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Dicot family: Difference between revisions

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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 '''dicot family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] [[25/24]], the classical chromatic semitone.
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-01-02 14:21:24 UTC</tt>.<br>
: The original revision id was <tt>289100111</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]]


The [[5-limit]] parent [[comma]] for the dicot family is 25/24, the [[chromatic semitone]]. Its [[monzo]] is |-3 -1 2&gt;, and flipping that yields &lt;&lt;2 1 -3|| for the [[wedgie]]. This tells us the generator is a third (major and minor mean the same thing), and that two thirds gives a fifth. In fact, (5/4)^2 = 3/2 * 25/24. Possible tunings for dicot are [[7edo]], [[24edo]] using the val &lt;24 38 55| and [[31edo]] using the val &lt;31 49 71|. In a sense, what dicot is all about is using neutral thirds and pretending that's 5-limit, and like any temperament which seems to involve pretending dicot is at the edge of what can sensibly be called a temperament at all.
== Dicot ==
The head of this family, dicot, is [[generator|generated]] by a classical third (major and minor mean the same thing), and two such thirds give a fifth. In fact, {{nowrap|(5/4)<sup>2</sup> {{=}} (3/2)(25/24)}}. Its [[ploidacot]] is the same as its name, dicot.  


Possible tunings for dicot are [[7edo]], [[10edo]], [[17edo]], [[24edo]] using the val {{val| 24 38 55 }} (24c), and [[31edo]] using the val {{val| 31 49 71 }} (31c). In a sense, what dicot is all about is using neutral thirds and sixths and pretending that these are 5-limit, and like any temperament which seems to involve a lot of "pretending", dicot is close to the edge of what can be sensibly called a temperament at all. In other words, it is an [[exotemperament]].


==Seven limit children==
[[Subgroup]]: 2.3.5
The second comma of the [[Normal lists|normal comma list]] defines which [[7-limit]] family member we are looking at. Septimal dicot, with wedgie &lt;&lt;2 1 3 -3 -1 4|| adds 36/35, sharp with wedgie &lt;&lt;2 1 6 -3 4 11|| adds 28/27, and dichotic with wedgie &lt;&lt;2 1 -4 -3 -12 -12|| ads 64/63, all retaining the same period and generator. Decimal with wedgie &lt;&lt;4 2 2 -6 -8 -1|| adds 49/48, sidi with wedgie &lt;&lt;4 2 9 -3 6 15|| adds 245/243, and jamesbond with wedgie &lt;&lt;0 0 7 0 11 16|| adds 81/80. Here decimal divides the period to 1/2 octave, and sidi uses 9/7 as a generator, with two of them making up the combined 5/3 and 8/5 neutral sixth. Jamesbond has a period of 1/7 octave, and uses an approximate 15/14 as generator.


[[POTE tuning|POTE generator]]: 348.594
[[Comma list]]: 25/24


Map: [&lt;1 1 2|, &lt;0 2 1|]
{{Mapping|legend=1| 1 1 2 | 0 2 1 }}
EDOs: [[7edo|7]], [[10edo|10]], [[14edo|14c]], [[17edo|17]], [[24edo|24c]], [[31edo|31c]]


=Septimal dicot=
: mapping generators: ~2, ~5/4
[[Comma]]s: 15/14, 25/24


[[POTE tuning|POTE generator]]: 336.381
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1206.283{{c}}, ~6/5 = 350.420{{c}}
: [[error map]]: {{val| +6.283 +5.167 -23.328 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~5/4 = 351.086{{c}}
: error map: {{val| 0.000 +0.216 -35.228 }}


Map: [&lt;1 1 2 3|, &lt;0 2 1 3|]
[[Tuning ranges]]:
EDOs: [[11edo|11c]], [[14edo|14cd]], [[18edo|18bc]], [[25edo|25bcd]]
* [[5-odd-limit]] [[diamond monotone]]: ~5/4 = [300.000, 400.000] (1\4 to 1\3)
* 5-odd-limit [[diamond tradeoff]]: ~5/4 = [315.641, 386.314] (full comma to untempered)


=Sharp=
{{Optimal ET sequence|legend=1| 3, 4, 7, 17, 24c, 31c }}
Commas: 25/24, 28/27


[[POTE tuning|POTE generator]]: 357.938
[[Badness]] (Sintel): 0.306


Map: [&lt;1 1 2 1|, &lt;0 2 1 6|]
=== Overview to extensions ===
EDOs: [[10edo|10]], [[37edo|37cd]], [[57edo|57bcd]]
The second comma of the [[normal lists|normal comma list]] defines which [[7-limit]] family member we are looking at. Septimal dicot adds [[36/35]], flattie adds [[21/20]], sharpie adds [[28/27]], and dichotic adds [[64/63]], all retaining the same period and generator.


