Gariboh family: Difference between revisions

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m Units & misc. cleanup
Switch to Sintel's badness, WE & CWE tunings, per community consensus
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: 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]]s:
* [[WE]]: ~2 = 1199.9983{{c}}, ~3/2 = 702.4472{{c}}, ~25/21 = 293.7393{{c}}
: [[error map]]: {{val| -0.002 +0.490 -2.650 +2.316 }}
* [[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 }}
<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.4482{{c}}, ~25/21 = 293.7397{{c}} -->


{{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]] (Smith): 0.614 × 10<sup>-3</sup>
[[Badness]] (Sintel): 2.71


[[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
Line 25: Line 30:
{{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 = 1200.0000{{c}}, ~3 = 702.7001{{c}}, ~25/21 = 293.5587{{c}}
[[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 }}
<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 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, 90e, 94, 229c }}


[[Badness]] (Smith): 1.75 × 10<sup>-3</sup>
[[Badness]] (Sintel): 2.10


=== 13-limit ===
=== 13-limit ===
Line 38: Line 48:
Mapping: {{mapping| 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 = 1200.0000{{c}}, ~3 = 702.5381{{c}}, ~13/11 = 293.6878{{c}}
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}}
<!-- * POTE: ~2 = 1200.0000{{c}}, ~3/2 = 702.5381{{c}}, ~13/11 = 293.6878{{c}} -->


{{Optimal ET sequence|legend=0| 8d, 12e, 33cd, 41, 53, 94 }}
{{Optimal ET sequence|legend=0| 8d, 12e, 25bccddf, 33cd, 41, 53, 94 }}
 
Badness (Sintel): 1.22


== Androboh ==
== Androboh ==
Line 49: Line 64:
{{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 = 1200.0000{{c}}, ~3 = 705.0554{{c}}, ~25/21 = 293.1102{{c}}
[[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 }}
<!-- * [[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 }} *
Line 55: Line 75:
<nowiki>*</nowiki> [[optimal patent val]]: [[119edo|119]]
<nowiki>*</nowiki> [[optimal patent val]]: [[119edo|119]]


[[Badness]] (Smith): 1.20 × 10<sup>-3</sup>
[[Badness]] (Sintel): 1.44


== Trismegiboh ==
== Trismegiboh ==
Line 65: Line 85:
: 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]]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 }}
<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.5559{{c}}, ~12/11 = 147.0103{{c}} -->
 
{{Optimal ET sequence|legend=1| 8d, 16, 24d, 33cd, 41, 65d, 90e, 106, 147 }}


{{Optimal ET sequence|legend=1| 8d, 16, 33cd, 41, 49 }}
[[Badness]] (Sintel): 3.38


=== 13-limit ===
=== 13-limit ===
Line 76: Line 103:
Mapping: {{mapping| 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 = 1200.0000{{c}}, ~3/2 = 702.9404{{c}}, ~12/11 = 147.1132{{c}}
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}}
<!-- * POTE: ~2 = 1200.0000{{c}}, ~3/2 = 702.9404{{c}}, ~12/11 = 147.1132{{c}} -->
 
{{Optimal ET sequence|legend=0| 8d, 16, 24d, 33cd, 41, 65d, 106f }}


{{Optimal ET sequence|legend=0| 8d, 16, 33cd, 41, 49f }}
Badness (Sintel): 1.83


=== 17-limit ===
=== 17-limit ===
Line 87: Line 119:
Mapping: {{mapping| 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 = 1200.0000{{c}}, ~3/2 = 703.0799{{c}}, ~12/11 = 147.2446{{c}}
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}}
<!-- * POTE: ~2 = 1200.0000{{c}}, ~3/2 = 703.0799{{c}}, ~12/11 = 147.2446{{c}} -->
 
{{Optimal ET sequence|legend=0| 8d, 16, 24d, 33cd, 41, 49fg, 65d, 106fg }}


{{Optimal ET sequence|legend=0| 8d, 16, 33cd, 41, 49fg }}
Badness (Sintel): 1.55


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

Revision as of 17:23, 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 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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