domineering || 1.523 || 36/35 45/44 64/63 ||
|| 2 || <<2 -4 -4 0 -11 -12 -7 2 14 14]] || Pajaric || 1.722 || 45/44 50/49 56/55 ||
|| 3 || <<3 0 6 6 -7 1 -1 14 14 -4]] || August || 1.506 || 36/35 45/44 56/55 ||
|| 4 || <<4 4 4 0 -3 -5 -14 -2 -14 -14]] || Diminished || 1.582 || 36/35 50/49 56/55 ||
|| 5 || <<5 8 2 6 1 -11 -8 -18 -14 10]] || Ripple || 2.130 || 36/35 80/77 126/121 ||
|| 6 || <<6 0 0 0 -14 -17 -21 0 0 0]] || Hexe || 2.410 || 50/49 56/55 125/121 ||

=13-limit temperaments= 
|| Number || Wedgie || Name || Complexity || Commas ||
|| 1 || <<1 4 -2 6 3 4 -6 6 1 -16 0 -8 24 16 -12]] || Dominatrix || 1.367 || 27/26 36/35 45/44 64/63 ||
|| 2 || <<2 -4 -4 0 -6 -11 -12 -7 -17 2 14 1 14 -2 -21]] || Pajaric || 1.701 || 40/39 45/44 50/49 56/55 ||
|| 3 || <<3 0 6 6 9 -7 1 -1 3 14 14 21 -4 3 9]] || August || 1.536 || 27/26 36/35 45/44 56/55 ||
|| 4 || <<4 4 4 0 0 -3 -5 -14 -15 -2 -14 -15 -14 -15 0]] || Diminished || 1.564 || 36/35 40/39 50/49 66/65 ||
|| 5 || <<5 8 2 6 3 1 -11 -8 -14 -18 -14 -23 10 1 -12]] || Ripple || 1.996 || 36/35 40/39 66/65 147/143 ||
|| 6 || <<6 0 0 0 6 -14 -17 -21 -13 0 0 14 0 17 21]] || Hexe || 2.216 || 50/49 56/55 66/65 105/104 ||

Original HTML content:

<html><head><title>List of edo-distinct 12f rank two temperaments</title></head><body>The temperaments listed are 12edo-distinct, meaning that they are all different even if tuned in 12edo. The ordering is by increasing complexity of 3. The temperament of lowest TE complexity supported by the 12f val (&lt;12 19 28 34 42 45|) was chosen as the representative for each class of edo-distinctness.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x5-limit temperaments"></a><!-- ws:end:WikiTextHeadingRule:0 -->5-limit temperaments</h1>
 

<table class="wiki_table">
    <tr>
        <td>Number<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>&lt;&lt;1 4 4]]<br />
</td>
        <td>Meantone<br />
</td>
        <td>1.231<br />
</td>
        <td>81/80<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>&lt;&lt;2 -4 -11]]<br />
</td>
        <td>Srutal<br />
</td>
        <td>2.121<br />
</td>
        <td>2048/2025<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>&lt;&lt;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>&lt;&lt;4 4 -3]]<br />
</td>
        <td>Diminished<br />
</td>
        <td>1.826<br />
</td>
        <td>648/625<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>&lt;&lt;5 8 1]]<br />
</td>
        <td>Ripple<br />
</td>
        <td>2.702<br />
</td>
        <td>6561/6250<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>&lt;&lt;6 12 5]]<br />
</td>
        <td>Wronecki<br />
</td>
        <td>3.781<br />
</td>
        <td>531441/500000<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="x7-limit temperaments"></a><!-- ws:end:WikiTextHeadingRule:2 -->7-limit temperaments</h1>
 

