Jubilismic family: Difference between revisions

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- POTE tunings
 
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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 '''jubilismic family''' of [[rank-3 temperament|rank-3]] [[regular temperament|temperaments]] [[tempering out|tempers out]] [[50/49]] in the full [[7-limit]]. It therefore identifies the two septimal tritones [[7/5]] and [[10/7]], an identification familiar from [[12edo]]. While many rank-3 temperaments are planar, a jubilismic temperament divides the [[2/1|octave]] in two. Related to this is the 2.5.7-subgroup {50/49} temperament [[jubilic]].  
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-01-03 17:28:43 UTC</tt>.<br>
: The original revision id was <tt>190734308</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">Jubilismic temperament tempers out the interval 50/49, variously called the tritonic diesis, jubilisma or [[http://en.wikipedia.org/wiki/Septimal_sixth-tone|septimal sixth-tone]]. It therefore identifies the two septimal tritones [[7_5|7/5]] and [[10_7|10/7]], an identification familiar from [[12edo]]. While most rank three temperaments are planar, jubilismic temperament divides the octave in two.


[[Comma]]: 50/49
== Jubilismic ==
[[Subgroup]]: 2.3.5.7


7 and 9 limit minimax tuning
[[Comma list]]: 50/49
[|1 0 0 0&gt;, |0 1 0 0&gt;, |-1/4 0 1/2 1/2&gt;,
|1/4 0 1/2 1/2&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 3/2, 35/32


Map: [&lt;2 0 0 1|, &lt;0 1 0 0|, &lt;0 0 1 1|]
{{Mapping|legend=1| 2 0 0 1 | 0 1 0 0 | 0 0 1 1 }}
[[Generator|Generators]]: 7/5, 3, 5
[[edo|Edos]]: [[10edo|10]], [[12edo|12]], [[22edo|22]], [[26edo|26]], [[38edo|38]], [[48edo|48]]
Scales: [[jubilismic10]]


==Jubilee==
: mapping generators: ~7/5, ~3, ~5
Commas: 50/49, 99/98


Map: [&lt;2 0 0 1 4|, &lt;0 1 0 0 -2|, &lt;0 0 1 1 2|]
[[Optimal tuning]]s:  
EDOS: 12, 22, 48
* [[WE]]: ~7/5 = 599.6673{{c}}, ~3/2 = 702.5906{{c}}, ~5/4 = 380.6287{{c}}
Badness: 0.000600
: [[error map]]: {{val| -0.665 -0.030 -7.016 +10.139 }}
* [[CWE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 702.4574{{c}}, ~5/4 = 380.0086{{c}}
: error map: {{val| 0.000 +0.502 -6.305 +11.183 }}


==Festival==
[[Minimax tuning]]:
Commas: 50/49, 45/44
* 7- and [[9-odd-limit]]
: {{monzo list| 1 0 0 0 | 0 1 0 0 | -1/4 0 1/2 1/2 | 1/4 0 1/2 1/2 }}
: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3.35


Map: [&lt;2 0 0 1 -4|, &lt;0 1 0 0 2|, &lt;0 0 1 1 1|]
{{Optimal ET sequence|legend=1| 4, 8d, 10, 12, 22, 34d, 48, 60d }}
EDOs: 10, 12, 26
Badness: 0.000689


==Fiesta==
[[Badness]] (Sintel): 0.561
Commas: 50/49, 56/55


Map: [&lt;2 0 0 1 7|, &lt;0 1 0 0 0|, &lt;0 0 1 1 0|]
Scales: [[jubilismic10]], [[jubilismic12]]
EDOs: 10, 12
Badness: 0.000717


==Jamboree==
== Jubilee ==
Commas: 50/49, 55/54
[[Subgroup]]: 2.3.5.7.11


Map: [&lt;-1 0 1 0 1|, &lt;0 1 0 0 0|, &lt;0 0 0 1 0|]
[[Comma list]]: 50/49, 99/98
EDOs: 10, 22
 
