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Hemimean clan: Difference between revisions

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Switch to Sintel's badness, WE & CWE tunings (4/)
Switch to Sintel's badness, WE & CWE tunings (5/)
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* CWE: ~2 = 1200.0000{{c}}, ~16/11 = 648.2442{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~16/11 = 648.2442{{c}}


{{Optimal ET sequence|legend=1| 37, 50, 87, 224d, 311d, 398d }}
{{Optimal ET sequence|legend=0| 37, 50, 87, 224d, 311d, 398d }}


Badness (Sintel): 1.23
Badness (Sintel): 1.23
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{{Mapping|legend=1| 1 1 2 2 | 0 29 16 40 }}
{{Mapping|legend=1| 1 1 2 2 | 0 29 16 40 }}
: mapping generators: ~2, ~686/675


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~686/675 = 24.217
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.8393{{c}}, ~686/675 = 24.2133{{c}}
: [[error map]]: {{val| -0.161 +0.070 +0.778 -0.615 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~686/675 = 24.2119{{c}}
: error map: {{val| 0.000 +0.191 +1.077 -0.349 }}


{{Optimal ET sequence|legend=1| 49, 50, 99, 248, 347, 446 }}
{{Optimal ET sequence|legend=1| 49, 50, 99, 248, 347, 446 }}


[[Badness]]: 0.057978
[[Badness]] (Sintel): 1.47


=== 11-limit ===
=== 11-limit ===
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{{Mapping|legend=0| 1 1 2 2 3 | 0 29 16 40 23 }}
{{Mapping|legend=0| 1 1 2 2 3 | 0 29 16 40 23 }}


Optimal tuning (POTE): ~2 = 1\1, ~99/98 = 24.235
Optimal tunings:
* WE: ~2 = 1199.3714{{c}}, ~99/98 = 24.2224{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~99/98 = 24.2176{{c}}


{{Optimal ET sequence|legend=1| 49, 50, 99e }}
{{Optimal ET sequence|legend=0| 49, 50, 99e }}


Badness: 0.053828
Badness (Sintel): 1.78


==== 13-limit ====
==== 13-limit ====
Line 748: Line 755:
{{Mapping|legend=0| 1 1 2 2 3 4 | 0 29 16 40 23 -15 }}
{{Mapping|legend=0| 1 1 2 2 3 4 | 0 29 16 40 23 -15 }}


Optimal tuning (POTE): ~2 = 1\1, ~99/98 = 24.181
Optimal tunings:
* WE: ~2 = 1200.0364{{c}}, ~99/98 = 24.1817{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~99/98 = 24.1815{{c}}


{{Optimal ET sequence|legend=1| 49, 50, 99e, 149e }}
{{Optimal ET sequence|legend=0| 49, 50, 99e, 149e }}


Badness: 0.053531
Badness (Sintel): 2.21


==== Sengage ====
==== Sengage ====
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{{Mapping|legend=0| 1 1 2 2 3 3 | 0 29 16 40 23 35 }}
{{Mapping|legend=0| 1 1 2 2 3 3 | 0 29 16 40 23 35 }}


Optimal tuning (POTE): ~2 = 1\1, ~99/98 = 24.234
Optimal tunings:
* WE: ~2 = 1199.1402{{c}}, ~99/98 = 24.2164{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~99/98 = 24.2092{{c}}


{{Optimal ET sequence|legend=1| 49f, 50, 99ef }}
{{Optimal ET sequence|legend=0| 49f, 50, 99ef }}


Badness: 0.037416
Badness (Sintel): 1.55


== Mowglic ==
== Mowglic ==
The mowglic temperament (19 & 161) is an extension of the [[Syntonic–kleismic equivalence continuum #Mowgli|mowgli]] temperament which tempers out the hemimean comma and the secanticornisma (177147/175000, laruquingu) in the 7-limit.
: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Mowgli]].''
 
Mowglic may be described as the 19 & 161 temperament.  


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 775: Line 788:


{{Mapping|legend=1| 1 0 0 -3 | 0 15 22 55 }}
{{Mapping|legend=1| 1 0 0 -3 | 0 15 22 55 }}
: mapping generators: ~2, ~27/25


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~27/25 = 126.706
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.0862{{c}}, ~27/25 = 126.7147{{c}}
: [[error map]]: {{val| +0.086 -1.234 +1.411 +0.226 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~27/25 = 126.7081{{c}}
: error map: {{val| 0.000 -1.333 +1.265 +0.122 }}


{{Optimal ET sequence|legend=1| 19, 123d, 142, 161 }}
{{Optimal ET sequence|legend=1| 19, …, 123d, 142, 161 }}


[[Badness]]: 0.129915
[[Badness]] (Sintel): 3.29


=== 11-limit ===
=== 11-limit ===
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{{Mapping|legend=0| 1 0 0 -3 8 | 0 15 22 55 -43 }}
{{Mapping|legend=0| 1 0 0 -3 8 | 0 15 22 55 -43 }}


Optimal tuning (POTE): ~2 = 1\1, ~27/25 = 126.711
Optimal tunings:
* WE: ~2 = 1200.0198{{c}}, ~27/25 = 126.7134{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~27/25 = 126.7114{{c}}


{{Optimal ET sequence|legend=1| 19, 123de, 142, 161 }}
{{Optimal ET sequence|legend=0| 19, 142, 161 }}


