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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Technical data page}} |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | The '''horwell family''' of rank-3 temperaments tempers out the [[horwell comma]], 65625/65536 = {{monzo| -16 1 5 1 }}. |
| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-01-01 14:47:09 UTC</tt>.<br>
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| : The original revision id was <tt>190425752</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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| <h4>Original Wikitext content:</h4>
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| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">The horwell family of rank three temperaments tempers out the horwell comma, 65625/65536.
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| Comma: 65625/65536
| | == Horwell == |
| | [[Subgroup]]: 2.3.5.7 |
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| 7-limit minimax
| | [[Comma list]]: 65625/65536 |
| [|1 0 0 0>, |16/7 6/7 -5/7 -1/7>, | |
| |16/7 -1/7 2/7 -1/7>, |16/7 -1/7 -5/7 6/7>]
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| Eigenmonzos: 2, 7/6, 6/5
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| 9-limit minimax
| | {{Mapping|legend=1| 1 0 0 16 | 0 1 0 -1 | 0 0 1 -5 }} |
| [|1 0 0 0>, |16/13 12/13 -5/13 -1/13>,
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| |32/13 -2/13 3/13 -2/13>, |32/13 -2/13 -10/13 11/13>] | |
| Eigenmonzos: 2, 9/7, 7/5
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| Lattice basis: 5/4 length=0.6213 16/15 length=1.3863
| | : mapping generators: ~2, ~3, ~5 |
| Angle(5/4, 16/15) = 64.6379
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| Map to lattice: [<0 -1 1 -4|, <0 -1 0 -1|]
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| Map: [<1 0 0 16|, <0 1 0 -1|, <0 0 1 -5|]
| | [[Mapping to lattice]]: [{{val| 0 -1 1 -4 }}, {{val| 0 -1 0 -1 }}] |
| Generators: 2, 3, 5
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| Edos: 9, 22, 25, 28, 31, 34, 40, 53, 56, 65, 75, 84, 87, 118, 140, 171, 824, 995
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| ==Horwellic== | | Lattice basis: |
| Commas: 3025/3024, 65625/65536
| | : 5/4 length = 0.6213, 16/15 length = 1.3863 |
| | : Angle (5/4, 16/15) = 64.6379 |
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| Map: [<1 0 0 16 10|, <0 1 0 -1 1|, <0 0 2 -10 -7|]
| | [[Minimax tuning]]: |
| EDOs: 31, 87, 118, 193, 224, 311, 342</pre></div>
| | * [[7-odd-limit]] |
| <h4>Original HTML content:</h4>
| | : {{monzo list| 1 0 0 0 | 16/7 6/7 -5/7 -1/7 | 16/7 -1/7 2/7 -1/7 | 16/7 -1/7 -5/7 6/7 }} |
| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Horwell family</title></head><body>The horwell family of rank three temperaments tempers out the horwell comma, 65625/65536.<br />
| | : [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5/3.7/3 |
| <br />
| | * [[9-odd-limit]] |
| Comma: 65625/65536<br />
| | : {{monzo list| 1 0 0 0 | 16/13 12/13 -5/13 -1/13 | 32/13 -2/13 3/13 -2/13 | 32/13 -2/13 -10/13 11/13 }} |
| <br />
| | : [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/5.9/7 |
| 7-limit minimax<br />
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| [|1 0 0 0&gt;, |16/7 6/7 -5/7 -1/7&gt;, <br />
| | {{Optimal ET sequence|legend=1| 22, 31, 53, 84, 87, 118, 140, 171, 1592c, 1763c, 1934c, 2074c, 2105c, 2245cd, 2416cd, 2587cd, 2758cd, 2929cd, 3100cd, 3271ccd, 3442ccd, 3613ccd, 5034bcccdd, 5205bcccdd }} |
| |16/7 -1/7 2/7 -1/7&gt;, |16/7 -1/7 -5/7 6/7&gt;]<br /> | | |
| Eigenmonzos: 2, 7/6, 6/5<br />
| | [[Badness]]: 0.173 × 10<sup>-3</sup> |
| <br />
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| 9-limit minimax<br /> | | [[Projection pair]]: 7 65536/9375 |
| [|1 0 0 0&gt;, |16/13 12/13 -5/13 -1/13&gt;, <br />
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| |32/13 -2/13 3/13 -2/13&gt;, |32/13 -2/13 -10/13 11/13&gt;]<br /> | | == Zelda == |
| Eigenmonzos: 2, 9/7, 7/5<br />
| | [[Subgroup]]: 2.3.5.7.11 |
| <br />
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| Lattice basis: 5/4 length=0.6213 16/15 length=1.3863<br />
| | [[Comma list]]: 385/384, 3388/3375 |
| Angle(5/4, 16/15) = 64.6379<br />
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| Map to lattice: [&lt;0 -1 1 -4|, &lt;0 -1 0 -1|]<br />
| | {{Mapping|legend=1| 1 0 0 16 -9 | 0 1 0 -1 2 | 0 0 1 -5 4 }} |
| <br />
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| Map: [&lt;1 0 0 16|, &lt;0 1 0 -1|, &lt;0 0 1 -5|]<br />
| | {{Optimal ET sequence|legend=1| 22, 31, 53, 84, 87, 118, 258e, 376de, 547de }} |
| Generators: 2, 3, 5<br />
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| Edos: 9, 22, 25, 28, 31, 34, 40, 53, 56, 65, 75, 84, 87, 118, 140, 171, 824, 995<br />
| | [[Badness]]: 0.642 × 10<sup>-3</sup> |
| <br />
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| <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Horwellic"></a><!-- ws:end:WikiTextHeadingRule:0 -->Horwellic</h2>
| | == Horwellic == |
| Commas: 3025/3024, 65625/65536<br />
| | [[Subgroup]]: 2.3.5.7.11 |
| <br />
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| Map: [&lt;1 0 0 16 10|, &lt;0 1 0 -1 1|, &lt;0 0 2 -10 -7|]<br />
| | [[Comma list]]: 3025/3024, 65625/65536 |
| EDOs: 31, 87, 118, 193, 224, 311, 342</body></html></pre></div>
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| | {{Mapping|legend=1| 1 0 0 16 10 | 0 1 0 -1 1 | 0 0 2 -10 -7 }} |
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| | {{Optimal ET sequence|legend=1| 31, 75e, 87, 118, 193, 224, 311, 342, 1592c, 1934ce, 2276cde, 2587cde, 2929cde, 3271ccde, 3613ccde, 5205bcccddee }} |
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| | [[Badness]]: 0.505 × 10<sup>-3</sup> |
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| | [[Category:Temperament families]] |
| | [[Category:Pages with mostly numerical content]] |
| | [[Category:Horwell family| ]] <!-- main article --> |
| | [[Category:Horwell| ]] <!-- key article --> |
| | [[Category:Rank 3]] |