<table class="wiki_table">
    <tr>
        <td>Number<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>&lt;&lt;1 4 -2 4 -6 -16]]<br />
</td>
        <td>Dominant<br />
</td>
        <td>1.466<br />
</td>
        <td>36/35 64/63<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>&lt;&lt;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>3<br />
</td>
        <td>&lt;&lt;3 0 6 -7 1 14]]<br />
</td>
        <td>August<br />
</td>
        <td>1.655<br />
</td>
        <td>36/35 128/125<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>&lt;&lt;4 4 4 -3 -5 -2]]<br />
</td>
        <td>Diminished<br />
</td>
        <td>1.494<br />
</td>
        <td>36/35 50/49<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>&lt;&lt;5 8 2 1 -11 -18]]<br />
</td>
        <td>Ripple<br />
</td>
        <td>2.454<br />
</td>
        <td>36/35 2560/2401<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>&lt;&lt;6 0 0 -14 -17 0]]<br />
</td>
        <td>Hexe<br />
</td>
        <td>2.689<br />
</td>
        <td>50/49 128/125<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="x11-limit temperaments"></a><!-- ws:end:WikiTextHeadingRule:4 -->11-limit temperaments</h1>
 

<table class="wiki_table">
    <tr>
        <td>Number<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>&lt;&lt;1 4 -2 6 4 -6 6 -16 0 24]]<br />
</td>
        <td>Domineering<br />
</td>
        <td>1.523<br />
</td>
        <td>36/35 45/44 64/63<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>&lt;&lt;2 -4 -4 0 -11 -12 -7 2 14 14]]<br />
</td>
        <td>Pajaric<br />
</td>
        <td>1.722<br />
</td>
        <td>45/44 50/49 56/55<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>&lt;&lt;3 0 6 6 -7 1 -1 14 14 -4]]<br />
</td>
        <td>August<br />
</td>
        <td>1.506<br />
</td>
        <td>36/35 45/44 56/55<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>&lt;&lt;4 4 4 0 -3 -5 -14 -2 -14 -14]]<br />
</td>
        <td>Diminished<br />
</td>
        <td>1.582<br />
</td>
        <td>36/35 50/49 56/55<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>&lt;&lt;5 8 2 6 1 -11 -8 -18 -14 10]]<br />
</td>
        <td>Ripple<br />
</td>
        <td>2.130<br />
</td>
        <td>36/35 80/77 126/121<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>&lt;&lt;6 0 0 0 -14 -17 -21 0 0 0]]<br />
</td>
        <td>Hexe<br />
</td>
        <td>2.410<br />
</td>
        <td>50/49 56/55 125/121<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="x13-limit temperaments"></a><!-- ws:end:WikiTextHeadingRule:6 -->13-limit temperaments</h1>
 

<table class="wiki_table">
    <tr>
        <td>Number<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>&lt;&lt;1 4 -2 6 3 4 -6 6 1 -16 0 -8 24 16 -12]]<br />
</td>
        <td>Dominatrix<br />
</td>
        <td>1.367<br />
</td>
        <td>27/26 36/35 45/44 64/63<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>&lt;&lt;2 -4 -4 0 -6 -11 -12 -7 -17 2 14 1 14 -2 -21]]<br />
</td>
        <td>Pajaric<br />
</td>
        <td>1.701<br />
</td>
        <td>40/39 45/44 50/49 56/55<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>&lt;&lt;3 0 6 6 9 -7 1 -1 3 14 14 21 -4 3 9]]<br />
</td>
        <td>August<br />
</td>
        <td>1.536<br />
</td>
        <td>27/26 36/35 45/44 56/55<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>&lt;&lt;4 4 4 0 0 -3 -5 -14 -15 -2 -14 -15 -14 -15 0]]<br />
</td>
        <td>Diminished<br />
</td>
        <td>1.564<br />
</td>
        <td>36/35 40/39 50/49 66/65<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>&lt;&lt;5 8 2 6 3 1 -11 -8 -14 -18 -14 -23 10 1 -12]]<br />
</td>
        <td>Ripple<br />
</td>
        <td>1.996<br />
</td>
        <td>36/35 40/39 66/65 147/143<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>&lt;&lt;6 0 0 0 6 -14 -17 -21 -13 0 0 14 0 17 21]]<br />
</td>
        <td>Hexe<br />
</td>
        <td>2.216<br />
</td>
        <td>50/49 56/55 66/65 105/104<br />
</td>
    </tr>
</table>

</body></html>
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