Gariboh 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 '''gariboh family''' of [[Rank-3 temperament|rank-3]] [[temperament]]s [[Tempering out|tempers out]] the gariboh comma, [[3125/3087]].  
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-08-22 13:01:33 UTC</tt>.<br>
: The original revision id was <tt>247705547</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">The gariboh family of [[planar temperament]]s tempers out the gariboh comma, 3125/3087.  


Comma: 3125/3087
== Gariboh ==
[[Subgroup]]: 2.3.5.7


Map: [&lt;1 0 0 0|, &lt;0 1 1 1|, &lt;0 0 3 5|]
[[Comma list]]: [[3125/3087]]
EDOs: 12, 29, 37, 41, 53, 94


[[Projection pair]]s: 5 15625/3087 7 9765625/1361367 to 2.3.25/7
{{Mapping|legend=1| 1 0 0 0 | 0 1 1 1 | 0 0 3 5 }}
</pre></div>
 
<h4>Original HTML content:</h4>
: Mapping generators: ~2, ~3, ~25/21
<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;Gariboh family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The gariboh family of &lt;a class="wiki_link" href="/planar%20temperament"&gt;planar temperament&lt;/a&gt;s tempers out the gariboh comma, 3125/3087. &lt;br /&gt;
 
&lt;br /&gt;
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3 = 702.4482, ~25/21 = 293.7397
Comma: 3125/3087&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 8d, 12, 29, 37, 41, 53, 94 }}
Map: [&amp;lt;1 0 0 0|, &amp;lt;0 1 1 1|, &amp;lt;0 0 3 5|]&lt;br /&gt;
 
EDOs: 12, 29, 37, 41, 53, 94&lt;br /&gt;
[[Badness]]: 0.614 × 10<sup>-3</sup>
&lt;br /&gt;
 
&lt;a class="wiki_link" href="/Projection%20pair"&gt;Projection pair&lt;/a&gt;s: 5 15625/3087 7 9765625/1361367 to 2.3.25/7&lt;/body&gt;&lt;/html&gt;</pre></div>
[[Projection pair]]s: 5 – 15625/3087, 7 – 9765625/1361367 to 2.3.25/7
 
== Undecimal gariboh ==
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 540/539, 3125/3087
 
{{Mapping|legend=1| 1 0 0 0 2 | 0 1 1 1 2 | 0 0 3 5 -7 }}
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3 = 702.7001, ~25/21 = 293.5587
 
{{Optimal ET sequence|legend=1| 8d, 12e, 25bccdd, 33cd, 37ee, 41, 53, 94, 229c }}
 
[[Badness]]: 1.75 × 10<sup>-3</sup>
 
=== 13-limit ===
[[Subgroup]]: 2.3.5.7.11.13
 
[[Comma list]]: 275/273, 325/324, 540/539
 
{{Mapping|legend=1| 1 0 0 0 2 2 | 0 1 1 1 2 2 | 0 0 3 5 -7 -6 }}
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3 = 702.5381, ~13/11 = 293.6878
 
{{Optimal ET sequence|legend=1| 8d, 12e, 33cd, 41, 53, 94 }}
 
== Androboh ==
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 100/99, 1375/1372
 
{{Mapping|legend=1| 1 0 0 0 2 | 0 1 1 1 0 | 0 0 3 5 6 }}
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3 = 705.0554, ~25/21 = 293.1102
 
{{Optimal ET sequence|legend=1| 8d, 12, 29, 37, 41, 90e, 131e }} *
 
<nowiki>*</nowiki> [[optimal patent val]]: [[119edo|119]]
 
[[Badness]]: 1.20 × 10<sup>-3</sup>
 
== Trismegiboh ==
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 3025/3024, 3125/3087
 
{{Mapping|legend=1| 1 0 0 0 2 | 0 1 1 1 1 | 0 0 6 10 -1 }}
 
: Mapping generators: ~2, ~3, ~12/11
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 702.5559, ~12/11 = 147.0103
 
