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Hemimean clan: Difference between revisions

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Switch to Sintel's badness, WE & CWE tunings (2/); restore the name *semihemiwürschmidt*, as there's no internal conflict
Switch to Sintel's badness, WE & CWE tunings (3/)
 
Line 213: Line 213:
* CWE: ~2 = 1200.0000{{c}}, ~220/147 = 696.9548{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~220/147 = 696.9548{{c}}


{{Optimal ET sequence|legend=1| 31, 105be, 136e, 167, 198, 427c }}
{{Optimal ET sequence|legend=0| 31, 105be, 136e, 167, 198, 427c }}


Badness (Sintel): 1.15
Badness (Sintel): 1.15
Line 259: Line 259:
* CWE: ~17/12 = 600.0000{{c}}, ~28/25 = 193.9092{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~28/25 = 193.9092{{c}}


{{Optimal ET sequence|legend=1| 62e, 68, 130, 198 }}
{{Optimal ET sequence|legend=0| 62e, 68, 130, 198 }}


Badness (Sintel): 1.48
Badness (Sintel): 1.48
Line 274: Line 274:
* CWE: ~17/12 = 600.0000{{c}}, ~19/17 = 193.9128{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~19/17 = 193.9128{{c}}


{{Optimal ET sequence|legend=1| 62e, 68, 130, 198 }}
{{Optimal ET sequence|legend=0| 62e, 68, 130, 198 }}


Badness (Sintel): 1.32
Badness (Sintel): 1.32
Line 289: Line 289:
* CWE: ~17/12 = 600.0000{{c}}, ~28/25 = 193.9238{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~28/25 = 193.9238{{c}}


{{Optimal ET sequence|legend=1| 68, 130g, 198g }}
{{Optimal ET sequence|legend=0| 68, 130g, 198g }}


Badness (Sintel): 1.51
Badness (Sintel): 1.51
Line 304: Line 304:
* CWE: ~17/12 = 600.0000{{c}}, ~28/25 = 193.9417{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~28/25 = 193.9417{{c}}


{{Optimal ET sequence|legend=1| 68, 130gh, 198gh }}
{{Optimal ET sequence|legend=0| 68, 130gh, 198gh }}


Badness (Sintel): 1.80
Badness (Sintel): 1.80
Line 315: Line 315:
[[Comma list]]: 1029/1024, 3136/3125
[[Comma list]]: 1029/1024, 3136/3125


{{Mapping|legend=1| 1 4 2 2 | 0 -15 2 5 }}
{{Mapping|legend=1| 1 -11 4 7 | 0 15 -2 -5 }}
: mapping generators: ~2, ~25/14


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~28/25 = 193.244
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.3104{{c}}, ~25/14 = 1007.0160{{c}} (~28/25 = 193.2944{{c}})
: [[error map]]: {{val| +0.310 -0.129 +0.896 -1.733 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~25/14 = 1006.7606{{c}} (~28/25 = 193.2394{{c}})
: error map: {{val| 0.000 -0.545 +0.165 -2.629 }}


[[Minimax tuning]]:
[[Minimax tuning]]:
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: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/7
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/7


{{Optimal ET sequence|legend=1| 25, 31, 87, 118 }}
{{Optimal ET sequence|legend=1| 25, 31, 87, 118, 267d, 385d }}


[[Badness]]: 0.044284
[[Badness]] (Sintel): 1.12


=== 11-limit ===
=== 11-limit ===
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Comma list: 385/384, 441/440, 3136/3125
Comma list: 385/384, 441/440, 3136/3125


{{Mapping|legend=0| 1 4 2 2 7 | 0 -15 2 5 -22 }}
{{Mapping|legend=0| 1 -11 4 7 -15 | 0 15 -2 -5 22 }}


Optimal tuning (POTE): ~2 = 1\1, ~28/25 = 193.227
Optimal tunings:
* WE: ~2 = 1200.3576{{c}}, ~25/14 = 1007.0732{{c}} (~28/25 = 193.2844{{c}})
* CWE: ~2 = 1200.0000{{c}}, ~25/14 = 1006.7807{{c}} (~28/25 = 193.2193{{c}})


Minimax tuning:
Minimax tuning:
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: Eigenmonzos (unchanged-intervals): 2, 11/7
: Eigenmonzos (unchanged-intervals): 2, 11/7