=Decimal=
Decimal adds [[49/48]], sidi adds [[245/243]], and jamesbond adds [[16/15]]. Here decimal divides the [[period]] to a [[sqrt(2)|semi-octave]], and sidi uses 14/9 as a generator, with two of them making up the combined 5/2~12/5 neutral tenth. Jamesbond has a period of 1/7 octave, and uses an approximate 15/14 as generator.
Commas: 25/24, 49/48


[[POTE tuning|POTE generator]]: ~7/6 = 251.557
Temperaments discussed elsewhere are:
* ''[[Geryon]]'' → [[Very low accuracy temperaments #Geryon|Very low accuracy temperaments]]
* ''[[Jamesbond]]'' → [[7th-octave temperaments #Jamesbond|7th-octave temperaments]]


Map: [&lt;2 0 3 4|, &lt;0 2 1 1|]
The rest are considered below.  
Wedgie: &lt;&lt;4 2 2 -6 -8 -1||
EDOs: [[10edo|10]], [[14edo|14c]], [[24edo|24c]], [[38edo|38cd]]
Badness: 0.0283


==11-limit==
=== 2.3.5.11 subgroup ===
Commas: 25/24, 45/44, 49/48
The 2.3.5.11-subgroup extension maps [[11/9]]~[[27/22]] to the neutral third. As such, it is related to most of the septimal extensions.


[[POTE tuning|POTE generator]]: ~7/6 = 253.493
Subgroup: 2.3.5.11


Map: [&lt;2 0 3 4 -1|, &lt;0 2 1 1 5|]
Comma list: 25/24, 45/44
EDOs: 10, 14c, 24c, 38cd
Badness: 0.0267


=Dichotic=
Subgroup val mapping: {{mapping| 1 1 2 2 | 0 2 1 5 }}
Commas: 25/24, 64/63


POTE generator: ~5/4 = 356.264
Gencom mapping: {{mapping| 1 1 2 0 2 | 0 2 1 0 5 }}


Map: [&lt;1 1 2 4|, &lt;0 2 1 -4|]
Optimal tunings:  
Wedgie: &lt;&lt;2 1 -4 -3 -12 -12||
* WE: ~2 = 1206.750{{c}}, ~6/5 = 348.684{{c}}
EDOs: 7, 10, 17, 27c, 37c
* CWE: ~2 = 1200.000{{c}}, ~6/5 = 348.954{{c}}
Badness: 0.0376


==11-limit==
{{Optimal ET sequence|legend=0| 3e, 4e, 7, 24c, 31c }}
Commas: 25/24, 45/44, 64/63


POTE generator: ~5/4 = 354.262
Badness (Sintel): 0.370


Map: [&lt;1 1 2 4 2|, &lt;0 2 1 -4 5|]
==== 2.3.5.11.13 subgroup ====
EDOs: 7, 10, 17, 27ce, 44ce
Subgroup: 2.3.5.11.13
Badness: 0.0307


=Jamesbond=
Comma list: 25/24, 40/39, 45/44
Commas: 25/24, 81/80


[[POTE tuning|POTE generator]]: 86.710
Subgroup val mapping: {{mapping| 1 1 2 2 4 | 0 2 1 5 -1 }}


Map: [&lt;7 11 16 20|, &lt;0 0 0 -1|]
Gencom mapping: {{mapping| 1 1 2 0 2 4 | 0 2 1 0 5 -1 }}
EDOs: 7, [[14edo|14c]]


