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]] [[regular temperament|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 ==
Gariboh is generated by a perfect fifth and a narrow minor third of ~25/21, three make ~5/3 and five make ~7/3. [[94edo]] makes for an excellent tuning for it.


Map: [&lt;1 0 0 0|, &lt;0 1 1 1|, &lt;0 0 3 5|]
Another notable tuning is given by [[TE]], [[CTE]] and [[POTE]], all coinciding at 702.4482{{c}}, 293.7397{{c}} with pure octaves since prime 2 is not involved in the comma to begin with, though its difference from [[CWE]] is practically unnoticeable.
EDOs: 12, 29, 37, 41, 53, 94


[[Projection pair]]s: 5 15625/3087 7 9765625/1361367 to 2.3.25/7
[[Subgroup]]: 2.3.5.7
</pre></div>
 
<h4>Original HTML content:</h4>
[[Comma list]]: [[3125/3087]]
<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;
{{Mapping|legend=1| 1 0 0 0 | 0 1 1 1 | 0 0 3 5 }}
Comma: 3125/3087&lt;br /&gt;
: mapping generators: ~2, ~3, ~25/21
&lt;br /&gt;
 
Map: [&amp;lt;1 0 0 0|, &amp;lt;0 1 1 1|, &amp;lt;0 0 3 5|]&lt;br /&gt;
[[Optimal tuning]]s:
EDOs: 12, 29, 37, 41, 53, 94&lt;br /&gt;
* [[WE]]: ~2 = 1199.9983{{c}}, ~3/2 = 702.4472{{c}}, ~25/21 = 293.7393{{c}}
&lt;br /&gt;
: [[error map]]: {{val| -0.002 +0.490 -2.650 +2.316 }}
&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>
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.4468{{c}}, ~25/21 = 293.7395{{c}}
: error map: {{val| 0.000 +0.492 -2.648 +2.319 }}
 
{{Optimal ET sequence|legend=1| 8d, 12, 29, 37, 41, 53, 94 }}
 
[[Badness]] (Sintel): 2.71
 
[[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]]s:
* [[WE]]: ~2 = 1199.9983{{c}}, ~3/2 = 702.4472{{c}}, ~25/21 = 293.7393{{c}}
: [[error map]]: {{val| +0.086 +0.881 -2.738 +1.909 -0.531 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.7792{{c}}, ~25/21 = 293.5634{{c}}
: error map: {{val| 0.000 +0.824 -2.844 +1.770 -0.703 }}
 
{{Optimal ET sequence|legend=1| 8d, 12e, 25bccdd, 33cd, 37ee, 41, 53, 90e, 94, 229c }}
 
[[Badness]] (Sintel): 2.10
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 275/273, 325/324, 540/539
 
Mapping: {{mapping| 1 0 0 0 2 2 | 0 1 1 1 2 2 | 0 0 3 5 -7 -6 }}
 
Optimal tunings:  
* WE: ~2 = 1199.9929{{c}}, ~3/2 = 702.5339{{c}}, ~13/11 = 293.6861{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.5314{{c}}, ~13/11 = 293.6875{{c}}
 
{{Optimal ET sequence|legend=0| 8d, 12e, 25bccddf, 33cd, 41, 53, 94 }}
 
Badness (Sintel): 1.22
 
== 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]]s:
* [[WE]]: ~2 = 1199.2176{{c}}, ~3/2 = 704.5957{{c}}, ~25/21 = 292.9191{{c}}
: [[error map]]: {{val| -0.782 +1.858 -3.743 -0.417 +4.632 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 704.5845{{c}}, ~25/21 = 292.9597{{c}}
: error map: {{val| 0.000 +2.630 -2.850 +0.557 +6.440 }}
 
{{Optimal ET sequence|legend=1| 8d, 12, 29, 37, 41, 90e, 131e }} *
 
<nowiki>*</nowiki> [[optimal patent val]]: [[119edo|119]]
 
[[Badness]] (Sintel): 1.44
 
== 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]]s:
* [[WE]]: ~2 = 1199.5499{{c}}, ~3/2 = 702.2924{{c}}, ~12/11 = 146.9551{{c}}
: [[error map]]: {{val| -0.450 -0.113 -2.741 +2.568 +2.669 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.1698{{c}}, ~12/11 = 146.9960{{c}}
: error map: {{val| 0.000 +0.215 -2.168 +3.304 +3.856 }}
 
{{Optimal ET sequence|legend=1| 8d, 16, 24d, 33cd, 41, 65d, 90e, 106, 147 }}
 
[[Badness]] (Sintel): 3.38
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 144/143, 275/273, 847/845
 
Mapping: {{mapping| 1 0 0 0 2 2 | 0 1 1 1 1 1 | 0 0 6 10 -1 1 }}
 
Optimal tunings:
* WE: ~2 = 1198.9833{{c}}, ~3/2 = 702.3448{{c}}, ~12/11 = 146.9886{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.0567{{c}}, ~12/11 = 147.0902{{c}}
 