{{Optimal ET sequence|legend=1| 8d, 16, 33cd, 41, 49 }}
 
=== 13-limit ===
[[Subgroup]]: 2.3.5.7.11.13
 
[[Comma list]]: 144/143, 275/273, 847/845
 
{{Mapping|legend=1| 1 0 0 0 2 2 | 0 1 1 1 1 1 | 0 0 6 10 -1 1 }}
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 702.9404, ~12/11 = 147.1132
 
{{Optimal ET sequence|legend=1| 8d, 16, 33cd, 41, 49f }}
 
=== 17-limit ===
[[Subgroup]]: 2.3.5.7.11.13.17
 
[[Comma list]]: 120/119, 144/143, 170/169, 847/845
 
{{Mapping|legend=1| 1 0 0 0 2 2 3 | 0 1 1 1 1 1 1 | 0 0 6 10 -1 1 -4 }}
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 703.0799, ~12/11 = 147.2446
 
{{Optimal ET sequence|legend=1| 8d, 16, 33cd, 41, 49fg }}
 
[[Category:Temperament families]]
[[Category:Pages with mostly numerical content]]
[[Category:Gariboh family| ]] <!-- main article -->
[[Category:Gariboh| ]] <!-- key article -->
[[Category:Rank 3]]

Latest revision as of 00:34, 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 gariboh family of rank-3 temperaments tempers out the gariboh comma, 3125/3087.

Gariboh

Subgroup: 2.3.5.7

Comma list: 3125/3087

Mapping: [⟨1 0 0 0], ⟨0 1 1 1], ⟨0 0 3 5]]

Mapping generators: ~2, ~3, ~25/21

Optimal tuning (POTE): ~2 = 1\1, ~3 = 702.4482, ~25/21 = 293.7397

Optimal ET sequence: 8d, 12, 29, 37, 41, 53, 94

Badness: 0.614 × 10-3

Projection pairs: 5 – 15625/3087, 7 – 9765625/1361367 to 2.3.25/7

Undecimal gariboh

Subgroup: 2.3.5.7.11

Comma list: 540/539, 3125/3087

Mapping: [⟨1 0 0 0 2], ⟨0 1 1 1 2], ⟨0 0 3 5 -7]]

Optimal tuning (POTE): ~2 = 1\1, ~3 = 702.7001, ~25/21 = 293.5587

Optimal ET sequence: 8d, 12e, 25bccdd, 33cd, 37ee, 41, 53, 94, 229c

Badness: 1.75 × 10-3

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 275/273, 325/324, 540/539

Mapping: [⟨1 0 0 0 2 2], ⟨0 1 1 1 2 2], ⟨0 0 3 5 -7 -6]]

Optimal tuning (POTE): ~2 = 1\1, ~3 = 702.5381, ~13/11 = 293.6878

Optimal ET sequence: 8d, 12e, 33cd, 41, 53, 94

Androboh

Subgroup: 2.3.5.7.11

Comma list: 100/99, 1375/1372

Mapping: [⟨1 0 0 0 2], ⟨0 1 1 1 0], ⟨0 0 3 5 6]]

Optimal tuning (POTE): ~2 = 1\1, ~3 = 705.0554, ~25/21 = 293.1102

Optimal ET sequence: 8d, 12, 29, 37, 41, 90e, 131e *

* optimal patent val: 119

Badness: 1.20 × 10-3

Trismegiboh

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 3125/3087

Mapping: [⟨1 0 0 0 2], ⟨0 1 1 1 1], ⟨0 0 6 10 -1]]

Mapping generators: ~2, ~3, ~12/11

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.5559, ~12/11 = 147.0103

Optimal ET sequence: 8d, 16, 33cd, 41, 49

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 144/143, 275/273, 847/845

Mapping: [⟨1 0 0 0 2 2], ⟨0 1 1 1 1 1], ⟨0 0 6 10 -1 1]]

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.9404, ~12/11 = 147.1132

Optimal ET sequence: 8d, 16, 33cd, 41, 49f

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 120/119, 144/143, 170/169, 847/845

Mapping: [⟨1 0 0 0 2 2 3], ⟨0 1 1 1 1 1 1], ⟨0 0 6 10 -1 1 -4]]

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 703.0799, ~12/11 = 147.2446

Optimal ET sequence: 8d, 16, 33cd, 41, 49fg

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