===Sidi===
Optimal tunings:
Commas: 25/24, 245/243
* WE: ~2 = 1202.433{{c}}, ~5/4 = 351.237{{c}}
* CWE: ~2 = 1200.000{{c}}, ~5/4 = 350.978{{c}}


[[POTE tuning|POTE generator]]: 427.208
{{Optimal ET sequence|legend=0| 3e, 7, 17 }}


Map: [&lt;1 3 3 6|, &lt;0 -4 -2 -9|]
Badness (Sintel): 0.536
EDOs: [[14edo|14c]], [[45edo|45c]], &lt;59 93 135 165|


</pre></div>
== Septimal dicot ==
<h4>Original HTML content:</h4>
Septimal dicot is the extension where [[7/6]] and [[9/7]] are also conflated into 5/4~6/5. Although 5/4~6/5 covers a giant block of pitches already, 7/6 and 9/7 are often considered as thirds too. On that account one could argue for the canonicity of this extension, despite the relatively poor accuracy.
<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;Dicot family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:18:&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:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt;&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;!-- ws:start:WikiTextTocRule:20: --&gt; | &lt;a href="#Septimal dicot"&gt;Septimal dicot&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:20 --&gt;&lt;!-- ws:start:WikiTextTocRule:21: --&gt; | &lt;a href="#Sharp"&gt;Sharp&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:21 --&gt;&lt;!-- ws:start:WikiTextTocRule:22: --&gt; | &lt;a href="#Decimal"&gt;Decimal&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:22 --&gt;&lt;!-- ws:start:WikiTextTocRule:23: --&gt;&lt;!-- ws:end:WikiTextTocRule:23 --&gt;&lt;!-- ws:start:WikiTextTocRule:24: --&gt; | &lt;a href="#Dichotic"&gt;Dichotic&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:24 --&gt;&lt;!-- ws:start:WikiTextTocRule:25: --&gt;&lt;!-- ws:end:WikiTextTocRule:25 --&gt;&lt;!-- ws:start:WikiTextTocRule:26: --&gt; | &lt;a href="#Jamesbond"&gt;Jamesbond&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:26 --&gt;&lt;!-- ws:start:WikiTextTocRule:27: --&gt;&lt;!-- ws:end:WikiTextTocRule:27 --&gt;&lt;!-- ws:start:WikiTextTocRule:28: --&gt;
 
&lt;!-- ws:end:WikiTextTocRule:28 --&gt;&lt;br /&gt;
[[Subgroup]]: 2.3.5.7
The &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt; parent &lt;a class="wiki_link" href="/comma"&gt;comma&lt;/a&gt; for the dicot family is 25/24, the &lt;a class="wiki_link" href="/chromatic%20semitone"&gt;chromatic semitone&lt;/a&gt;. Its &lt;a class="wiki_link" href="/monzo"&gt;monzo&lt;/a&gt; is |-3 -1 2&amp;gt;, and flipping that yields &amp;lt;&amp;lt;2 1 -3|| for the &lt;a class="wiki_link" href="/wedgie"&gt;wedgie&lt;/a&gt;. This tells us the generator is a third (major and minor mean the same thing), and that two thirds gives a fifth. In fact, (5/4)^2 = 3/2 * 25/24. Possible tunings for dicot are &lt;a class="wiki_link" href="/7edo"&gt;7edo&lt;/a&gt;, &lt;a class="wiki_link" href="/24edo"&gt;24edo&lt;/a&gt; using the val &amp;lt;24 38 55| and &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; using the val &amp;lt;31 49 71|. In a sense, what dicot is all about is using neutral thirds and pretending that's 5-limit, and like any temperament which seems to involve pretending dicot is at the edge of what can sensibly be called a temperament at all.&lt;br /&gt;
 
