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**Imported revision 395459664 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
__FORCETOC__
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>2013-01-02 17:46:48 UTC</tt>.<br>
: The original revision id was <tt>395459664</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>
<h4>Original Wikitext content:</h4>
<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">[[toc|flat]]
 
This tempers out 16/15, the just diatonic semitone. This equates 4/3 with 5/4, so these are "fourth-thirds", or father, temperaments.
This tempers out 16/15, the just diatonic semitone. This equates 4/3 with 5/4, so these are "fourth-thirds", or father, temperaments.


=Father=  
=Father=
Comma: 16/15
Comma: 16/15


Line 16: Line 8:


Map: [&lt;1 0 4|, &lt;0 1 -1|]
Map: [&lt;1 0 4|, &lt;0 1 -1|]
EDOs: 1, 2, 3, 5, 8, 10c, 11b, 13c, 21bc
EDOs: 1, 2, 3, 5, 8, 10c, 11b, 13c, 21bc
Badness: 0.0149
Badness: 0.0149


==7-limit==  
==7-limit==
Commas: 16/15, 28/27
Commas: 16/15, 28/27


7-limit minimax
7-limit minimax
[&lt;1 0 0 0|, &lt;3/2 0 -1/4 1/4|, &lt;5/2 0 1/4 -1/4|, &lt;5/2 0 -3/4 3/4|]
[&lt;1 0 0 0|, &lt;3/2 0 -1/4 1/4|, &lt;5/2 0 1/4 -1/4|, &lt;5/2 0 -3/4 3/4|]
[[Eigenmonzo subgroup]]: 2.7/5
 
[[Eigenmonzo_subgroup|Eigenmonzo subgroup]]: 2.7/5


9-limit eigenmonzo subgroup: 2.9/5
9-limit eigenmonzo subgroup: 2.9/5


[[POTE tuning|POTE generator]]: 742.002
[[POTE_tuning|POTE generator]]: 742.002


Map: [&lt;1 0 4 -2|, &lt;0 1 -1 3|]
Map: [&lt;1 0 4 -2|, &lt;0 1 -1 3|]
Wedgie: &lt;&lt;1 -1 3 -4 2 10||
Wedgie: &lt;&lt;1 -1 3 -4 2 10||
EDOs: 5, 8d, 13cd, 21bcd
EDOs: 5, 8d, 13cd, 21bcd
Badness: 0.0213
Badness: 0.0213


=Pater=  
=Pater=
Commas: 16/15, 126/125
Commas: 16/15, 126/125


Line 41: Line 40:


Map: [&lt;1 0 4 11|, &lt;0 1 -1 -5|]
Map: [&lt;1 0 4 11|, &lt;0 1 -1 -5|]
Wedgie: &lt;&lt;1 -1 -5 -4 -11 -9||
Wedgie: &lt;&lt;1 -1 -5 -4 -11 -9||
EDOs: 3, 11b, 16bcd, 27bcd
EDOs: 3, 11b, 16bcd, 27bcd
Badness: 0.0530
Badness: 0.0530


=Walid=  
=Walid=
Commas: 16/15, 50/49
Commas: 16/15, 50/49


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Map: [&lt;2 0 8 9|, &lt;0 1 -1 -1|]
Map: [&lt;2 0 8 9|, &lt;0 1 -1 -1|]
Wedgie: &lt;&lt;2 -2 -2 -8 -9 1||
Wedgie: &lt;&lt;2 -2 -2 -8 -9 1||
EDOs: 2, 6, 10cd, 14bd, 16bcd
EDOs: 2, 6, 10cd, 14bd, 16bcd
Badness: 0.0490
Badness: 0.0490


=Baba=  
=Baba=
Commas: 16/15, 49/45
Commas: 16/15, 49/45


Line 61: Line 66:


Map: [&lt;1 0 4 2|, &lt;0 2 -2 1|]
Map: [&lt;1 0 4 2|, &lt;0 2 -2 1|]
Wedgie: &lt;&lt;2 -2 1 -8 -4 8||
Wedgie: &lt;&lt;2 -2 1 -8 -4 8||
EDOs: 1, 5, 11b, 16bc
EDOs: 1, 5, 11b, 16bc
Badness: 0.0443
Badness: 0.0443


=Quint=  
=Quint=
Commas: 16/15, 27/25
Commas: 16/15, 27/25


Line 71: Line 79:


Map: [&lt;5 8 12 0|, &lt;0 0 0 -1|]
Map: [&lt;5 8 12 0|, &lt;0 0 0 -1|]
Wedgie: &lt;&lt;0 0 5 0 8 12||
Wedgie: &lt;&lt;0 0 5 0 8 12||
EDOs: 5, 15cd
EDOs: 5, 15cd
Badness: 0.0483</pre></div>
 
