Gariboh family: Difference between revisions

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{{Technical data page}}
{{Technical data page}}
The '''gariboh family''' of [[Rank-3 temperament|rank-3]] [[temperament]]s [[Tempering out|tempers out]] the gariboh comma, [[3125/3087]].  
The '''gariboh family''' of [[rank-3 temperament|rank-3]] [[regular temperament|temperament]]s [[tempering out|tempers out]] the gariboh comma, [[3125/3087]].  


== Gariboh ==
== Gariboh ==
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{{Mapping|legend=1| 1 0 0 0 | 0 1 1 1 | 0 0 3 5 }}
{{Mapping|legend=1| 1 0 0 0 | 0 1 1 1 | 0 0 3 5 }}
: mapping generators: ~2, ~3, ~25/21


: Mapping generators: ~2, ~3, ~25/21
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3 = 702.4482{{c}}, ~25/21 = 293.7397{{c}}
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3 = 702.4482, ~25/21 = 293.7397


{{Optimal ET sequence|legend=1| 8d, 12, 29, 37, 41, 53, 94 }}
{{Optimal ET sequence|legend=1| 8d, 12, 29, 37, 41, 53, 94 }}


[[Badness]]: 0.614 × 10<sup>-3</sup>
[[Badness]] (Smith): 0.614 × 10<sup>-3</sup>


[[Projection pair]]s: 5 – 15625/3087, 7 – 9765625/1361367 to 2.3.25/7
[[Projection pair]]s: 5 – 15625/3087, 7 – 9765625/1361367 to 2.3.25/7
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{{Mapping|legend=1| 1 0 0 0 2 | 0 1 1 1 2 | 0 0 3 5 -7 }}
{{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 tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3 = 702.7001{{c}}, ~25/21 = 293.5587{{c}}


{{Optimal ET sequence|legend=1| 8d, 12e, 25bccdd, 33cd, 37ee, 41, 53, 94, 229c }}
{{Optimal ET sequence|legend=1| 8d, 12e, 25bccdd, 33cd, 37ee, 41, 53, 94, 229c }}


[[Badness]]: 1.75 × 10<sup>-3</sup>
[[Badness]] (Smith): 1.75 × 10<sup>-3</sup>


=== 13-limit ===
=== 13-limit ===
[[Subgroup]]: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


[[Comma list]]: 275/273, 325/324, 540/539
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 }}
Mapping: {{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 tuning (POTE): ~2 = 1200.0000{{c}}, ~3 = 702.5381{{c}}, ~13/11 = 293.6878{{c}}


{{Optimal ET sequence|legend=1| 8d, 12e, 33cd, 41, 53, 94 }}
{{Optimal ET sequence|legend=0| 8d, 12e, 33cd, 41, 53, 94 }}


== Androboh ==
== Androboh ==
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{{Mapping|legend=1| 1 0 0 0 2 | 0 1 1 1 0 | 0 0 3 5 6 }}
{{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 tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3 = 705.0554{{c}}, ~25/21 = 293.1102{{c}}


{{Optimal ET sequence|legend=1| 8d, 12, 29, 37, 41, 90e, 131e }} *
{{Optimal ET sequence|legend=1| 8d, 12, 29, 37, 41, 90e, 131e }} *
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<nowiki>*</nowiki> [[optimal patent val]]: [[119edo|119]]
<nowiki>*</nowiki> [[optimal patent val]]: [[119edo|119]]


[[Badness]]: 1.20 × 10<sup>-3</sup>
[[Badness]] (Smith): 1.20 × 10<sup>-3</sup>


== Trismegiboh ==
== Trismegiboh ==
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{{Mapping|legend=1| 1 0 0 0 2 | 0 1 1 1 1 | 0 0 6 10 -1 }}
{{Mapping|legend=1| 1 0 0 0 2 | 0 1 1 1 1 | 0 0 6 10 -1 }}
: mapping generators: ~2, ~3, ~12/11


: Mapping generators: ~2, ~3, ~12/11
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 702.5559{{c}}, ~12/11 = 147.0103{{c}}
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 702.5559, ~12/11 = 147.0103


{{Optimal ET sequence|legend=1| 8d, 16, 33cd, 41, 49 }}
{{Optimal ET sequence|legend=1| 8d, 16, 33cd, 41, 49 }}


=== 13-limit ===
=== 13-limit ===
[[Subgroup]]: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


[[Comma list]]: 144/143, 275/273, 847/845
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 }}
Mapping: {{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 tuning (POTE): ~2 = 1200.0000{{c}}, ~3/2 = 702.9404{{c}}, ~12/11 = 147.1132{{c}}


{{Optimal ET sequence|legend=1| 8d, 16, 33cd, 41, 49f }}
{{Optimal ET sequence|legend=0| 8d, 16, 33cd, 41, 49f }}


=== 17-limit ===
=== 17-limit ===
[[Subgroup]]: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


[[Comma list]]: 120/119, 144/143, 170/169, 847/845
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 }}
Mapping: {{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 tuning (POTE): ~2 = 1200.0000{{c}}, ~3/2 = 703.0799{{c}}, ~12/11 = 147.2446{{c}}


{{Optimal ET sequence|legend=1| 8d, 16, 33cd, 41, 49fg }}
{{Optimal ET sequence|legend=0| 8d, 16, 33cd, 41, 49fg }}


[[Category:Temperament families]]
[[Category:Temperament families]]

Revision as of 13:14, 8 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

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 = 1200.0000 ¢, ~3 = 702.4482 ¢, ~25/21 = 293.7397 ¢

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

Badness (Smith): 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 = 1200.0000 ¢, ~3 = 702.7001 ¢, ~25/21 = 293.5587 ¢

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

Badness (Smith): 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 = 1200.0000 ¢, ~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 = 1200.0000 ¢, ~3 = 705.0554 ¢, ~25/21 = 293.1102 ¢

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

* optimal patent val: 119

Badness (Smith): 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 = 1200.0000 ¢, ~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 = 1200.0000 ¢, ~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 = 1200.0000 ¢, ~3/2 = 703.0799 ¢, ~12/11 = 147.2446 ¢

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

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