&lt;br /&gt;
[[Comma list]]: 15/14, 25/24
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Seven limit children"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Seven limit children&lt;/h2&gt;
{{Mapping|legend=1| 1 1 2 2 | 0 2 1 3 }}
The second comma of the &lt;a class="wiki_link" href="/Normal%20lists"&gt;normal comma list&lt;/a&gt; defines which &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt; family member we are looking at. Septimal dicot, with wedgie &amp;lt;&amp;lt;2 1 3 -3 -1 4|| adds 36/35, sharp with wedgie &amp;lt;&amp;lt;2 1 6 -3 4 11|| adds 28/27, and dichotic with wedgie &amp;lt;&amp;lt;2 1 -4 -3 -12 -12|| ads 64/63, all retaining the same period and generator. Decimal with wedgie &amp;lt;&amp;lt;4 2 2 -6 -8 -1|| adds 49/48, sidi with wedgie &amp;lt;&amp;lt;4 2 9 -3 6 15|| adds 245/243, and jamesbond with wedgie &amp;lt;&amp;lt;0 0 7 0 11 16|| adds 81/80. Here decimal divides the period to 1/2 octave, and sidi uses 9/7 as a generator, with two of them making up the combined 5/3 and 8/5 neutral sixth. Jamesbond has a period of 1/7 octave, and uses an approximate 15/14 as generator.&lt;br /&gt;
 
&lt;br /&gt;
[[Optimal tuning]]s:  
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 348.594&lt;br /&gt;
* [[WE]]: ~2 = 1205.532{{c}}, ~6/5 = 337.931{{c}}
&lt;br /&gt;
: [[error map]]: {{val| +5.532 -20.561 -37.319 +56.032 }}
Map: [&amp;lt;1 1 2|, &amp;lt;0 2 1|]&lt;br /&gt;
* [[CWE]]: ~2 = 1200.000{{c}}, ~6/5 = 338.561{{c}}
EDOs: &lt;a class="wiki_link" href="/7edo"&gt;7&lt;/a&gt;, &lt;a class="wiki_link" href="/10edo"&gt;10&lt;/a&gt;, &lt;a class="wiki_link" href="/14edo"&gt;14c&lt;/a&gt;, &lt;a class="wiki_link" href="/17edo"&gt;17&lt;/a&gt;, &lt;a class="wiki_link" href="/24edo"&gt;24c&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31c&lt;/a&gt;&lt;br /&gt;
: error map: {{val| 0.000 -24.834 -47.753 +46.856 }}
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Septimal dicot"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Septimal dicot&lt;/h1&gt;
{{Optimal ET sequence|legend=1| 3d, 4, 7 }}
&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 15/14, 25/24&lt;br /&gt;
 
&lt;br /&gt;
[[Badness]] (Sintel): 0.504
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 336.381&lt;br /&gt;
 
&lt;br /&gt;
=== 11-limit ===
Map: [&amp;lt;1 1 2 3|, &amp;lt;0 2 1 3|]&lt;br /&gt;
Subgroup: 2.3.5.7.11
EDOs: &lt;a class="wiki_link" href="/11edo"&gt;11c&lt;/a&gt;, &lt;a class="wiki_link" href="/14edo"&gt;14cd&lt;/a&gt;, &lt;a class="wiki_link" href="/18edo"&gt;18bc&lt;/a&gt;, &lt;a class="wiki_link" href="/25edo"&gt;25bcd&lt;/a&gt;&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 15/14, 22/21, 25/24
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Sharp"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Sharp&lt;/h1&gt;
 
Commas: 25/24, 28/27&lt;br /&gt;
Mapping: {{mapping| 1 1 2 2 2 | 0 2 1 3 5 }}
&lt;br /&gt;
 
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 357.938&lt;br /&gt;
Optimal tunings:  
&lt;br /&gt;
* WE: ~2 = 1203.346{{c}}, ~6/5 = 343.078{{c}}
Map: [&amp;lt;1 1 2 1|, &amp;lt;0 2 1 6|]&lt;br /&gt;
* CWE: ~2 = 1200.000{{c}}, ~6/5 = 343.260{{c}}
EDOs: &lt;a class="wiki_link" href="/10edo"&gt;10&lt;/a&gt;, &lt;a class="wiki_link" href="/37edo"&gt;37cd&lt;/a&gt;, &lt;a class="wiki_link" href="/57edo"&gt;57bcd&lt;/a&gt;&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=0| 3de, 4e, 7 }}
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Decimal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Decimal&lt;/h1&gt;
 
Commas: 25/24, 49/48&lt;br /&gt;
Badness (Sintel): 0.656
&lt;br /&gt;
 
