Octagar family: Difference between revisions

Revision as of 13:18, 22 August 2011

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This revision was by author genewardsmith and made on 2011-08-22 13:18:34 UTC.

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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]]: [[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

[[Projection pair]]s: 5 3969/800 7 27783/4000 to 2.3.7/5

===[[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
Associated linear temperament: [[Tetracot family|octacot]]
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

Projection pairs: 5 242/49 7 21296/3087 11 234256/21609 to 2.3.11/7

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:&lt;h3&gt; --><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&gt;, |5/6 1/3 1/2 -1/3&gt;, <br />
|0 0 1 0&gt;, |5/6 -2/3 1/2 2/3&gt;]<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&gt;, |5/8 1/2 3/8 -1/4&gt;, <br />
|0 0 1 0&gt;, |5/4 -1 3/4 1/2&gt;]<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: [&lt;0 -1 -2 -1|, &lt;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 />
<a class="wiki_link" href="/Projection%20pair">Projection pair</a>s: 5 3969/800 7 27783/4000 to 2.3.7/5<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><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:&lt;h2&gt; --><h2 id="toc2"><a name="x-Nakika"></a><!-- ws:end:WikiTextHeadingRule:4 -->Nakika</h2>
Commas: 100/99, 245/242<br />
Associated linear temperament: <a class="wiki_link" href="/Tetracot%20family">octacot</a><br />
Lattice basis: 11/7 0.798 22/21 0.906<br />
Angle(11/7, 22/21) = 97.747 degrees<br />
Map to lattice: [&lt;0 1 2 1 2|, &lt;0 -1 0 2 2|]<br />
<br />
Map: [&lt;1 0 1 4 4|, &lt;0 1 0 -2 -2|, &lt;0 0 2 3 4|]<br />
EDOs: 12, 15, 26, 29, 41<br />
Badness: 0.000539<br />
<br />
Projection pairs: 5 242/49 7 21296/3087 11 234256/21609 to 2.3.11/7<br />
<br />
Scales: <a class="wiki_link" href="/nakika12">nakika12</a></body></html>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-01-13 19:42:42 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-08-22 13:18:34 UTC</tt>.<br>
-: The original revision id was <tt>193167794</tt>.<br>
+: The original revision id was <tt>247708793</tt>.<br>
 : The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
@@ Line 26: / Line 26: @@
 [[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
+[[Projection pair]]s: 5 3969/800 7 27783/4000 to 2.3.7/5
 ===[[Hobbits|Hobbit bases]]===
@@ Line 44: / Line 46: @@
 EDOs: 12, 15, 26, 29, 41
 Badness: 0.000539
+Projection pairs: 5 242/49 7 21296/3087 11 234256/21609 to 2.3.11/7
 Scales: [[nakika12]]</pre></div>
@@ Line 67: / Line 71: @@
 &lt;a class="wiki_link" href="/edo"&gt;EDOs&lt;/a&gt;: &lt;a class="wiki_link" href="/12edo"&gt;12&lt;/a&gt;, &lt;a class="wiki_link" href="/26edo"&gt;26&lt;/a&gt;, &lt;a class="wiki_link" href="/27edo"&gt;27&lt;/a&gt;, &lt;a class="wiki_link" href="/41edo"&gt;41&lt;/a&gt;, &lt;a class="wiki_link" href="/53edo"&gt;53&lt;/a&gt;, &lt;a class="wiki_link" href="/94edo"&gt;94&lt;/a&gt;, &lt;a class="wiki_link" href="/121edo"&gt;121&lt;/a&gt;, &lt;a class="wiki_link" href="/162edo"&gt;162&lt;/a&gt;, &lt;a class="wiki_link" href="/189edo"&gt;189&lt;/a&gt;, &lt;a class="wiki_link" href="/215edo"&gt;215&lt;/a&gt;, &lt;a class="wiki_link" href="/230edo"&gt;230&lt;/a&gt;&lt;br /&gt;
 Badness: 0.000216&lt;br /&gt;
+&lt;br /&gt;
+&lt;a class="wiki_link" href="/Projection%20pair"&gt;Projection pair&lt;/a&gt;s: 5 3969/800 7 27783/4000 to 2.3.7/5&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x--Hobbit bases"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;&lt;a class="wiki_link" href="/Hobbits"&gt;Hobbit bases&lt;/a&gt;&lt;/h3&gt;
@@ Line 85: / Line 91: @@
 EDOs: 12, 15, 26, 29, 41&lt;br /&gt;
 Badness: 0.000539&lt;br /&gt;
+&lt;br /&gt;
+Projection pairs: 5 242/49 7 21296/3087 11 234256/21609 to 2.3.11/7&lt;br /&gt;
 &lt;br /&gt;
 Scales: &lt;a class="wiki_link" href="/nakika12"&gt;nakika12&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>

Octagar family: Difference between revisions

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