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Fixed typo (CWE tuning of 11-limit 3&5, mother)
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Technical data page}}
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
The '''father family''' is a family of [[rank-2 temperament]]s which [[temper out]] the classic diatonic semitone, [[16/15]]. This equates [[4/3]] with [[5/4]] and [[8/5]] with [[3/2]], so the generator is a "fourth-third" (or "fifth-sixth"), hence the name ''father''. In a sense, what father is all about is using [[semisixth]]s or [[subfourth]]s and pretending that these are 5-limit, and like any temperament which seems to involve a lot of "pretending", father is close to the edge of what can be sensibly called a temperament at all. In other words, it is an [[exotemperament]].
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-01-08 20:41:51 UTC</tt>.<br>
: The original revision id was <tt>290447551</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.
== Father ==
{{Main| Father }}


=Father=
[[Subgroup]]: 2.3.5
Comma: 16/15


POTE generator: ~3/2 = 743.986
[[Comma list]]: 16/15


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


==7-limit==
: mapping generators: ~2, ~3
Commas: 16/15, 28/27


7-limit minimax
[[Optimal tuning]]s:
[&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|]
* [[WE]]: ~2 = 1180.875{{c}}, ~3/2 = 732.129{{c}}
[[Eigenmonzo subgroup]]: 2.7/5
: [[error map]]: {{val| -19.125 +11.048 +24.181 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 742.290{{c}}
: error map: {{val| 0.000 +40.335 +71.396 }}


9-limit eigenmonzo subgroup: 2.9/5
[[Minimax tuning]]:
* [[5-odd-limit]]: ~3/2 = {{monzo| 1 1/2 -1/2 }}
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5/3


[[POTE tuning|POTE generator]]: 742.002
{{Optimal ET sequence|legend=1| 1, 2, 3, 5, 8, 13c, 21bcc }}


Map: [&lt;1 0 4 -2|, &lt;0 1 -1 3|]
[[Badness]] (Sintel): 0.349
Wedgie: &lt;&lt;1 -1 3 -4 2 10||
EDOs: 5, 8d, 13cd, 21bcd
Badness: 0.0213


=Pater=
=== Overview to extensions ===
Commas: 16/15, 126/125
Strong extensions of father to include an approximation of harmonic 7 are septimal father (5 & 8d), mother (2 & 3), and pater (3 & 5d), all considered below.


POTE generator: ~3/2 = 753.113
Temperaments discussed elsewhere include:  
* ''[[Baba]]'' → [[Semaphoresmic clan #Baba|Semaphoresmic clan]]
* ''[[Walid]]'' → [[Jubilismic clan #Walid|Jubilismic clan]]


Map: [&lt;1 0 4 11|, &lt;0 1 -1 -5|]
== Septimal father ==
Wedgie: &lt;&lt;1 -1 -5 -4 -11 -9||
{{Main| Father }}
EDOs: 3, 11b, 16bcd, 27bcd
{{See also| Trienstonic clan }}
Badness: 0.0530


</pre></div>
Septimal father tempers out [[28/27]], making it a strong extension of [[trienstonian]].
<h4>Original HTML 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;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:6:&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:6 --&gt;&lt;!-- ws:start:WikiTextTocRule:7: --&gt;&lt;a href="#Father"&gt;Father&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:7 --&gt;&lt;!-- ws:start:WikiTextTocRule:8: --&gt;&lt;!-- ws:end:WikiTextTocRule:8 --&gt;&lt;!-- ws:start:WikiTextTocRule:9: --&gt; | &lt;a href="#Pater"&gt;Pater&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:9 --&gt;&lt;!-- ws:start:WikiTextTocRule:10: --&gt;
[[Subgroup]]: 2.3.5.7
&lt;!-- ws:end:WikiTextTocRule:10 --&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;
[[Comma list]]: 16/15, 28/27
&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;
{{Mapping|legend=1| 1 0 4 -2 | 0 1 -1 3 }}
Comma: 16/15&lt;br /&gt;
 