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~7/6 = 251.557&lt;br /&gt;
=== Eudicot ===
&lt;br /&gt;
Subgroup: 2.3.5.7.11
Map: [&amp;lt;2 0 3 4|, &amp;lt;0 2 1 1|]&lt;br /&gt;
 
Wedgie: &amp;lt;&amp;lt;4 2 2 -6 -8 -1||&lt;br /&gt;
Comma list: 15/14, 25/24, 33/32
EDOs: &lt;a class="wiki_link" href="/10edo"&gt;10&lt;/a&gt;, &lt;a class="wiki_link" href="/14edo"&gt;14c&lt;/a&gt;, &lt;a class="wiki_link" href="/24edo"&gt;24c&lt;/a&gt;, &lt;a class="wiki_link" href="/38edo"&gt;38cd&lt;/a&gt;&lt;br /&gt;
 
Badness: 0.0283&lt;br /&gt;
Mapping: {{mapping| 1 1 2 2 4 | 0 2 1 3 -2 }}
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Decimal-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;11-limit&lt;/h2&gt;
Optimal tunings:  
Commas: 25/24, 45/44, 49/48&lt;br /&gt;
* WE: ~2 = 1205.828{{c}}, ~6/5 = 337.683{{c}}
&lt;br /&gt;
* CWE: ~2 = 1200.000{{c}}, ~6/5 = 336.909{{c}}
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~7/6 = 253.493&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=0| 3d, 4, 7, 18bc, 25bccd }}
Map: [&amp;lt;2 0 3 4 -1|, &amp;lt;0 2 1 1 5|]&lt;br /&gt;
 
EDOs: 10, 14c, 24c, 38cd&lt;br /&gt;
Badness (Sintel): 0.896
Badness: 0.0267&lt;br /&gt;
 
&lt;br /&gt;
==== 13-limit ====
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Dichotic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Dichotic&lt;/h1&gt;
Subgroup: 2.3.5.7.11.13
Commas: 25/24, 64/63&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 15/14, 25/24, 33/32, 40/39
POTE generator: ~5/4 = 356.264&lt;br /&gt;
 
&lt;br /&gt;
Mapping: {{mapping| 1 1 2 2 4 4 | 0 2 1 3 -2 -1 }}
Map: [&amp;lt;1 1 2 4|, &amp;lt;0 2 1 -4|]&lt;br /&gt;
 
Wedgie: &amp;lt;&amp;lt;2 1 -4 -3 -12 -12||&lt;br /&gt;
Optimal tunings:
EDOs: 7, 10, 17, 27c, 37c&lt;br /&gt;
* WE: ~2 = 1202.660{{c}}, ~6/5 = 339.597{{c}}
Badness: 0.0376&lt;br /&gt;
* CWE: ~2 = 1200.000{{c}}, ~6/5 = 339.104{{c}}
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Dichotic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;11-limit&lt;/h2&gt;
{{Optimal ET sequence|legend=0| 3d, 4, 7 }}
Commas: 25/24, 45/44, 64/63&lt;br /&gt;
 
&lt;br /&gt;
Badness (Sintel): 0.985
POTE generator: ~5/4 = 354.262&lt;br /&gt;
 
&lt;br /&gt;
== Flattie ==
Map: [&amp;lt;1 1 2 4 2|, &amp;lt;0 2 1 -4 5|]&lt;br /&gt;
This temperament used to be known as ''flat''. Unlike septimal dicot where 7/6 is added to the neutral third, here [[8/7]] is added instead.
EDOs: 7, 10, 17, 27ce, 44ce&lt;br /&gt;
 
Badness: 0.0307&lt;br /&gt;
[[Subgroup]]: 2.3.5.7
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="Jamesbond"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Jamesbond&lt;/h1&gt;
[[Comma list]]: 21/20, 25/24
Commas: 25/24, 81/80&lt;br /&gt;
 
&lt;br /&gt;
{{Mapping|legend=1| 1 1 2 3 | 0 2 1 -1 }}
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 86.710&lt;br /&gt;
 
