Ditonmic family: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
Wikispaces>guest
**Imported revision 357159938 - Original comment: **
Tags: Mobile edit Mobile web edit
 
(20 intermediate revisions by 8 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]] ([[ratio]]: 1220703125/1207959552, {{monzo|legend=1| -27 -2 13 }}).
: This revision was by author [[User:guest|guest]] and made on <tt>2012-08-10 04:14:50 UTC</tt>.<br>
: The original revision id was <tt>357159938</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 can be described as the 50 & 53 temperament. It splits [[~]][[8/5]] in two for a generator, which happens to be an interval very close in size to the [[ditone]], ~81/64. Note that the ditone itself is 52 generator steps away.


POTE generator: ~15625/12288 = 407.574
[[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 6 3 | 0 -13 -2 }}
Commas: 225/224, 2125764/2100875


POTE generator: ~1225/972 = 407.690
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~15625/12288 = 407.534
: [[error map]]: {{val| 0.000 +0.099 -1.382 }}
* [[POTE]]: ~2 = 1200.000, ~15625/12288 = 407.574
: error map: {{val| 0.000 -0.416 -1.462 }}


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]] (Smith): 0.167086
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 6 3 13 | 0 -13 -2 -30 }}
Commas: 99/98, 176/175, 325/324, 847/845


POTE generator: ~33/26 = 407.541
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~1225/972 = 407.642
: [[error map]]: {{val| 0.000 -1.298 -1.597 +1.921 }}
* [[POTE]]: ~2 = 1200.000, ~1225/972 = 407.690
: error map: {{val| 0.000 -1.921 -1.693 +0.483 }}


Map: [&lt;1 6 3 13 15 20|, &lt;0 -13 -2 -30 -34 -48|]
{{Optimal ET sequence|legend=1| 3d, 50, 53, 103, 156 }}
EDOs: 53
 
Badness: 0.0440</pre></div>
[[Badness]] (Smith): 0.064356
<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;Ditonmic family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This tempers out the ditonma, 1220703125/1207959552.&lt;br /&gt;
=== 11-limit ===
&lt;br /&gt;
Subgroup: 2.3.5.7.11
&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;
Comma list: 225/224, 385/384, 78408/78125
&lt;br /&gt;
 
POTE generator: ~15625/12288 = 407.574&lt;br /&gt;
Mapping: {{mapping| 1 6 3 13 -3 | 0 -13 -2 -30 19 }}
&lt;br /&gt;
 
Map: [&amp;lt;1 6 3|, &amp;lt;0 -13 -2|]&lt;br /&gt;
Optimal tunings:  
EDOs: 47, 50, 53, 474c, 527c&lt;br /&gt;
* CTE: ~2 = 1200.000, ~1225/972 = 407.688
Badness: 0.1671&lt;br /&gt;
* POTE: ~2 = 1200.000, ~1225/972 = 407.741
&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;
{{Optimal ET sequence|legend=0| 50, 53, 103 }}
Commas: 225/224, 2125764/2100875&lt;br /&gt;
 
&lt;br /&gt;
Badness (Smith): 0.044329
POTE generator: ~1225/972 = 407.690&lt;br /&gt;
 
&lt;br /&gt;
==== 13-limit ====
Map: [&amp;lt;1 6 3 13|, &amp;lt;0 -13 -2 -30|]&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
EDOs: 50, 53, 103, 156&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 225/224, 351/350, 385/384, 847/845
&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;
Mapping: {{mapping| 1 6 3 13 -3 2 | 0 -13 -2 -30 19 5 }}
&lt;br /&gt;
 
POTE generator: ~242/189 = 407.567&lt;br /&gt;
Optimal tunings:
&lt;br /&gt;
* CTE: ~2 = 1200.000, ~325/256 = 407.691
Map: [&amp;lt;1 6 3 13 15|, &amp;lt;0 -13 -2 -30 -34|]&lt;br /&gt;
* POTE: ~2 = 1200.000, ~325/256 = 407.736
EDOs: 53&lt;br /&gt;
 