Badness: 0.000781
{{Mapping|legend=1| 2 0 0 1 4 | 0 1 0 0 -2 | 0 0 1 1 2 }}
</pre></div>
 
<h4>Original HTML content:</h4>
[[Optimal tuning]]s:  
<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;Jubilismic family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Jubilismic temperament tempers out the interval 50/49, variously called the tritonic diesis, jubilisma or &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Septimal_sixth-tone" rel="nofollow"&gt;septimal sixth-tone&lt;/a&gt;. It therefore identifies the two septimal tritones &lt;a class="wiki_link" href="/7_5"&gt;7/5&lt;/a&gt; and &lt;a class="wiki_link" href="/10_7"&gt;10/7&lt;/a&gt;, an identification familiar from &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;. While most rank three temperaments are planar, jubilismic temperament divides the octave in two.&lt;br /&gt;
* [[WE]]: ~7/5 = 599.6219{{c}}, ~3/2 = 702.9722{{c}}, ~5/4 = 380.4574{{c}}
&lt;br /&gt;
: [[error map]]: {{val| -0.756 +0.261 -7.369 +9.741 +0.628 }}
&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;: 50/49&lt;br /&gt;
* [[CWE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 702.9249{{c}}, ~5/4 = 379.6796{{c}}
&lt;br /&gt;
: error map: {{val| 0.000 +0.970 -6.634 +10.854 +2.192 }}
7 and 9 limit minimax tuning&lt;br /&gt;
 
[|1 0 0 0&amp;gt;, |0 1 0 0&amp;gt;, |-1/4 0 1/2 1/2&amp;gt;, &lt;br /&gt;
{{Optimal ET sequence|legend=1| 4, 8d, 10e, 12, 22, 34d, 48 }}
|1/4 0 1/2 1/2&amp;gt;]&lt;br /&gt;
 
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 3/2, 35/32&lt;br /&gt;
[[Badness]] (Sintel): 0.673
&lt;br /&gt;
 
Map: [&amp;lt;2 0 0 1|, &amp;lt;0 1 0 0|, &amp;lt;0 0 1 1|]&lt;br /&gt;
== Festival ==
&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 7/5, 3, 5&lt;br /&gt;
[[Subgroup]]: 2.3.5.7.11
&lt;a class="wiki_link" href="/edo"&gt;Edos&lt;/a&gt;: &lt;a class="wiki_link" href="/10edo"&gt;10&lt;/a&gt;, &lt;a class="wiki_link" href="/12edo"&gt;12&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo"&gt;22&lt;/a&gt;, &lt;a class="wiki_link" href="/26edo"&gt;26&lt;/a&gt;, &lt;a class="wiki_link" href="/38edo"&gt;38&lt;/a&gt;, &lt;a class="wiki_link" href="/48edo"&gt;48&lt;/a&gt;&lt;br /&gt;
 
Scales: &lt;a class="wiki_link" href="/jubilismic10"&gt;jubilismic10&lt;/a&gt;&lt;br /&gt;
[[Comma list]]: 45/44, 50/49
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Jubilee"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Jubilee&lt;/h2&gt;
{{Mapping|legend=1| 2 0 0 1 -4 | 0 1 0 0 2 | 0 0 1 1 1 }}
Commas: 50/49, 99/98&lt;br /&gt;
 
&lt;br /&gt;
[[Optimal tuning]]s:
Map: [&amp;lt;2 0 0 1 4|, &amp;lt;0 1 0 0 -2|, &amp;lt;0 0 1 1 2|]&lt;br /&gt;
* [[WE]]: ~7/5 = 600.8501{{c}}, ~3/2 = 694.6084{{c}}, ~5/4 = 371.7918{{c}}
EDOS: 12, 22, 48&lt;br /&gt;
: [[error map]]: {{val| +1.700 -5.646 -11.121 +7.216 +13.091 }}
Badness: 0.000600&lt;br /&gt;
* [[CWE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 694.5001{{c}}, ~5/4 = 372.9799{{c}}
&lt;br /&gt;
: error map: {{val| 0.000 -7.455 -13.334 +4.154 +10.662 }}
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-Festival"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Festival&lt;/h2&gt;
 