&lt;br /&gt;
[[Optimal tuning]]s:  
Map: [&amp;lt;7 11 16 20|, &amp;lt;0 0 0 -1|]&lt;br /&gt;
* [[WE]]: ~2 = 1220.466{{c}}, ~6/5 = 337.577{{c}}
EDOs: 7, &lt;a class="wiki_link" href="/14edo"&gt;14c&lt;/a&gt;&lt;br /&gt;
: [[error map]]: {{val| +20.466 -6.335 -7.804 -45.004 }}
&lt;br /&gt;
* [[CWE]]: ~2 = 1200.000{{c}}, ~6/5 = 335.391{{c}}
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc8"&gt;&lt;a name="Jamesbond--Sidi"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Sidi&lt;/h3&gt;
: error map: {{val| 0.000 -31.173 -50.922 -104.217 }}
Commas: 25/24, 245/243&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 3, 4, 7d, 11cd, 18bcddd }}
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 427.208&lt;br /&gt;
 
&lt;br /&gt;
[[Badness]] (Sintel): 0.642
Map: [&amp;lt;1 3 3 6|, &amp;lt;0 -4 -2 -9|]&lt;br /&gt;
 
EDOs: &lt;a class="wiki_link" href="/14edo"&gt;14c&lt;/a&gt;, &lt;a class="wiki_link" href="/45edo"&gt;45c&lt;/a&gt;, &amp;lt;59 93 135 165|&lt;/body&gt;&lt;/html&gt;</pre></div>
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 21/20, 25/24, 33/32
 
Mapping: {{mapping| 1 1 2 3 4 | 0 2 1 -1 -2 }}
 
Optimal tunings:
* WE: ~2 = 1216.069{{c}}, ~6/5 = 342.052{{c}}
* CWE: ~2 = 1200.000{{c}}, ~6/5 = 338.467{{c}}
 
{{Optimal ET sequence|legend=0| 3, 4, 7d }}
 
Badness (Sintel): 0.826
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 14/13, 21/20, 25/24, 33/32
 
Mapping: {{mapping| 1 1 2 3 4 4 | 0 2 1 -1 -2 -1 }}
 
Optimal tunings:
* WE: ~2 = 1211.546{{c}}, ~6/5 = 344.304{{c}}
* CWE: ~2 = 1200.000{{c}}, ~6/5 = 341.373{{c}}
 
{{Optimal ET sequence|legend=0| 3, 4, 7d }}
 
Badness (Sintel): 0.968
 
== Sharpie ==
This temperament used to be known as ''sharp''. This is where you find 7/6 at the major second and [[7/4]] at the major sixth.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 25/24, 28/27
 
{{Mapping|legend=1| 1 1 2 1 | 0 2 1 6 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1202.488{{c}}, ~5/4 = 358.680{{c}}
: [[error map]]: {{val| +2.488 +17.893 -22.658 -14.258 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~5/4 = 358.495{{c}}
: error map: {{val| 0.000 +15.035 -27.818 -17.854 }}
 
{{Optimal ET sequence|legend=1| 3d, 7d, 10 }}
 
[[Badness]] (Sintel): 0.732
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 25/24, 28/27, 35/33
 
Mapping: {{mapping| 1 1 2 1 2 | 0 2 1 6 5 }}
 
Optimal tunings:  
* WE: ~2 = 1201.518{{c}}, ~5/4 = 356.557{{c}}
* CWE: ~2 = 1200.000{{c}}, ~5/4 = 356.457{{c}}
 
{{Optimal ET sequence|legend=0| 3de, 7d, 10, 17d }}
 
Badness (Sintel): 0.739
 
== Dichotic ==
In dichotic, 7/4 is found at a stack of two perfect fourths.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 25/24, 64/63
 
{{Mapping|legend=1| 1 1 2 4 | 0 2 1 -4 }}
 
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1200.802{{c}}, ~5/4 = 356.502{{c}}
: [[error map]]: {{val| +0.802 +11.851 -28.208 +8.374 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~5/4 = 356.275{{c}}
: error map: {{val| 0.000 +10.595 -30.039 +6.074 }}
 
{{Optimal ET sequence|legend=1| 3, 7, 10, 17, 27c }}
 
[[Badness]] (Sintel): 0.951
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 25/24, 45/44, 64/63
 
