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Catalog of rank-4 temperaments: Difference between revisions

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→Olympic (131072/130977): correct a ratio. Move part of the description of metaolympic to the no-17 extension
 
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==== Commas 2080/2079, 3250/3249, 4096/4095 ====
==== Commas 2080/2079, 3250/3249, 4096/4095 ====
This is a [[weak extension]] of olympic, requiring the split of the prime 7 in half; or alternatively, the septimal comma or the garischisma.
Subgroup: 2.3.5.7.11.13.19
Subgroup: 2.3.5.7.11.13.19


Line 1,023: Line 1,025:


Optimal tunings:
Optimal tunings:
* WE: ~2 = 1199.9639{{c}}, ~3/2 = 702.0643{{c}}, ~5/4 = 386.3218{{c}}, ~187/100 = 1084.4676{{c}}
* WE: ~2 = 1199.9639{{c}}, ~3/2 = 702.0643{{c}}, ~5/4 = 386.3218{{c}}, ~247/132 = 1084.4676{{c}}
: error map: {{val| -0.036 +0.073 -0.064 +0.073 +0.129 -0.166 -0.004 }}
: error map: {{val| -0.036 +0.073 -0.064 +0.073 +0.129 -0.166 -0.004 }}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.0887{{c}}, ~5/4 = 386.3257{{c}}, ~187/100 = 1084.5006{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.0887{{c}}, ~5/4 = 386.3257{{c}}, ~247/132 = 1084.5006{{c}}
: error map: {{val| 0.000 +0.134 +0.012 +0.175 +0.236 -0.032 +0.135 }}
: error map: {{val| 0.000 +0.134 +0.012 +0.175 +0.236 -0.032 +0.135 }}


Line 1,040: Line 1,042:


Optimal tunings:
Optimal tunings:
* WE: ~2 = 1199.9594{{c}}, ~3/2 = 702.0487{{c}}, ~5/4 = 386.3262{{c}}, ~187/100 = 1084.4677{{c}}
* WE: ~2 = 1199.9594{{c}}, ~3/2 = 702.0487{{c}}, ~5/4 = 386.3262{{c}}, ~247/132 = 1084.4677{{c}}
: error map: {{val| -0.041 +0.053 -0.069 +0.069 +0.163 -0.170 +0.005 +0.048 }}
: error map: {{val| -0.041 +0.053 -0.069 +0.069 +0.163 -0.170 +0.005 +0.048 }}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.0709{{c}}, ~5/4 = 386.3327{{c}}, ~187/100 = 1084.5064{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.0709{{c}}, ~5/4 = 386.3327{{c}}, ~247/132 = 1084.5064{{c}}
: error map: {{val| -0.000 +0.116 +0.019 +0.187 +0.302 -0.015 +0.171 +0.241 }}
: error map: {{val| -0.000 +0.116 +0.019 +0.187 +0.302 -0.015 +0.171 +0.241 }}


Line 1,050: Line 1,052:


==== Metaolympic ====
==== Metaolympic ====
Metaolympic is a [[weak extension]] of olympic, requiring the split of the prime 7 in half; or alternatively, the septimal comma or the garischisma. It is better without prime 17, but prime 17 can be added easily into the temperament by also tempering out 4200/4199, which also takes advantage of the split prime 7 at the cost of higher complexity.  
Metaolympic is the above extension with prime 17 added. It is better without prime 17, but prime 17 can be added easily into the temperament by also tempering out 4200/4199, which also takes advantage of the split prime 7 at the cost of higher complexity.  


Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17
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