Badness: 0.0639&lt;br /&gt;
{{Optimal ET sequence|legend=0| 50, 53, 103 }}
&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;
Badness (Smith): 0.024352
Commas: 99/98, 176/175, 325/324, 847/845&lt;br /&gt;
 
&lt;br /&gt;
=== Coditonic ===
POTE generator: ~33/26 = 407.541&lt;br /&gt;
Subgroup: 2.3.5.7.11
&lt;br /&gt;
 
Map: [&amp;lt;1 6 3 13 15 20|, &amp;lt;0 -13 -2 -30 -34 -48|]&lt;br /&gt;
Comma list: 99/98, 176/175, 6655/6561
EDOs: 53&lt;br /&gt;
 
Badness: 0.0440&lt;/body&gt;&lt;/html&gt;</pre></div>
Mapping: {{mapping| 1 6 3 13 15 | 0 -13 -2 -30 -34 }}
 
Optimal tunings:
* CTE: ~2 = 1200.000, ~242/189 = 407.528
* POTE: ~2 = 1200.000, ~242/189 = 407.567
 
{{Optimal ET sequence|legend=0| 3de, 50e, 53 }}
 
Badness (Smith): 0.063876
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 99/98, 176/175, 325/324, 847/845
 
Mapping: {{mapping| 1 6 3 13 15 20 | 0 -13 -2 -30 -34 -48 }}
 
Optimal tunings:
* CTE: ~2 = 1200.000, ~242/189 = 407.514
* POTE: ~2 = 1200.000, ~33/26 = 407.541
 
{{Optimal ET sequence|legend=0| 3def, 50eff, 53 }}
 
Badness (Smith): 0.043989
 
== Diton ==
This extension is known as ''ditonic'' in [[Graham Breed]]'s temperament finder.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 126/125, 8751645/8388608
 
{{Mapping|legend=1| 1 6 3 -4 | 0 -13 -2 20 }}
 
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~2625/2048 = 407.922
: [[error map]]: {{val| 0.000 -4.939 -2.157 -10.388 }}
* [[POTE]]: ~2 = 1200.000, ~2625/2048 = 407.954
: error map: {{val| 0.000 -5.353 -2.221 -9.751 }}
 
{{Optimal ET sequence|legend=1| 3, 47, 50 }}
 
[[Badness]] (Smith): 0.242101
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 126/125, 245/242, 2079/2048
 
Mapping: {{mapping| 1 6 3 -4 -3 | 0 -13 -2 20 19 }}
 
Optimal tunings:
* CTE: ~2 = 1200.000, ~14/11 = 407.930
* POTE: ~2 = 1200.000, ~14/11 = 407.892
 
{{Optimal ET sequence|legend=0| 3, 47, 50 }}
 
Badness (Smith): 0.100884
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 105/104, 126/125, 245/242, 1287/1280
 
Mapping: {{mapping| 1 6 3 -4 -3 2 | 0 -13 -2 20 19 5 }}
 
Optimal tunings:
* CTE: ~2 = 1200.000, ~14/11 = 407.933
* POTE: ~2 = 1200.000, ~14/11 = 407.887
 
{{Optimal ET sequence|legend=0| 3, 47, 50 }}
 
Badness (Smith): 0.054997
 
== Notes ==
 
[[Category:Temperament families]]
[[Category:Pages with mostly numerical content]]
[[Category:Ditonmic family| ]] <!-- main article -->
[[Category:Ditonmic]]
[[Category:Rank 2]]

Latest revision as of 00:29, 24 June 2025

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 ditonmic family of temperaments tempers out the ditonma (ratio: 1220703125/1207959552, monzo: [-27 -2 13⟩).

Ditonic

Named by Petr Pařízek in 2011[1], ditonic can be described as the 50 & 53 temperament. It splits ~8/5 in two for a generator, which happens to be an interval very close in size to the ditone, ~81/64. Note that the ditone itself is 52 generator steps away.

