Gariboh family: Difference between revisions

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== 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{{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.

[[Subgroup]]: 2.3.5.7

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* [[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 }}

~~~~

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* [[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 }}

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* 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 }}

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* [[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 }} *

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* [[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 }}

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* 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 }}

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* 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 }}

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[[Category:Temperament families]]

~~[[Category:Pages with mostly numerical content]]~~

[[Category:Gariboh family| ]]

[[Category:Rank 3]]

@@ Line 3: / Line 3: @@
 == 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{{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.
 [[Subgroup]]: 2.3.5.7
@@ Line 15: / Line 19: @@
 * [[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 }}
@@ Line 35: / Line 38: @@
 * [[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, 90e, 94, 229c }}
@@ Line 51: / Line 53: @@
 * 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, 25bccddf, 33cd, 41, 53, 94 }}
@@ Line 69: / Line 70: @@
 * [[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 }} *
@@ Line 90: / Line 90: @@
 * [[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 }}
@@ Line 106: / Line 105: @@
 * 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 }}
@@ Line 122: / Line 120: @@
 * 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 }}
@@ Line 129: / Line 126: @@
 [[Category:Temperament families]]
-[[Category:Pages with mostly numerical content]]
 [[Category:Gariboh family| ]] <!-- main article -->
 [[Category:Rank 3]]