Xenharmonic Wiki

Ditonmic family: Difference between revisions

VisualWikitext
Wikispaces>genewardsmith
**Imported revision 330232786 - Original comment: **
 
m Text replacement - "Mapping: {{mapping| " to "{{Mapping|legend=0| "
Tags: Mobile edit Mobile web edit
 
(27 intermediate revisions by 10 users not shown)
Line 1: Line 1:
<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 '''ditonmic family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[ditonma]] ({{monzo|legend=1| -27 -2 13 }}, [[ratio]]: 1 220 703 125 / 1 207 959 552).
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-05-04 18:01:55 UTC</tt>.<br>
: The original revision id was <tt>330232786</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">This tempers out the ditonma, 1220703125/1207959552.


=Ditonic=
== Ditonic ==
Commas: 1220703125/1207959552
Named by [[Petr Pařízek]] in 2011<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>, ditonic splits [[~]][[5/2]] in two for a generator, which happens to be an interval very close in size to the [[octave complement]] of the ditone (i.e. the Pythagorean major third, [[81/64]]). It can be described as 3 & 53, and is part of the [[schismic–Mercator equivalence continuum]] with equivalence number ''n'' = 13/2. Its [[ploidacot]] is eta-13-cot. Note that the ditone itself is 52 generator steps away.


POTE generator: ~15625/12288 = 415.927
[[Subgroup]]: 2.3.5


Map: [&lt;1 6 3|, &lt;0 -13 -2|]
[[Comma list]]: 1220703125/1207959552
EDOs: 47, 50, 53, 474c, 527c
Badness: 0.1671


=Coditone=
{{Mapping|legend=1| 1 -7 1 | 0 13 2 }}
Commas: 225/224, 2125764/2100875
: mapping generators: ~2, ~24576/15625


POTE generator: ~1225/972 = 407.690
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.2971{{c}}, ~24576/15625 = 792.6223{{c}}
: [[error map]]: {{val| +0.297 +0.055 -0.772 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~24576/15625 = 792.4403{{c}}
: error map: {{val| 0.000 -0.231 -1.433 }}


Map: [&lt;1 6 3 13|, &lt;0 -13 -2 -30|]
{{Optimal ET sequence|legend=1| 3, …, 47, 50, 53, 474c, 527c, 580c, 633c, 686c, 739c, 792c, 845cc }}
EDOs: 50, 53, 103, 156


==11-limit==
[[Badness]] (Sintel): 3.92
Commas: 99/98, 176/175, 6655/6561


POTE generator: ~242/189 = 407.567
== Coditone ==
[[Subgroup]]: 2.3.5.7


Map: [&lt;1 6 3 13 15|, &lt;0 -13 -2 -30 -34|]
[[Comma list]]: 225/224, 2125764/2100875
EDOs: 53
Badness: 0.0639


==13-limit==
{{Mapping|legend=1| 1 -7 1 -17 | 0 13 2 30 }}
Commas: 99/98, 176/175, 325/324, 847/845


POTE generator: ~33/26 = 407.541
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1200.4411{{c}}, ~1944/1225 = 792.6016{{c}}
: [[error map]]: {{val| +0.441 -1.223 -0.669 +1.722 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~1944/1225 = 792.3270{{c}}
: error map: {{val| 0.000 -1.704 -1.660 +0.985 }}


Map: [&lt;1 6 3 13 15 20|, &lt;0 -13 -2 -30 -34 -48|]
{{Optimal ET sequence|legend=1| 50, 53, 103, 156 }}
EDOs: 53
Badness: 0.0440


[[Badness]] (Sintel): 1.63


</pre></div>
=== 11-limit ===
<h4>Original HTML content:</h4>
Subgroup: 2.3.5.7.11
<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;Ditonmic family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This tempers out the ditonma, 1220703125/1207959552.&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 225/224, 385/384, 78408/78125
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Ditonic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Ditonic&lt;/h1&gt;
 
Commas: 1220703125/1207959552&lt;br /&gt;
{{Mapping|legend=0| 1 -7 1 -17 16 | 0 13 2 30 -19 }}
&lt;br /&gt;
 
POTE generator: ~15625/12288 = 415.927&lt;br /&gt;
Optimal tunings:  
&lt;br /&gt;
* WE: ~2 = 1200.8016{{c}}, ~198/125 = 792.7878{{c}}
Map: [&amp;lt;1 6 3|, &amp;lt;0 -13 -2|]&lt;br /&gt;
* CWE: ~2 = 1200.0000{{c}}, ~198/125 = 792.2692{{c}}
EDOs: 47, 50, 53, 474c, 527c&lt;br /&gt;
 
Badness: 0.1671&lt;br /&gt;
{{Optimal ET sequence|legend=0| 50, 53, 103, 259be, 362bcee }}
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Coditone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Coditone&lt;/h1&gt;
Badness (Sintel): 1.47
Commas: 225/224, 2125764/2100875&lt;br /&gt;
 
