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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>2012-02-05 14:12:09 UTC</tt>.<br>
: The original revision id was <tt>298610088</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


=Walid=
Septimal father tempers out [[28/27]], making it a strong extension of [[trienstonian]].
Commas: 16/15, 50/49


POTE generator: ~3/2 = 749.415
[[Subgroup]]: 2.3.5.7


Map: [&lt;2 0 8 9|, &lt;0 1 -1 -1|]
[[Comma list]]: 16/15, 28/27
Wedgie: &lt;&lt;2 -2 -2 -8 -9 1||
EDOs: 2, 6, 10cd, 14bd, 16bcd
Badness: 0.0490


=Baba=
{{Mapping|legend=1| 1 0 4 -2 | 0 1 -1 3 }}
Commas: 16/15, 49/45


POTE generator: ~8/7 = 226.704
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1180.634{{c}}, ~3/2 = 730.027{{c}}
: [[error map]]: {{val| -19.366 +8.706 +25.561 +1.890 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 738.443{{c}}
: error map: {{val| 0.000 +36.488 +75.244 +46.502 }}


Map: [&lt;1 0 4 2|, &lt;0 2 -2 1|]
[[Minimax tuning]]:  
Wedgie: &lt;&lt;2 -2 1 -8 -4 8||
* [[7-odd-limit]]: ~3/2 = {{monzo| 1/2 0 -1/4 1/4 }}
EDOs: 1, 5, 11b, 16bc
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/5
Badness: 0.0443
* [[9-odd-limit]]: ~3/2 = {{monzo| 1 -2 0 1 }} = 14/9
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/7


=Quint=
{{Optimal ET sequence|legend=1| 2d, 3d, 5, 8d, 13cd, 21bccdd }}
Commas: 16/15, 27/25


POTE generator: ~8/7 = 182.097
[[Badness]] (Sintel): 0.539


Map: [&lt;5 8 12 0|, &lt;0 0 0 1|]
=== 11-limit ===
Wedgie: &lt;&lt;0 0 5 0 8 12||
Subgroup: 2.3.5.7.11
EDOs: 5, 15cd
 
Badness: 0.0483</pre></div>
Comma list: 16/15, 22/21, 28/27
<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: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;
Mapping: {{mapping| 1 0 4 -2 -3 | 0 1 -1 3 4 }}
&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;
Optimal tunings:
&lt;br /&gt;
* WE: ~2 = 1180.894{{c}}, ~3/2 = 735.260{{c}}
&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;
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 743.387{{c}}
Comma: 16/15&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=0| 2de, 3de, 5, 8d }}
POTE generator: ~3/2 = 743.986&lt;br /&gt;
 
&lt;br /&gt;
Badness (Sintel): 0.681
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;
== Mother ==
Badness: 0.0149&lt;br /&gt;
[[Subgroup]]: 2.3.5.7
&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;
[[Comma list]]: 16/15, 21/20
Commas: 16/15, 28/27&lt;br /&gt;
 
&lt;br /&gt;
{{Mapping|legend=1| 1 0 4 6 | 0 1 -1 -2 }}
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;
[[Optimal tuning]]s:
&lt;a class="wiki_link" href="/Eigenmonzo%20subgroup"&gt;Eigenmonzo subgroup&lt;/a&gt;: 2.7/5&lt;br /&gt;
* [[WE]]: ~2 = 1186.985{{c}}, ~3/2 = 713.743{{c}}
&lt;br /&gt;
: [[error map]]: {{val| -13.015 -1.228 +60.898 -48.372 }}
9-limit eigenmonzo subgroup: 2.9/5&lt;br /&gt;
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 722.866{{c}}
&lt;br /&gt;
: error map: {{val| 0.000 +20.911 +90.820 -14.559 }}
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 742.002&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 2, 3, 5 }}
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;
[[Badness]] (Sintel): 0.611
EDOs: 5, 8d, 13cd, 21bcd&lt;br /&gt;
 
Badness: 0.0213&lt;br /&gt;
=== 11-limit ===
&lt;br /&gt;
Subgroup: 2.3.5.7.11
&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;
Comma list: 11/10, 16/15, 21/20
&lt;br /&gt;
 
POTE generator: ~3/2 = 753.113&lt;br /&gt;
Mapping: {{mapping| 1 0 4 6 5 | 0 1 -1 -2 -1 }}
&lt;br /&gt;
 
Map: [&amp;lt;1 0 4 11|, &amp;lt;0 1 -1 -5|]&lt;br /&gt;
Optimal tunings:
Wedgie: &amp;lt;&amp;lt;1 -1 -5 -4 -11 -9||&lt;br /&gt;
* WE: ~2 = 1192.016{{c}}, ~3/2 = 712.592{{c}}
EDOs: 3, 11b, 16bcd, 27bcd&lt;br /&gt;
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 718.370{{c}}
Badness: 0.0530&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=0| 2, 3, 5 }}
&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;
Badness (Sintel): 0.726
&lt;br /&gt;
 
POTE generator: ~3/2 = 749.415&lt;br /&gt;
== Pater ==
&lt;br /&gt;
[[Subgroup]]: 2.3.5.7
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;
[[Comma list]]: 16/15, 126/125
EDOs: 2, 6, 10cd, 14bd, 16bcd&lt;br /&gt;
 