Commas: 50/49, 45/44&lt;br /&gt;
{{Optimal ET sequence|legend=1| 10, 12, 22e, 26 }}
&lt;br /&gt;
 
Map: [&amp;lt;2 0 0 1 -4|, &amp;lt;0 1 0 0 2|, &amp;lt;0 0 1 1 1|]&lt;br /&gt;
[[Badness]] (Sintel): 0.827
EDOs: 10, 12, 26&lt;br /&gt;
 
Badness: 0.000689&lt;br /&gt;
== Fiesta ==
&lt;br /&gt;
[[Subgroup]]: 2.3.5.7.11
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x-Fiesta"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Fiesta&lt;/h2&gt;
 
Commas: 50/49, 56/55&lt;br /&gt;
[[Comma list]]: 50/49, 56/55
&lt;br /&gt;
 
Map: [&amp;lt;2 0 0 1 7|, &amp;lt;0 1 0 0 0|, &amp;lt;0 0 1 1 0|]&lt;br /&gt;
{{Mapping|legend=1| 2 0 0 1 7 | 0 1 0 0 0 | 0 0 1 1 0 }}
EDOs: 10, 12&lt;br /&gt;
 
Badness: 0.000717&lt;br /&gt;
[[Optimal tuning]]:
&lt;br /&gt;
* [[WE]]: ~7/5 = 596.3068{{c}}, ~3/2 = 709.1930{{c}}, ~5/4 = 395.2472{{c}}
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x-Jamboree"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Jamboree&lt;/h2&gt;
: [[error map]]: {{val| -7.386 -0.148 -5.839 +7.955 +22.830 }}
Commas: 50/49, 55/54&lt;br /&gt;
* [[CWE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 709.6819{{c}}, ~5/4 = 391.4911{{c}}
&lt;br /&gt;
: error map: {{val| 0.000 +7.727 +5.177 +22.665 +48.682 }}
Map: [&amp;lt;-1 0 1 0 1|, &amp;lt;0 1 0 0 0|, &amp;lt;0 0 0 1 0|]&lt;br /&gt;
 
EDOs: 10, 22&lt;br /&gt;
{{Optimal ET sequence|legend=1| 8d, 10, 12, 22e, 30dee, 42ddeee }}
Badness: 0.000781&lt;/body&gt;&lt;/html&gt;</pre></div>
 
[[Badness]] (Sintel): 0.861
 
== Jamboree ==
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 50/49, 55/54
 
{{Mapping|legend=1| 2 0 0 1 2 | 0 1 0 0 3 | 0 0 1 1 -1 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~7/5 = 600.0436{{c}}, ~3/2 = 706.7073{{c}}, ~5/4 = 376.8582{{c}}
: [[error map]]: {{val| +0.087 +4.839 -9.281 +8.250 -7.880 }}
* [[CWE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 706.7334{{c}}, ~5/4 = 376.9332{{c}}
: error map: {{val| 0.000 +4.778 -9.381 +8.107 -8.051 }}
 
{{Optimal ET sequence|legend=1| 8d, 10, 12e, 14c, 22, 58ce }}
 
[[Badness]] (Sintel): 0.938
 
[[Category:Temperament families]]
[[Category:Pages with mostly numerical content]]
[[Category:Jubilismic family| ]] <!-- main article -->
[[Category:Jubilismic| ]] <!-- key article -->
[[Category:Rank 3]]

Latest revision as of 14:18, 22 July 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 jubilismic family of rank-3 temperaments tempers out 50/49 in the full 7-limit. It therefore identifies the two septimal tritones 7/5 and 10/7, an identification familiar from 12edo. While many rank-3 temperaments are planar, a jubilismic temperament divides the octave in two. Related to this is the 2.5.7-subgroup {50/49} temperament jubilic.