<h4>Original HTML content:</h4>
Badness: 0.0483
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Father family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:12:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:12 --&gt;&lt;!-- ws:start:WikiTextTocRule:13: --&gt;&lt;a href="#Father"&gt;Father&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:13 --&gt;&lt;!-- ws:start:WikiTextTocRule:14: --&gt;&lt;!-- ws:end:WikiTextTocRule:14 --&gt;&lt;!-- ws:start:WikiTextTocRule:15: --&gt; | &lt;a href="#Pater"&gt;Pater&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:15 --&gt;&lt;!-- ws:start:WikiTextTocRule:16: --&gt; | &lt;a href="#Walid"&gt;Walid&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:16 --&gt;&lt;!-- ws:start:WikiTextTocRule:17: --&gt; | &lt;a href="#Baba"&gt;Baba&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:17 --&gt;&lt;!-- ws:start:WikiTextTocRule:18: --&gt; | &lt;a href="#Quint"&gt;Quint&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt;
&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;br /&gt;
This tempers out 16/15, the just diatonic semitone. This equates 4/3 with 5/4, so these are &amp;quot;fourth-thirds&amp;quot;, or father, temperaments.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Father"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Father&lt;/h1&gt;
Comma: 16/15&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~3/2 = 743.986&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 4|, &amp;lt;0 1 -1|]&lt;br /&gt;
EDOs: 1, 2, 3, 5, 8, 10c, 11b, 13c, 21bc&lt;br /&gt;
Badness: 0.0149&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Father-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;7-limit&lt;/h2&gt;
Commas: 16/15, 28/27&lt;br /&gt;
&lt;br /&gt;
7-limit minimax&lt;br /&gt;
[&amp;lt;1 0 0 0|, &amp;lt;3/2 0 -1/4 1/4|, &amp;lt;5/2 0 1/4 -1/4|, &amp;lt;5/2 0 -3/4 3/4|]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo%20subgroup"&gt;Eigenmonzo subgroup&lt;/a&gt;: 2.7/5&lt;br /&gt;
&lt;br /&gt;
9-limit eigenmonzo subgroup: 2.9/5&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 742.002&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 4 -2|, &amp;lt;0 1 -1 3|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;1 -1 3 -4 2 10||&lt;br /&gt;
EDOs: 5, 8d, 13cd, 21bcd&lt;br /&gt;
Badness: 0.0213&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Pater"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Pater&lt;/h1&gt;
Commas: 16/15, 126/125&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~3/2 = 753.113&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 4 11|, &amp;lt;0 1 -1 -5|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;1 -1 -5 -4 -11 -9||&lt;br /&gt;
EDOs: 3, 11b, 16bcd, 27bcd&lt;br /&gt;
Badness: 0.0530&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Walid"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Walid&lt;/h1&gt;
Commas: 16/15, 50/49&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~3/2 = 749.415&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 0 8 9|, &amp;lt;0 1 -1 -1|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;2 -2 -2 -8 -9 1||&lt;br /&gt;
EDOs: 2, 6, 10cd, 14bd, 16bcd&lt;br /&gt;
Badness: 0.0490&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Baba"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Baba&lt;/h1&gt;
Commas: 16/15, 49/45&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~8/7 = 226.704&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 4 2|, &amp;lt;0 2 -2 1|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;2 -2 1 -8 -4 8||&lt;br /&gt;
EDOs: 1, 5, 11b, 16bc&lt;br /&gt;
Badness: 0.0443&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Quint"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Quint&lt;/h1&gt;
Commas: 16/15, 27/25&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~8/7 = 182.097&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;5 8 12 0|, &amp;lt;0 0 0 -1|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;0 0 5 0 8 12||&lt;br /&gt;
EDOs: 5, 15cd&lt;br /&gt;
Badness: 0.0483&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

This tempers out 16/15, the just diatonic semitone. This equates 4/3 with 5/4, so these are "fourth-thirds", or father, temperaments.

Father

Comma: 16/15

POTE generator: ~3/2 = 743.986

Map: [<1 0 4|, <0 1 -1|]

EDOs: 1, 2, 3, 5, 8, 10c, 11b, 13c, 21bc

Badness: 0.0149

7-limit

Commas: 16/15, 28/27

7-limit minimax

[<1 0 0 0|, <3/2 0 -1/4 1/4|, <5/2 0 1/4 -1/4|, <5/2 0 -3/4 3/4|]

Eigenmonzo subgroup: 2.7/5

9-limit eigenmonzo subgroup: 2.9/5

POTE generator: 742.002

Map: [<1 0 4 -2|, <0 1 -1 3|]

Wedgie: <<1 -1 3 -4 2 10||

EDOs: 5, 8d, 13cd, 21bcd

Badness: 0.0213

Pater

Commas: 16/15, 126/125

POTE generator: ~3/2 = 753.113

Map: [<1 0 4 11|, <0 1 -1 -5|]

Wedgie: <<1 -1 -5 -4 -11 -9||

EDOs: 3, 11b, 16bcd, 27bcd

Badness: 0.0530

Walid

Commas: 16/15, 50/49

POTE generator: ~3/2 = 749.415

Map: [<2 0 8 9|, <0 1 -1 -1|]

Wedgie: <<2 -2 -2 -8 -9 1||

EDOs: 2, 6, 10cd, 14bd, 16bcd

Badness: 0.0490

Baba

Commas: 16/15, 49/45

POTE generator: ~8/7 = 226.704

Map: [<1 0 4 2|, <0 2 -2 1|]

Wedgie: <<2 -2 1 -8 -4 8||

EDOs: 1, 5, 11b, 16bc

Badness: 0.0443

Quint

Commas: 16/15, 27/25

POTE generator: ~8/7 = 182.097

Map: [<5 8 12 0|, <0 0 0 -1|]

Wedgie: <<0 0 5 0 8 12||

EDOs: 5, 15cd

Badness: 0.0483

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