Badness: 0.0490&lt;br /&gt;
{{Mapping|legend=1| 1 0 4 11 | 0 1 -1 -5 }}
&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;
[[Optimal tuning]]s:  
Commas: 16/15, 49/45&lt;br /&gt;
* [[WE]]: ~2 = 1179.316{{c}}, ~3/2 = 740.132{{c}}
&lt;br /&gt;
: [[error map]]: {{val| -20.684 +17.493 +11.503 +6.412 }}
POTE generator: ~8/7 = 226.704&lt;br /&gt;
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 755.156{{c}}
&lt;br /&gt;
: error map: {{val| 0.000 +53.201 +58.530 +55.392 }}
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;
{{Optimal ET sequence|legend=1| 3, 5d, 8d, 27bbccdd }}
EDOs: 1, 5, 11b, 16bc&lt;br /&gt;
 
Badness: 0.0443&lt;br /&gt;
[[Badness]] (Sintel): 1.34
&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;
=== 11-limit ===
Commas: 16/15, 27/25&lt;br /&gt;
Subgroup: 2.3.5.7.11
&lt;br /&gt;
 
POTE generator: ~8/7 = 182.097&lt;br /&gt;
Comma list: 16/15, 22/21, 100/99
&lt;br /&gt;
 
Map: [&amp;lt;5 8 12 0|, &amp;lt;0 0 0 1|]&lt;br /&gt;
Mapping: {{mapping| 1 0 4 11 10 | 0 1 -1 -5 -4 }}
Wedgie: &amp;lt;&amp;lt;0 0 5 0 8 12||&lt;br /&gt;
 
EDOs: 5, 15cd&lt;br /&gt;
Optimal tunings:  
Badness: 0.0483&lt;/body&gt;&lt;/html&gt;</pre></div>
* 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]]

Latest revision as of 02:20, 8 March 2026

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

The father family is a family of rank-2 temperaments 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 semisixths or subfourths 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.

Father

Main article: Father

Subgroup: 2.3.5

Comma list: 16/15

Mapping: [⟨1 0 4], ⟨0 1 -1]]

mapping generators: ~2, ~3

Optimal tunings:

  • WE: ~2 = 1180.875 ¢, ~3/2 = 732.129 ¢
error map: ⟨-19.125 +11.048 +24.181]
  • CWE: ~2 = 1200.000 ¢, ~3/2 = 742.290 ¢
error map: ⟨0.000 +40.335 +71.396]

Minimax tuning:

unchanged-interval (eigenmonzo) basis: 2.5/3

Optimal ET sequence: 1, 2, 3, 5, 8, 13c, 21bcc

Badness (Sintel): 0.349

Overview to extensions

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.

Temperaments discussed elsewhere include:

Septimal father

Main article: Father
See also: Trienstonic clan

Septimal father tempers out 28/27, making it a strong extension of trienstonian.

Subgroup: 2.3.5.7

Comma list: 16/15, 28/27

Mapping: [⟨1 0 4 -2], ⟨0 1 -1 3]]

Optimal tunings:

  • WE: ~2 = 1180.634 ¢, ~3/2 = 730.027 ¢
error map: ⟨-19.366 +8.706 +25.561 +1.890]
  • CWE: ~2 = 1200.000 ¢, ~3/2 = 738.443 ¢
error map: ⟨0.000 +36.488 +75.244 +46.502]

Minimax tuning:

unchanged-interval (eigenmonzo) basis: 2.7/5
unchanged-interval (eigenmonzo) basis: 2.9/7

Optimal ET sequence: 2d, 3d, 5, 8d, 13cd, 21bccdd

Badness (Sintel): 0.539

11-limit

Subgroup: 2.3.5.7.11

Comma list: 16/15, 22/21, 28/27

Mapping: [⟨1 0 4 -2 -3], ⟨0 1 -1 3 4]]

Optimal tunings:

  • WE: ~2 = 1180.894 ¢, ~3/2 = 735.260 ¢
  • CWE: ~2 = 1200.000 ¢, ~3/2 = 743.387 ¢

Optimal ET sequence: 2de, 3de, 5, 8d

Badness (Sintel): 0.681

Mother

Subgroup: 2.3.5.7

Comma list: 16/15, 21/20

Mapping: [⟨1 0 4 6], ⟨0 1 -1 -2]]

Optimal tunings:

  • WE: ~2 = 1186.985 ¢, ~3/2 = 713.743 ¢
error map: ⟨-13.015 -1.228 +60.898 -48.372]
  • CWE: ~2 = 1200.000 ¢, ~3/2 = 722.866 ¢
error map: ⟨0.000 +20.911 +90.820 -14.559]

Optimal ET sequence: 2, 3, 5

Badness (Sintel): 0.611

11-limit

Subgroup: 2.3.5.7.11

Comma list: 11/10, 16/15, 21/20

Mapping: [⟨1 0 4 6 5], ⟨0 1 -1 -2 -1]]

Optimal tunings:

  • WE: ~2 = 1192.016 ¢, ~3/2 = 712.592 ¢
  • CWE: ~2 = 1200.000 ¢, ~3/2 = 718.370 ¢

Optimal ET sequence: 2, 3, 5

Badness (Sintel): 0.726

Pater

Subgroup: 2.3.5.7

Comma list: 16/15, 126/125

Mapping: [⟨1 0 4 11], ⟨0 1 -1 -5]]

Optimal tunings:

  • WE: ~2 = 1179.316 ¢, ~3/2 = 740.132 ¢
error map: ⟨-20.684 +17.493 +11.503 +6.412]
  • CWE: ~2 = 1200.000 ¢, ~3/2 = 755.156 ¢
error map: ⟨0.000 +53.201 +58.530 +55.392]

Optimal ET sequence: 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: [⟨1 0 4 11 10], ⟨0 1 -1 -5 -4]]

Optimal tunings:

  • WE: ~2 = 1180.290 ¢, ~3/2 = 739.054 ¢
  • CWE: ~2 = 1200.000 ¢, ~3/2 = 753.774 ¢

Optimal ET sequence: 3, 5de, 8d

Badness (Sintel): 1.17

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