Subgroup: 2.3.5

Comma list: 1220703125/1207959552

Mapping: [⟨1 6 3], ⟨0 -13 -2]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~15625/12288 = 407.534
error map: ⟨0.000 +0.099 -1.382]
  • POTE: ~2 = 1200.000, ~15625/12288 = 407.574
error map: ⟨0.000 -0.416 -1.462]

Optimal ET sequence: 3, …, 47, 50, 53, 474c, 527c, 580c, 633c, 686c, 739c, 792c, 845cc

Badness (Smith): 0.167086

Coditone

Subgroup: 2.3.5.7

Comma list: 225/224, 2125764/2100875

Mapping: [⟨1 6 3 13], ⟨0 -13 -2 -30]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~1225/972 = 407.642
error map: ⟨0.000 -1.298 -1.597 +1.921]
  • POTE: ~2 = 1200.000, ~1225/972 = 407.690
error map: ⟨0.000 -1.921 -1.693 +0.483]

Optimal ET sequence: 3d, 50, 53, 103, 156

Badness (Smith): 0.064356

11-limit

Subgroup: 2.3.5.7.11

Comma list: 225/224, 385/384, 78408/78125

Mapping: [⟨1 6 3 13 -3], ⟨0 -13 -2 -30 19]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~1225/972 = 407.688
  • POTE: ~2 = 1200.000, ~1225/972 = 407.741

Optimal ET sequence: 50, 53, 103

Badness (Smith): 0.044329

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 225/224, 351/350, 385/384, 847/845

Mapping: [⟨1 6 3 13 -3 2], ⟨0 -13 -2 -30 19 5]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~325/256 = 407.691
  • POTE: ~2 = 1200.000, ~325/256 = 407.736

Optimal ET sequence: 50, 53, 103

Badness (Smith): 0.024352

Coditonic

Subgroup: 2.3.5.7.11

Comma list: 99/98, 176/175, 6655/6561

Mapping: [⟨1 6 3 13 15], ⟨0 -13 -2 -30 -34]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~242/189 = 407.528
  • POTE: ~2 = 1200.000, ~242/189 = 407.567

Optimal ET sequence: 3de, 50e, 53

Badness (Smith): 0.063876

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 99/98, 176/175, 325/324, 847/845

Mapping: [⟨1 6 3 13 15 20], ⟨0 -13 -2 -30 -34 -48]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~242/189 = 407.514
  • POTE: ~2 = 1200.000, ~33/26 = 407.541

Optimal ET sequence: 3def, 50eff, 53

Badness (Smith): 0.043989

Diton

This extension is known as ditonic in Graham Breed's temperament finder.

Subgroup: 2.3.5.7

Comma list: 126/125, 8751645/8388608

Mapping: [⟨1 6 3 -4], ⟨0 -13 -2 20]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~2625/2048 = 407.922
error map: ⟨0.000 -4.939 -2.157 -10.388]
  • POTE: ~2 = 1200.000, ~2625/2048 = 407.954
error map: ⟨0.000 -5.353 -2.221 -9.751]

Optimal ET sequence: 3, 47, 50

Badness (Smith): 0.242101

11-limit

Subgroup: 2.3.5.7.11

Comma list: 126/125, 245/242, 2079/2048

Mapping: [⟨1 6 3 -4 -3], ⟨0 -13 -2 20 19]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~14/11 = 407.930
  • POTE: ~2 = 1200.000, ~14/11 = 407.892

Optimal ET sequence: 3, 47, 50

Badness (Smith): 0.100884

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 105/104, 126/125, 245/242, 1287/1280

Mapping: [⟨1 6 3 -4 -3 2], ⟨0 -13 -2 20 19 5]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~14/11 = 407.933
  • POTE: ~2 = 1200.000, ~14/11 = 407.887

Optimal ET sequence: 3, 47, 50

Badness (Smith): 0.054997

Notes

  1. ↑ Yahoo! Tuning Group | Suggested names for the unclasified temperaments
Retrieved from "https://en.xen.wiki/index.php?title=Ditonmic_family&oldid=200842"