&lt;br /&gt;
==== 13-limit ====
POTE generator: ~1225/972 = 407.690&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
&lt;br /&gt;
 
Map: [&amp;lt;1 6 3 13|, &amp;lt;0 -13 -2 -30|]&lt;br /&gt;
Comma list: 225/224, 351/350, 385/384, 847/845
EDOs: 50, 53, 103, 156&lt;br /&gt;
 
&lt;br /&gt;
{{Mapping|legend=0| 1 -7 1 -17 16 7 | 0 13 2 30 -19 -5 }}
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Coditone-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;11-limit&lt;/h2&gt;
 
Commas: 99/98, 176/175, 6655/6561 &lt;br /&gt;
Optimal tunings:
&lt;br /&gt;
* WE: ~2 = 1200.7372{{c}}, ~198/125 = 792.7511{{c}}
POTE generator: ~242/189 = 407.567&lt;br /&gt;
* CWE: ~2 = 1200.0000{{c}}, ~198/125 = 792.2715{{c}}
&lt;br /&gt;
 
Map: [&amp;lt;1 6 3 13 15|, &amp;lt;0 -13 -2 -30 -34|]&lt;br /&gt;
{{Optimal ET sequence|legend=0| 50, 53, 103, 259be, 362bceef }}
EDOs: 53&lt;br /&gt;
 
Badness: 0.0639&lt;br /&gt;
Badness (Sintel): 1.01
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Coditone-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;13-limit&lt;/h2&gt;
=== Coditonic ===
Commas: 99/98, 176/175, 325/324, 847/845&lt;br /&gt;
Subgroup: 2.3.5.7.11
&lt;br /&gt;
 
POTE generator: ~33/26 = 407.541&lt;br /&gt;
Comma list: 99/98, 176/175, 6655/6561
&lt;br /&gt;
 
Map: [&amp;lt;1 6 3 13 15 20|, &amp;lt;0 -13 -2 -30 -34 -48|]&lt;br /&gt;
{{Mapping|legend=0| 1 -7 1 -17 -19 | 0 13 2 30 34 }}
EDOs: 53&lt;br /&gt;
 
Badness: 0.0440&lt;/body&gt;&lt;/html&gt;</pre></div>
Optimal tunings:
* WE: ~2 = 1200.3578{{c}}, ~189/121 = 792.6693{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~189/121 = 792.4463{{c}}
 
{{Optimal ET sequence|legend=0| 3de, 50e, 53 }}
 
Badness (Sintel): 2.11
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 99/98, 176/175, 325/324, 847/845
 
{{Mapping|legend=0| 1 -7 1 -17 -19 -28 | 0 13 2 30 34 48 }}
 
Optimal tunings:
* WE: ~2 = 1200.2797{{c}}, ~52/33 = 792.6439{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~52/33 = 792.4682{{c}}
 
{{Optimal ET sequence|legend=0| 3def, 50eff, 53 }}
 
Badness (Sintel): 1.82
 
== Diton ==
This low-accuracy temperament was considered the canonical extension of ditonic, and catalogued as so in [[Graham Breed]]'s Temperament Finder.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 126/125, 8751645/8388608
 
{{Mapping|legend=1| 1 -7 1 16 | 0 13 2 -20 }}
 
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1201.9455{{c}}, ~2048/1323 = 793.3304{{c}}
: [[error map]]: {{val| +1.946 -2.278 +2.293 -4.305 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~2048/1323 = 792.0527{{c}}
: error map: {{val| 0.000 -5.270 -2.208 -9.879 }}
 
{{Optimal ET sequence|legend=1| 3, 47, 50 }}
 
[[Badness]] (Sintel): 6.13
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 126/125, 245/242, 2079/2048
 
{{Mapping|legend=0| 1 -7 1 16 16 | 0 13 2 -20 -19 }}
 
Optimal tunings:
* WE: ~2 = 1201.6076{{c}}, ~11/7 = 793.1692{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/7 = 792.1016{{c}}
 
{{Optimal ET sequence|legend=0| 3, 47, 50 }}
 
Badness (Sintel): 3.34
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 105/104, 126/125, 245/242, 1287/1280
 
{{Mapping|legend=0| 1 -7 1 16 16 7 | 0 13 2 -20 -19 -5 }}
 
Optimal tunings:
* WE: ~2 = 1201.3885{{c}}, ~11/7 = 793.0294{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/7 = 792.1096{{c}}
 
{{Optimal ET sequence|legend=0| 3, 47, 50 }}
 
Badness (Sintel): 2.27
 
== References ==
 
[[Category:Ditonmic family| ]] <!-- main article -->
[[Category:Ditonic]] <!-- key article -->
[[Category:Temperament families]]
[[Category:Catalogs of rank-2 temperaments]]
Retrieved from "https://en.xen.wiki/w/Ditonmic_family"