Octagar family
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- This revision was by author genewardsmith and made on 2010-10-25 00:16:23 UTC.
- The original revision id was 173261719.
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Original Wikitext content:
Octagar temperament is the 7-limit [[planar temperament]] tempering out 4000/3969. While most 7-limit planar temperaments exhibit a tendency towards tuning flat, many people seem to prefer a slight sharp tendency instead. Octagar provides this; for instance the 7 odd limit minimax tuning has fifths and 7s 2.245 cents sharp, with just major thirds.
===Vital statistics===
[[Comma]] c = 4000/3969
7-limit minimax: 3 and 7 1/6c sharp, 5 just
[|1 0 0 0>, |5/6 1/3 1/2 -1/3>,
|0 0 1 0>, |5/6 -2/3 1/2 2/3>]
[[Eigenmonzo|Eigenmonzos]]: 2, 7/6, 5/4
9-limit minimax: 3 1/8c sharp, 5 just, 7 1/4c sharp
[|1 0 0 0>, |5/8 1/2 3/8 -1/4>,
|0 0 1 0>, |5/4 -1 3/4 1/2>]
[[Eigenmonzo|Eigenmonzos]]: 2, 5/4, 9/7
Lattice basis: 63/50 length 0.8966, 21/20 length 1.0605
Angle(63/50, 21/20) = 97.743 cents
Map to lattice: [<0 -1 -2 -1|, <0 -1 0 2|]
[[edo|EDOs]]: [[162edo|162]], [[189edo|189]], [[215edo|215]], [[230edo|230]]
===[[Hobbit bases]]===
{2, 3, 7/5} subgroup
12: 50/49, 256000/250047
15: 256000/250047, 1029/1000
23: 12800000/12252303, 107163/102400Original HTML content:
<html><head><title>Octagar family</title></head><body>Octagar temperament is the 7-limit <a class="wiki_link" href="/planar%20temperament">planar temperament</a> tempering out 4000/3969. While most 7-limit planar temperaments exhibit a tendency towards tuning flat, many people seem to prefer a slight sharp tendency instead. Octagar provides this; for instance the 7 odd limit minimax tuning has fifths and 7s 2.245 cents sharp, with just major thirds.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:<h3> --><h3 id="toc0"><a name="x--Vital statistics"></a><!-- ws:end:WikiTextHeadingRule:0 -->Vital statistics</h3>
<a class="wiki_link" href="/Comma">Comma</a> c = 4000/3969<br />
<br />
7-limit minimax: 3 and 7 1/6c sharp, 5 just<br />
[|1 0 0 0>, |5/6 1/3 1/2 -1/3>, <br />
|0 0 1 0>, |5/6 -2/3 1/2 2/3>]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 7/6, 5/4<br />
<br />
9-limit minimax: 3 1/8c sharp, 5 just, 7 1/4c sharp<br />
[|1 0 0 0>, |5/8 1/2 3/8 -1/4>, <br />
|0 0 1 0>, |5/4 -1 3/4 1/2>]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 5/4, 9/7<br />
<br />
Lattice basis: 63/50 length 0.8966, 21/20 length 1.0605<br />
Angle(63/50, 21/20) = 97.743 cents<br />
Map to lattice: [<0 -1 -2 -1|, <0 -1 0 2|]<br />
<a class="wiki_link" href="/edo">EDOs</a>: <a class="wiki_link" href="/162edo">162</a>, <a class="wiki_link" href="/189edo">189</a>, <a class="wiki_link" href="/215edo">215</a>, <a class="wiki_link" href="/230edo">230</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:<h3> --><h3 id="toc1"><a name="x--Hobbit bases"></a><!-- ws:end:WikiTextHeadingRule:2 --><a class="wiki_link" href="/Hobbit%20bases">Hobbit bases</a></h3>
{2, 3, 7/5} subgroup<br />
<br />
12: 50/49, 256000/250047<br />
15: 256000/250047, 1029/1000<br />
23: 12800000/12252303, 107163/102400</body></html>