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Landscape microtemperaments: Difference between revisions

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Switch to Sintel's badness, WE & CWE tunings (4/). + source of names
Switch to Sintel's badness, WE & CWE tunings (5/5)
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{{Mapping|legend=1| 30 2 15 66 | 0 5 6 2 }}
{{Mapping|legend=1| 30 2 15 66 | 0 5 6 2 }}
: mapping generators: ~53747712/52521875, ~216/175


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[WE]]: ~53747712/52521875 = 40.0002{{c}}, ~216/175 = 364.3890{{c}} (~{{monzo| 21 3 1 -10 }} = 4.3869{{c}})
* [[WE]]: ~53747712/52521875 = 40.0002{{c}}, ~216/175 = 364.3890{{c}} (~{{monzo| 21 3 1 -10 }} = 4.3869{{c}})
: [[error map]]: {{val| +0.007 -0.009 +0.024 -0.032 }}
* [[CWE]]: ~53747712/52521875 = 40.0000{{c}}, ~216/175 = 364.3879{{c}} (~{{monzo| 21 3 1 -10 }} = 4.3879{{c}})
* [[CWE]]: ~53747712/52521875 = 40.0000{{c}}, ~216/175 = 364.3879{{c}} (~{{monzo| 21 3 1 -10 }} = 4.3879{{c}})
: error map: {{val| 0.000 -0.015 +0.014 -0.050 }}


{{Optimal ET sequence|legend=1| 270, 1380, 1650, 1920, 2190, 4650 }}
{{Optimal ET sequence|legend=1| 270, 1380, 1650, 1920, 2190, 4650 }}
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[[Badness]] (Sintel): 1.88
[[Badness]] (Sintel): 1.88


=== 11-limit===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 702: Line 705:


Optimal tunings:  
Optimal tunings:  
* CTE: ~18865/18432 = 40.0000{{c}}, ~216/175 = 364.3886{{c}} (~385/384 = 4.3886{{c}})
* WE: ~18865/18432 = 40.0005{{c}}, ~216/175 = 364.3881{{c}} (~385/384 = 4.3837{{c}})
* CWE: ~18865/18432 = 40.0000{{c}}, ~216/175 = 364.3849{{c}} (~385/384 = 4.3849{{c}})
* CWE: ~18865/18432 = 40.0000{{c}}, ~216/175 = 364.3849{{c}} (~385/384 = 4.3849{{c}})


{{Optimal ET sequence|legend=0| 270, 1110, 1380, 1650, 1920, 2190 }}
{{Optimal ET sequence|legend=0| 270, 1110, 1380, 1650, 1920, 2190 }}


Badness (Smith): 0.0220
Badness (Sintel): 0.727


=== 13-limit ===
=== 13-limit ===
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Optimal tunings:  
Optimal tunings:  
* CTE: ~351/343 = 40.0000{{c}}, ~216/175 = 364.3879{{c}} (~385/384 = 4.3879{{c}})
* WE: ~351/343 = 40.0003{{c}}, ~216/175 = 364.3894{{c}} (~385/384 = 4.3865{{c}})
* CWE: ~351/343 = 40.0000{{c}}, ~216/175 = 364.3867{{c}} (~385/384 = 4.3867{{c}})
* CWE: ~351/343 = 40.0000{{c}}, ~216/175 = 364.3867{{c}} (~385/384 = 4.3867{{c}})


{{Optimal ET sequence|legend=0| 270, 1380, 1650, 1920, 2190, 4650, 6840e, 11490de }}
{{Optimal ET sequence|legend=0| 270, 1380, 1650, 1920, 2190, 4650, 6840e, 11490de }}