Jubilismic

Subgroup: 2.3.5.7

Comma list: 50/49

Mapping: [⟨2 0 0 1], ⟨0 1 0 0], ⟨0 0 1 1]]

mapping generators: ~7/5, ~3, ~5

Optimal tunings:

  • WE: ~7/5 = 599.6673 ¢, ~3/2 = 702.5906 ¢, ~5/4 = 380.6287 ¢
error map: ⟨-0.665 -0.030 -7.016 +10.139]
  • CWE: ~7/5 = 600.0000 ¢, ~3/2 = 702.4574 ¢, ~5/4 = 380.0086 ¢
error map: ⟨0.000 +0.502 -6.305 +11.183]

Minimax tuning:

[[1 0 0 0⟩, [0 1 0 0⟩, [-1/4 0 1/2 1/2⟩, [1/4 0 1/2 1/2⟩]
unchanged-interval (eigenmonzo) basis: 2.3.35

Optimal ET sequence: 4, 8d, 10, 12, 22, 34d, 48, 60d

Badness (Sintel): 0.561

Scales: jubilismic10, jubilismic12

Jubilee

Subgroup: 2.3.5.7.11

Comma list: 50/49, 99/98

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

Optimal tunings:

  • WE: ~7/5 = 599.6219 ¢, ~3/2 = 702.9722 ¢, ~5/4 = 380.4574 ¢
error map: ⟨-0.756 +0.261 -7.369 +9.741 +0.628]
  • CWE: ~7/5 = 600.0000 ¢, ~3/2 = 702.9249 ¢, ~5/4 = 379.6796 ¢
error map: ⟨0.000 +0.970 -6.634 +10.854 +2.192]

Optimal ET sequence: 4, 8d, 10e, 12, 22, 34d, 48

Badness (Sintel): 0.673

Festival

Subgroup: 2.3.5.7.11

Comma list: 45/44, 50/49

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

Optimal tunings:

  • WE: ~7/5 = 600.8501 ¢, ~3/2 = 694.6084 ¢, ~5/4 = 371.7918 ¢
error map: ⟨+1.700 -5.646 -11.121 +7.216 +13.091]
  • CWE: ~7/5 = 600.0000 ¢, ~3/2 = 694.5001 ¢, ~5/4 = 372.9799 ¢
error map: ⟨0.000 -7.455 -13.334 +4.154 +10.662]

Optimal ET sequence: 10, 12, 22e, 26

Badness (Sintel): 0.827

Fiesta

Subgroup: 2.3.5.7.11

Comma list: 50/49, 56/55

Mapping: [⟨2 0 0 1 7], ⟨0 1 0 0 0], ⟨0 0 1 1 0]]

Optimal tuning:

  • WE: ~7/5 = 596.3068 ¢, ~3/2 = 709.1930 ¢, ~5/4 = 395.2472 ¢
error map: ⟨-7.386 -0.148 -5.839 +7.955 +22.830]
  • CWE: ~7/5 = 600.0000 ¢, ~3/2 = 709.6819 ¢, ~5/4 = 391.4911 ¢
error map: ⟨0.000 +7.727 +5.177 +22.665 +48.682]

Optimal ET sequence: 8d, 10, 12, 22e, 30dee, 42ddeee

Badness (Sintel): 0.861

Jamboree

Subgroup: 2.3.5.7.11

Comma list: 50/49, 55/54

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

Optimal tunings:

  • WE: ~7/5 = 600.0436 ¢, ~3/2 = 706.7073 ¢, ~5/4 = 376.8582 ¢
error map: ⟨+0.087 +4.839 -9.281 +8.250 -7.880]
  • CWE: ~7/5 = 600.0000 ¢, ~3/2 = 706.7334 ¢, ~5/4 = 376.9332 ¢
error map: ⟨0.000 +4.778 -9.381 +8.107 -8.051]

Optimal ET sequence: 8d, 10, 12e, 14c, 22, 58ce

Badness (Sintel): 0.938

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