{{Optimal ET sequence|legend=0| 8d, 16, 24d, 33cd, 41, 65d, 106f }}
 
Badness (Sintel): 1.83
 
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 120/119, 144/143, 170/169, 847/845
 
Mapping: {{mapping| 1 0 0 0 2 2 3 | 0 1 1 1 1 1 1 | 0 0 6 10 -1 1 -4 }}
 
Optimal tunings:
* WE: ~2 = 1198.6534{{c}}, ~3/2 = 702.2909{{c}}, ~12/11 = 147.0794{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.8744{{c}}, ~12/11 = 147.2433{{c}}
 
{{Optimal ET sequence|legend=0| 8d, 16, 24d, 33cd, 41, 49fg, 65d, 106fg }}
 
Badness (Sintel): 1.55
 
[[Category:Temperament families]]
[[Category:Gariboh family| ]] <!-- main article -->
[[Category:Rank 3]]

Latest revision as of 12:23, 27 November 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

Gariboh is generated by a perfect fifth and a narrow minor third of ~25/21, three make ~5/3 and five make ~7/3. 94edo makes for an excellent tuning for it.

Another notable tuning is given by TE, CTE and POTE, all coinciding at 702.4482 ¢, 293.7397 ¢ with pure octaves since prime 2 is not involved in the comma to begin with, though its difference from CWE is practically unnoticeable.

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 tunings:

  • WE: ~2 = 1199.9983 ¢, ~3/2 = 702.4472 ¢, ~25/21 = 293.7393 ¢
error map: ⟨-0.002 +0.490 -2.650 +2.316]
  • CWE: ~2 = 1200.0000 ¢, ~3/2 = 702.4468 ¢, ~25/21 = 293.7395 ¢
error map: ⟨0.000 +0.492 -2.648 +2.319]

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

Badness (Sintel): 2.71

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 tunings:

  • WE: ~2 = 1199.9983 ¢, ~3/2 = 702.4472 ¢, ~25/21 = 293.7393 ¢
error map: ⟨+0.086 +0.881 -2.738 +1.909 -0.531]
  • CWE: ~2 = 1200.0000 ¢, ~3/2 = 702.7792 ¢, ~25/21 = 293.5634 ¢
error map: ⟨0.000 +0.824 -2.844 +1.770 -0.703]

Optimal ET sequence: 8d, 12e, 25bccdd, 33cd, 37ee, 41, 53, 90e, 94, 229c

Badness (Sintel): 2.10

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 tunings:

  • WE: ~2 = 1199.9929 ¢, ~3/2 = 702.5339 ¢, ~13/11 = 293.6861 ¢
  • CWE: ~2 = 1200.0000 ¢, ~3/2 = 702.5314 ¢, ~13/11 = 293.6875 ¢

Optimal ET sequence: 8d, 12e, 25bccddf, 33cd, 41, 53, 94

Badness (Sintel): 1.22

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 tunings:

  • WE: ~2 = 1199.2176 ¢, ~3/2 = 704.5957 ¢, ~25/21 = 292.9191 ¢
error map: ⟨-0.782 +1.858 -3.743 -0.417 +4.632]
  • CWE: ~2 = 1200.0000 ¢, ~3/2 = 704.5845 ¢, ~25/21 = 292.9597 ¢
error map: ⟨0.000 +2.630 -2.850 +0.557 +6.440]

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

* optimal patent val: 119

Badness (Sintel): 1.44

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 tunings:

  • WE: ~2 = 1199.5499 ¢, ~3/2 = 702.2924 ¢, ~12/11 = 146.9551 ¢
error map: ⟨-0.450 -0.113 -2.741 +2.568 +2.669]
  • CWE: ~2 = 1200.0000 ¢, ~3/2 = 702.1698 ¢, ~12/11 = 146.9960 ¢
error map: ⟨0.000 +0.215 -2.168 +3.304 +3.856]

Optimal ET sequence: 8d, 16, 24d, 33cd, 41, 65d, 90e, 106, 147

Badness (Sintel): 3.38

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 tunings:

  • WE: ~2 = 1198.9833 ¢, ~3/2 = 702.3448 ¢, ~12/11 = 146.9886 ¢
  • CWE: ~2 = 1200.0000 ¢, ~3/2 = 702.0567 ¢, ~12/11 = 147.0902 ¢

Optimal ET sequence: 8d, 16, 24d, 33cd, 41, 65d, 106f

Badness (Sintel): 1.83

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 tunings:

  • WE: ~2 = 1198.6534 ¢, ~3/2 = 702.2909 ¢, ~12/11 = 147.0794 ¢
  • CWE: ~2 = 1200.0000 ¢, ~3/2 = 701.8744 ¢, ~12/11 = 147.2433 ¢

Optimal ET sequence: 8d, 16, 24d, 33cd, 41, 49fg, 65d, 106fg

Badness (Sintel): 1.55

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