Mapping: {{mapping| 1 1 2 4 2 | 0 2 1 -4 5 }}
 
Optimal tunings:
* WE: ~2 = 1199.504{{c}}, ~5/4 = 354.115{{c}}
* CWE: ~2 = 1200.000{{c}}, ~5/4 = 354.236{{c}}
 
{{Optimal ET sequence|legend=0| 7, 10, 17 }}
 
Badness (Sintel): 1.01
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 25/24, 40/39, 45/44, 64/63
 
Mapping: {{mapping| 1 1 2 4 2 4 | 0 2 1 -4 5 -1 }}
 
Optimal tunings:  
* WE: ~2 = 1199.289{{c}}, ~5/4 = 354.156{{c}}
* CWE: ~2 = 1200.000{{c}}, ~5/4 = 354.340{{c}}
 
{{Optimal ET sequence|legend=0| 7, 10, 17, 27ce, 44cce }}
 
Badness (Sintel): 0.896
 
=== Dichotomic ===
Subgroup: 2.3.5.7.11
 
Comma list: 22/21, 25/24, 33/32
 
Mapping: {{mapping| 1 1 2 4 4 | 0 2 1 -4 -2 }}
 
Optimal tunings:
* WE: ~2 = 1203.949{{c}}, ~5/4 = 355.239{{c}}
* CWE: ~2 = 1200.000{{c}}, ~5/4 = 354.024{{c}}
 
{{Optimal ET sequence|legend=0| 3, 7, 10e }}
 
Badness (Sintel): 1.05
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 22/21, 25/24, 33/32, 40/39
 
Mapping: {{mapping| 1 1 2 4 4 4 | 0 2 1 -4 -2 -1 }}
 
Optimal tunings:
* WE: ~2 = 1202.979{{c}}, ~5/4 = 355.193{{c}}
* CWE: ~2 = 1200.000{{c}}, ~5/4 = 354.254{{c}}
 
{{Optimal ET sequence|legend=0| 3, 7, 10e }}
 
Badness (Sintel): 0.940
 
=== Dichosis ===
Subgroup: 2.3.5.7.11
 
Comma list: 25/24, 35/33, 64/63
 
Mapping: {{mapping| 1 1 2 4 5 | 0 2 1 -4 -5 }}
 
Optimal tunings:
* WE: ~2 = 1197.526{{c}}, ~5/4 = 359.915{{c}}
* CWE: ~2 = 1200.000{{c}}, ~5/4 = 360.745{{c}}
 
{{Optimal ET sequence|legend=0| 3, 7e, 10 }}
 
Badness (Sintel): 1.37
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 25/24, 35/33, 40/39, 64/63
 
Mapping: {{mapping| 1 1 2 4 5 4 | 0 2 1 -4 -5 -1 }}
 
Optimal tunings:
* WE: ~2 = 1197.922{{c}}, ~5/4 = 360.021{{c}}
* CWE: ~2 = 1200.000{{c}}, ~5/4 = 360.722{{c}}
 
{{Optimal ET sequence|legend=0| 3, 7e, 10 }}
 
Badness (Sintel): 1.15
 
== Decimal ==
{{Main| Decimal }}
{{See also| Jubilismic clan }}
 
Decimal tempers out 49/48 and [[50/49]], and has a semi-octave period for 7/5~10/7 and a hemitwelfth generator for 7/4~12/7. Its ploidacot is diploid dicot. [[10edo]] makes for a good tuning, from which it derives its name. [[14edo]] in the 14c val and [[24edo]] in the 24c val are also among the possibilities.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 25/24, 49/48
 
{{Mapping|legend=1| 2 0 3 4 | 0 2 1 1 }}
 
: mapping generators: ~7/5, ~7/4
 
[[Optimal tuning]]s:
* [[WE]]: ~7/5 = 603.286{{c}}, ~7/4 = 953.637{{c}} (~7/6 = 252.935{{c}})
: [[error map]]: {{val| +6.571 +5.318 -22.821 -2.047 }}
* [[CWE]]: ~7/5 = 600.000{{c}}, ~7/4 = 950.957{{c}} (~7/6 = 249.043{{c}})
: error map: {{val| 0.000 -0.041 -35.357 -17.869 }}
 