Badness (Smith): 0.0155
Badness (Sintel): 0.640


=== 2.3.5.7.11.13.19 subgroup (neozinc) ===
=== 2.3.5.7.11.13.19 subgroup (neozinc) ===
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Optimal tunings:  
Optimal tunings:  
* CTE: ~175/171 = 40.0000{{c}}, ~216/175 = 364.3876{{c}} (~400/399 = 4.3876{{c}})
* CTE: ~175/171 = 40.0002{{c}}, ~216/175 = 364.3885{{c}} (~400/399 = 4.3862{{c}})
* CWE: ~175/171 = 40.0000{{c}}, ~216/175 = 364.3864{{c}} (~400/399 = 4.3864{{c}})
* CWE: ~175/171 = 40.0000{{c}}, ~216/175 = 364.3864{{c}} (~400/399 = 4.3864{{c}})


{{Optimal ET sequence|legend=0| 270, 1380, 1650, 1920, 2190, 4650, 6840e }}
{{Optimal ET sequence|legend=0| 270, 1380, 1650, 1920, 2190, 4650, 6840e }}


Badness (Smith): 0.00921
Badness (Sintel): 0.477


== Poe ==
== Poe ==
Named by [[Tristan Bay]] in 2025, poe may be described as the {{nowrap| 60 & 270 }} temperament.
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


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{{Mapping|legend=1| 30 0 -73 -106 | 0 1 3 4 }}
{{Mapping|legend=1| 30 0 -73 -106 | 0 1 3 4 }}
: mapping generators: ~2240/2187, ~3


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2240/2187 = 40.000{{c}}, ~3/2 = 702.141{{c}}
* [[WE]]: ~2240/2187 = 39.9982{{c}}, ~3/2 = 702.1533{{c}}
* [[CWE]]: ~2240/2187 = 40.000{{c}}, ~3/2 = 702.166{{c}}
: [[error map]]: {{val| -0.055 +0.143 +0.115 -0.238 }}
* [[CWE]]: ~2240/2187 = 40.0000{{c}}, ~3/2 = 702.1656{{c}}
: error map: {{val| 0.000 +0.211 +0.183 -0.163 }}


{{Optimal ET sequence|legend=1| 60, 210, 270 }}
{{Optimal ET sequence|legend=1| 60, 150cd, 210, 270, 1950, 2220, 2490, 2760b, 3030bc, 3300bc }}


[[Badness]] (Sintel): 2.90
[[Badness]] (Sintel): 2.90
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Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 9801/9800, 19712/19683, 250047/250000
Comma list: 9801/9800, 19712/19683, 151263/151250


Mapping: {{mapping| 30 0 -73 -106 -134 | 0 1 3 4 5 }}
Mapping: {{mapping| 30 0 -73 -106 -134 | 0 1 3 4 5 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~45/44 = 40.000, ~3/2 = 702.182{{c}}
* WE: ~45/44 = 39.9976{{c}}, ~3/2 = 702.1955{{c}}
* CWE: ~45/44 = 40.000{{c}}, ~3/2 = 702.213{{c}}
* CWE: ~45/44 = 40.0000{{c}}, ~3/2 = 702.2129{{c}}


{{Optimal ET sequence|legend=0| 60e, 210e, 270 }}
{{Optimal ET sequence|legend=0| 60e, …, 210e, 270 }}


Badness (Sintel): 1.31
Badness (Sintel): 1.31
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Optimal tunings:  
Optimal tunings:  
* CTE: ~45/44 = 40.000{{c}}, ~3/2 = 702.182{{c}}
* WE: ~45/44 = 40.0008{{c}}, ~3/2 = 702.1778{{c}}
* CWE: ~45/44 = 40.000{{c}}, ~3/2 = 702.170{{c}}
* CWE: ~45/44 = 40.0000{{c}}, ~3/2 = 702.1699{{c}}


{{Optimal ET sequence|legend=0| 60e, 210e, 270 }}
{{Optimal ET sequence|legend=0| 60e, 210e, 270, 1410ef, 1680ef }}


Badness (Sintel): 1.19
Badness (Sintel): 1.19
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