&lt;br /&gt;
[[Optimal tuning]]s:
POTE generator: ~3/2 = 743.986&lt;br /&gt;
* [[WE]]: ~2 = 1180.634{{c}}, ~3/2 = 730.027{{c}}
&lt;br /&gt;
: [[error map]]: {{val| -19.366 +8.706 +25.561 +1.890 }}
Map: [&amp;lt;1 0 4|, &amp;lt;0 1 -1|]&lt;br /&gt;
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 738.443{{c}}
EDOs: 1, 2, 3, 5, 8, 10c, 11b, 13c, 21bc&lt;br /&gt;
: error map: {{val| 0.000 +36.488 +75.244 +46.502 }}
Badness: 0.0149&lt;br /&gt;
 
&lt;br /&gt;
[[Minimax tuning]]:  
&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;
* [[7-odd-limit]]: ~3/2 = {{monzo| 1/2 0 -1/4 1/4 }}
Commas: 16/15, 28/27&lt;br /&gt;
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/5
&lt;br /&gt;
* [[9-odd-limit]]: ~3/2 = {{monzo| 1 -2 0 1 }} = 14/9
7-limit minimax&lt;br /&gt;
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/7
[&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;
{{Optimal ET sequence|legend=1| 2d, 3d, 5, 8d, 13cd, 21bccdd }}
&lt;br /&gt;
 
9-limit eigenmonzo subgroup: 2.9/5&lt;br /&gt;
[[Badness]] (Sintel): 0.539
&lt;br /&gt;
 
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 742.002&lt;br /&gt;
=== 11-limit ===
&lt;br /&gt;
Subgroup: 2.3.5.7.11
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;
Comma list: 16/15, 22/21, 28/27
EDOs: 5, 8d, 13cd, 21bcd&lt;br /&gt;
 
Badness: 0.0213&lt;br /&gt;
Mapping: {{mapping| 1 0 4 -2 -3 | 0 1 -1 3 4 }}
&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;
Optimal tunings:
Commas: 16/15, 126/125&lt;br /&gt;
* WE: ~2 = 1180.894{{c}}, ~3/2 = 735.260{{c}}
&lt;br /&gt;
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 743.387{{c}}
POTE generator: ~3/2 = 753.113&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=0| 2de, 3de, 5, 8d }}
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;
Badness (Sintel): 0.681
EDOs: 3, 11b, 16bcd, 27bcd&lt;br /&gt;
 
Badness: 0.0530&lt;/body&gt;&lt;/html&gt;</pre></div>
== Mother ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 16/15, 21/20
 
{{Mapping|legend=1| 1 0 4 6 | 0 1 -1 -2 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1186.985{{c}}, ~3/2 = 713.743{{c}}
: [[error map]]: {{val| -13.015 -1.228 +60.898 -48.372 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 722.866{{c}}
: error map: {{val| 0.000 +20.911 +90.820 -14.559 }}
 
{{Optimal ET sequence|legend=1| 2, 3, 5 }}
 
[[Badness]] (Sintel): 0.611
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 11/10, 16/15, 21/20
 
Mapping: {{mapping| 1 0 4 6 5 | 0 1 -1 -2 -1 }}
 
Optimal tunings:
* WE: ~2 = 1192.016{{c}}, ~3/2 = 712.592{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 718.370{{c}}
 
{{Optimal ET sequence|legend=0| 2, 3, 5 }}
 
Badness (Sintel): 0.726
 
== Pater ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 16/15, 126/125
 
{{Mapping|legend=1| 1 0 4 11 | 0 1 -1 -5 }}
 
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1179.316{{c}}, ~3/2 = 740.132{{c}}
: [[error map]]: {{val| -20.684 +17.493 +11.503 +6.412 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 755.156{{c}}
: error map: {{val| 0.000 +53.201 +58.530 +55.392 }}
 
{{Optimal ET sequence|legend=1| 3, 5d, 8d, 27bbccdd }}
 
[[Badness]] (Sintel): 1.34
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 16/15, 22/21, 100/99
 
Mapping: {{mapping| 1 0 4 11 10 | 0 1 -1 -5 -4 }}
 
Optimal tunings:
* WE: ~2 = 1180.290{{c}}, ~3/2 = 739.054{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 753.774{{c}}
 
{{Optimal ET sequence|legend=0| 3, 5de, 8d }}
 
Badness (Sintel): 1.17
 
[[Category:Temperament families]]
[[Category:Father family| ]] <!-- main article -->
[[Category:Father| ]] <!-- key article -->
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Father_family"