{{Optimal ET sequence|legend=1| 25e, 31, 87, 118 }}
{{Optimal ET sequence|legend=0| 25e, 31, 87, 118 }}


Badness: 0.019003
Badness (Sintel): 0.628


=== 13-limit ===
=== 13-limit ===
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Comma list: 196/195, 352/351, 385/384, 625/624
Comma list: 196/195, 352/351, 385/384, 625/624


{{Mapping|legend=0| 1 4 2 2 7 0 | 0 -15 2 5 -22 23 }}
{{Mapping|legend=0| 1 4 2 2 7 0 | 0 15 -2 -5 22 -23 }}


Optimal tuning (POTE): ~2 = 1\1, ~28/25 = 193.166
Optimal tunings:
* WE: ~2 = 1200.0602{{c}}, ~25/14 = 1006.8844{{c}} (~28/25 = 193.1757{{c}})
* CWE: ~2 = 1200.0000{{c}}, ~25/14 = 1006.8343{{c}} (~28/25 = 193.1457{{c}})


{{Optimal ET sequence|legend=1| 31, 56, 87, 118, 205d }}
{{Optimal ET sequence|legend=0| 31, 56, 87, 118, 205d }}


Badness: 0.021738
Badness (Sintel): 0.898


== Spell ==
== Spell ==
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{{Mapping|legend=1| 1 0 2 2 | 0 10 2 5 }}
{{Mapping|legend=1| 1 0 2 2 | 0 10 2 5 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~28/25 = 189.927
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1202.8089{{c}}, ~28/25 = 190.3712{{c}}
: [[error map]]: {{val| +2.809 +1.757 +0.047 -11.352 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~28/25 = 190.1078{{c}}
: error map: {{val| 0.000 -0.877 -6.098 -18.287 }}


{{Optimal ET sequence|legend=1| 6, 19, 82dd }}
{{Optimal ET sequence|legend=1| 6, 13b, 19, 82dd }}


[[Badness]]: 0.080958
[[Badness]] (Sintel): 2.05


=== 11-limit ===
=== 11-limit ===
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{{Mapping|legend=0| 1 0 2 2 3 | 0 10 2 5 3 }}
{{Mapping|legend=0| 1 0 2 2 3 | 0 10 2 5 3 }}


Optimal tuning (POTE): ~2 = 1\1, ~11/10 = 190.285
Optimal tunings:
* WE: ~2 = 1200.4163{{c}}, ~11/10 = 190.3511{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 190.3091{{c}}


{{Optimal ET sequence|legend=1| 6, 19, 44de, 63dee, 82ddee }}
{{Optimal ET sequence|legend=0| 6, 13b, 19 }}


Badness: 0.059791
Badness (Sintel): 1.98


==== 13-limit ====
==== 13-limit ====
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{{Mapping|legend=0| 1 0 2 2 3 4 | 0 10 2 5 3 -2 }}
{{Mapping|legend=0| 1 0 2 2 3 4 | 0 10 2 5 3 -2 }}


Optimal tuning (POTE): ~2 = 1\1, ~11/10 = 189.928
Optimal tunings:
* WE: ~2 = 1201.8239{{c}}, ~11/10 = 190.2163{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 190.0020{{c}}


{{Optimal ET sequence|legend=1| 6, 19, 82ddeeff }}
{{Optimal ET sequence|legend=0| 6, 13b, 19 }}


Badness: 0.045591
Badness (Sintel): 1.88


==== Cantrip ====
==== Cantrip ====
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{{Mapping|legend=0| 1 0 2 2 3 1 | 0 10 2 5 3 17 }}
{{Mapping|legend=0| 1 0 2 2 3 1 | 0 10 2 5 3 17 }}


Optimal tuning (POTE): ~2 = 1\1, ~11/10 = 190.360
Optimal tunings:
* WE: ~2 = 1200.4118{{c}}, ~11/10 = 190.4253{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 190.3835{{c}}


{{Optimal ET sequence|legend=1| 19, 44de, 63dee, 82ddee }}
{{Optimal ET sequence|legend=0| 6f, 19 }}


Badness: 0.041603
Badness (Sintel): 1.72


= Weak extensions =
= Weak extensions =
== Semisept ==
== Semisept ==
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Semisept]].''
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Semisept]].''
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