Octagar family
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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]]: [[12edo|12]], [[26edo|26]], [[27edo|27]], [[41edo|41]], [[53edo|53]], [[94edo|94]], [[121edo|121]], [[162edo|162]], [[189edo|189]], [[215edo|215]], [[230edo|230]]
Badness: 0.000216
===[[Hobbits|Hobbit bases]]===
{2, 3, 7/5} subgroup
12: 50/49, 256000/250047
15: 256000/250047, 1029/1000
23: 12800000/12252303, 107163/102400
==Nakika==
Commas: 100/99, 245/242
Lattice basis: 11/7 0.798 22/21 0.906
Angle(11/7, 22/21) = 97.747 degrees
Map to lattice: [<0 1 2 1 2|, <0 -1 0 2 2|]
Map: [<1 0 1 4 4|, <0 1 0 -2 -2|, <0 0 2 3 4|]
EDOs: 12, 15, 26, 29, 41
Badness: 0.000539
Scales: [[nakika12]]Original 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="/12edo">12</a>, <a class="wiki_link" href="/26edo">26</a>, <a class="wiki_link" href="/27edo">27</a>, <a class="wiki_link" href="/41edo">41</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/94edo">94</a>, <a class="wiki_link" href="/121edo">121</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 />
Badness: 0.000216<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="/Hobbits">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<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="x-Nakika"></a><!-- ws:end:WikiTextHeadingRule:4 -->Nakika</h2>
Commas: 100/99, 245/242<br />
<br />
Lattice basis: 11/7 0.798 22/21 0.906<br />
Angle(11/7, 22/21) = 97.747 degrees<br />
Map to lattice: [<0 1 2 1 2|, <0 -1 0 2 2|]<br />
<br />
Map: [<1 0 1 4 4|, <0 1 0 -2 -2|, <0 0 2 3 4|]<br />
EDOs: 12, 15, 26, 29, 41<br />
Badness: 0.000539<br />
<br />
Scales: <a class="wiki_link" href="/nakika12">nakika12</a></body></html>