Mint temperaments

From Xenharmonic Wiki
Revision as of 14:36, 26 February 2011 by Wikispaces>genewardsmith (**Imported revision 205266502 - Original comment: **)
Jump to navigation Jump to search

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author genewardsmith and made on 2011-02-26 14:36:06 UTC.
The original revision id was 205266502.
The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

These are low complexity, high error temperaments tempering out the septimal quarter-tone, 36/35. 36 is both a square and a triangular number, and this helps make 36/35 a septimal interval of considerable significance. Temperaments tempering it out include beep, dicot, dominant, father, diminished, august, hystrix, penta, hexadecimal, ripple and gorgo.

==Progression==
Commas: 36/35, 392/375

[[POTE tuning|POTE generator]]: ~15/14 = 140.927

Map: [<1 1 2 2|, <0 5 3 7|]
EDOs: 8, 9, 17
Badness: 0.0484

===11-limit===
Commas: 36/35, 56/55, 77/75

[[POTE tuning|POTE generator]]: ~15/14 = 140.747

Map: [<1 1 2 2 3|, <0 5 3 7 4|]
EDOs: 8, 9, 17
Badness: 0.0261

===13-limit===
Commas: 26/25, 36/35, 56/55, 66/65

[[POTE tuning|POTE generator]]: ~15/14 = 140.751

Map: Map: [<1 1 2 2 3 3|, <0 5 3 7 4 6|]
EDOs: 8, 9, 17
Badness: 0.0182

===17-limit===
Commas: 26/25, 36/35, 51/50, 56/55, 66/65

[[POTE tuning|POTE generator]]: ~15/14 = 141.404

Map: [<1 1 2 2 3 3 4|, <0 5 3 7 4 6 1|]
EDOs: 8, 9, 17
Badness: 0.0167

===19-limit===
Commas: 26/25, 36/35, 51/50, 56/55, 57/55, 66/65

[[POTE tuning|POTE generator]]: ~15/14 = 140.479

Map: [<1 1 2 2 3 3 4 4|, <0 5 3 7 4 6 1 2|]
EDOs: 8, 9, 17, 94
Badness: 0.0168

==Ripple==
Commas: 36/35, 2560/2401

[[POTE tuning|POTE generator]]:

Map: [<1 2 3 3|, <0 -5 -8 -2|]
Wedgie: <<5 8 2 1 -11 -18||
EDOs: 12
Badness: 0.0597

Original HTML content:

<html><head><title>Mint temperaments</title></head><body>These are low complexity, high error temperaments tempering out the septimal quarter-tone, 36/35. 36 is both a square and a triangular number, and this helps make 36/35 a septimal interval of considerable significance. Temperaments tempering it out include beep, dicot, dominant, father, diminished, august, hystrix, penta, hexadecimal, ripple and gorgo.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Progression"></a><!-- ws:end:WikiTextHeadingRule:0 -->Progression</h2>
Commas: 36/35, 392/375<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~15/14 = 140.927<br />
<br />
Map: [&lt;1 1 2 2|, &lt;0 5 3 7|]<br />
EDOs: 8, 9, 17<br />
Badness: 0.0484<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x-Progression-11-limit"></a><!-- ws:end:WikiTextHeadingRule:2 -->11-limit</h3>
Commas: 36/35, 56/55, 77/75<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~15/14 = 140.747<br />
<br />
Map: [&lt;1 1 2 2 3|, &lt;0 5 3 7 4|]<br />
EDOs: 8, 9, 17<br />
Badness: 0.0261<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x-Progression-13-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->13-limit</h3>
Commas: 26/25, 36/35, 56/55, 66/65<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~15/14 = 140.751<br />
<br />
Map: Map: [&lt;1 1 2 2 3 3|, &lt;0 5 3 7 4 6|]<br />
EDOs: 8, 9, 17<br />
Badness: 0.0182<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc3"><a name="x-Progression-17-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->17-limit</h3>
Commas: 26/25, 36/35, 51/50, 56/55, 66/65<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~15/14 = 141.404<br />
<br />
Map: [&lt;1 1 2 2 3 3 4|, &lt;0 5 3 7 4 6 1|]<br />
EDOs: 8, 9, 17<br />
Badness: 0.0167<br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><a name="x-Progression-19-limit"></a><!-- ws:end:WikiTextHeadingRule:8 -->19-limit</h3>
Commas: 26/25, 36/35, 51/50, 56/55, 57/55, 66/65<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~15/14 = 140.479<br />
<br />
Map: [&lt;1 1 2 2 3 3 4 4|, &lt;0 5 3 7 4 6 1 2|]<br />
EDOs: 8, 9, 17, 94<br />
Badness: 0.0168<br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="x-Ripple"></a><!-- ws:end:WikiTextHeadingRule:10 -->Ripple</h2>
Commas: 36/35, 2560/2401<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>:<br />
<br />
Map: [&lt;1 2 3 3|, &lt;0 -5 -8 -2|]<br />
Wedgie: &lt;&lt;5 8 2 1 -11 -18||<br />
EDOs: 12<br />
Badness: 0.0597</body></html>