{{Optimal ET sequence|legend=1| 4, 10, 14c, 24c, 38ccd }}
 
[[Badness]] (Sintel): 0.717
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 25/24, 45/44, 49/48
 
Mapping: {{mapping| 2 0 3 4 -1 | 0 2 1 1 5 }}
 
Optimal tunings:
* WE: ~7/5 = 603.558{{c}}, ~7/4 = 952.121{{c}} (~7/6 = 254.996{{c}})
* CWE: ~7/5 = 600.000{{c}}, ~7/4 = 948.610{{c}} (~7/6 = 251.390{{c}})
 
{{Optimal ET sequence|legend=0| 4e, 10, 14c, 24c }}
 
Badness (Sintel): 0.883
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 25/24, 45/44, 49/48, 91/90
 
Mapping: {{mapping| 2 0 3 4 -1 1| 0 2 1 1 5 4}}
 
Optimal tunings:
* WE: ~7/5 = 603.612{{c}}, ~7/4 = 953.663{{c}} (~7/6 = 253.562{{c}})
* CWE: ~7/5 = 600.000{{c}}, ~7/4 = 950.116{{c}} (~7/6 = 249.884{{c}})
 
{{Optimal ET sequence|legend=0| 4ef, 10, 14cf, 24cf }}
 
Badness (Sintel): 0.881
 
=== Decimated ===
Subgroup: 2.3.5.7.11
 
Comma list: 25/24, 33/32, 49/48
 
Mapping: {{mapping| 2 0 3 4 10 | 0 2 1 1 -2 }}
 
Optimal tunings:
* WE: ~7/5 = 604.535{{c}}, ~7/4 = 952.076{{c}} (~7/6 = 256.994{{c}})
* CWE: ~7/5 = 600.000{{c}}, ~7/4 = 946.108{{c}} (~7/6 = 253.892{{c}})
 
{{Optimal ET sequence|legend=0| 4, 10e, 14c }}
 
Badness (Sintel): 1.04
 
=== Decibel ===
Subgroup: 2.3.5.7.11
 
Comma list: 25/24, 35/33, 49/48
 
Mapping: {{mapping| 2 0 3 4 7 | 0 2 1 1 0 }}
 
Optimal tunings:
* WE: ~7/5 = 599.404{{c}}, ~7/4 = 955.557{{c}} (~8/7 = 243.251{{c}})
* CWE: ~7/5 = 600.000{{c}}, ~7/4 = 956.169{{c}} (~8/7 = 243.831{{c}})
 
{{Optimal ET sequence|legend=0| 4, 6, 10 }}
 
Badness (Sintel): 1.07
 
== Sidi ==
Sidi tempers out 245/243, and splits 5/2~12/5 in two. Its ploidacot is beta-tetracot. This relates it to [[squares]], to which it can be used as a simpler alternative. 14edo in the 14c val can be used as a tuning, in which case it is identical to squares, however.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 25/24, 245/243
 
{{Mapping|legend=1| 1 -1 1 -3 | 0 4 2 9 }}
 
: mapping generators: ~2, ~14/9
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1207.178{{c}}, ~14/9 = 777.414{{c}}
: [[error map]]: {{val| +7.178 +0.523 -24.308 +6.367 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~14/9 = 773.872{{c}}
: error map: {{val| 0.000 -6.464 -38.569 -3.973 }}
 
{{Optimal ET sequence|legend=1| 3d, …, 11cd, 14c }}
 
[[Badness]] (Sintel): 1.43
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 25/24, 45/44, 99/98
 
Mapping: {{mapping| 1 -1 1 -3 -3 | 0 4 2 9 10 }}
 
Optimal tunings:
* WE: ~2 = 1207.200{{c}}, ~11/7 = 777.363{{c}}
* CWE: ~2 = 1200.000{{c}}, ~11/7 = 773.777{{c}}
 
{{Optimal ET sequence|legend=0| 3de, …, 11cdee, 14c }}
 
Badness (Sintel): 1.09
 
[[Category:Temperament families]]
[[Category:Pages with mostly numerical content]]
[[Category:Dicot family| ]] <!-- main article -->
[[Category:Dicot| ]] <!-- key article -->
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Dicot_family"