Badness: 0.094032
Badness (Sintel): 3.11


=== 13-limit ===
=== 13-limit ===
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{{Mapping|legend=0| 1 0 0 -3 8 -2 | 0 15 22 55 -43 54 }}
{{Mapping|legend=0| 1 0 0 -3 8 -2 | 0 15 22 55 -43 54 }}


Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 126.705
Optimal tunings:
* WE: ~2 = 1199.9743{{c}}, ~14/13 = 126.7022{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 126.7047{{c}}


{{Optimal ET sequence|legend=1| 19, 123def, 142f, 161 }}
{{Optimal ET sequence|legend=0| 19, 142f, 161 }}


Badness: 0.051571
Badness (Sintel): 2.13


=== 17-limit ===
=== 17-limit ===
Line 815: Line 837:
{{Mapping|legend=0| 1 0 0 -3 8 -2 10 | 0 15 22 55 -43 54 -56 }}
{{Mapping|legend=0| 1 0 0 -3 8 -2 10 | 0 15 22 55 -43 54 -56 }}


Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 126.703
Optimal tunings:
* WE: ~2 = 1200.0016{{c}}, ~14/13 = 126.7029{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 126.7027{{c}}


{{Optimal ET sequence|legend=1| 19, 123defg, 142f, 161 }}
{{Optimal ET sequence|legend=0| 19, 123defg, 142f, 161 }}


Badness: 0.041918
Badness (Sintel): 2.14


=== 19-limit ===
=== 19-limit ===
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{{Mapping|legend=0| 1 0 0 -3 8 -2 10 9 | 0 15 22 55 -43 54 -56 -45 }}
{{Mapping|legend=0| 1 0 0 -3 8 -2 10 9 | 0 15 22 55 -43 54 -56 -45 }}


Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 126.705
Optimal tunings:
* WE: ~2 = 1199.9713{{c}}, ~14/13 = 126.7018{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 126.7048{{c}}


{{Optimal ET sequence|legend=1| 19, 123defg, 142f, 161 }}
{{Optimal ET sequence|legend=0| 19, 123defg, 142f, 161 }}


Badness: 0.032168
Badness (Sintel): 1.96


=== 23-limit ===
=== 23-limit ===
Line 841: Line 867:
{{Mapping|legend=0| 1 0 0 -3 8 -2 10 9 6 | 0 15 22 55 -43 54 -56 -45 -14 }}
{{Mapping|legend=0| 1 0 0 -3 8 -2 10 9 6 | 0 15 22 55 -43 54 -56 -45 -14 }}


Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 126.703
Optimal tunings:
* WE: ~2 = 1200.0296{{c}}, ~14/13 = 126.7061{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 126.7030{{c}}


{{Optimal ET sequence|legend=1| 19, 123defg, 142f, 161 }}
{{Optimal ET sequence|legend=0| 19, 142f, 161 }}


Badness: 0.026117
Badness (Sintel): 1.87


=== 29-limit ===
=== 29-limit ===
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{{Mapping|legend=0| 1 0 0 -3 8 -2 10 9 6 0 | 0 15 22 55 -43 54 -56 -45 -14 46 }}
{{Mapping|legend=0| 1 0 0 -3 8 -2 10 9 6 0 | 0 15 22 55 -43 54 -56 -45 -14 46 }}


Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 126.704
Optimal tunings:
* WE: ~2 = 1200.0491{{c}}, ~14/13 = 126.7094{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 126.7043{{c}}


{{Optimal ET sequence|legend=1| 19, 123defg, 142f, 161 }}
{{Optimal ET sequence|legend=0| 19, 142f, 161 }}


Badness: 0.021398
Badness (Sintel): 1.79


=== 31-limit ===
=== 31-limit ===
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{{Mapping|legend=0| 1 0 0 -3 8 -2 10 9 6 0 2 | 0 15 22 55 -43 54 -56 -45 -14 46 28 }}
{{Mapping|legend=0| 1 0 0 -3 8 -2 10 9 6 0 2 | 0 15 22 55 -43 54 -56 -45 -14 46 28 }}


Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 126.703
Optimal tunings:
* WE: ~2 = 1199.9986{{c}}, ~14/13 = 126.7027{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 126.7028{{c}}


{{Optimal ET sequence|legend=1| 19, 123defgk, 142fk, 161 }}
{{Optimal ET sequence|legend=0| 19, 142fk, 161 }}


Badness: 0.019331
Badness (Sintel): 1.85


== Tremka ==
== Tremka ==
The name ''tremka'' was initially used for the [[No-sevens subgroup temperaments|no-sevens version]] of 50 & 111 (especially in the 2.3.5.11.13 subgroup), but extending to full 13-limit or higher prime limit does no significant tuning damage, so for that we keep the 2.3.5.11.13 label tremka.
The name ''tremka'' was initially used for the [[no-sevens subgroup temperaments #Tremka|no-7's version]] of 50 & 111 (especially in the 2.3.5.11.13 subgroup), but extending to the full 13-limit or higher does no significant tuning damage, so for that we keep the 2.3.5.11.13 label tremka.


=== 7-limit ===
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


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{{Mapping|legend=1| 1 -4 -2 -8 | 0 31 24 60 }}
{{Mapping|legend=1| 1 -4 -2 -8 | 0 31 24 60 }}
: mapping generators: ~2, ~4375/3888


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~4375/3888 = 216.173
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.7671{{c}}, ~4375/3888 = 216.1302{{c}}
: [[error map]]: {{val| -0.233 -0.987 +1.277 +0.849 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~4375/3888 = 216.1665{{c}}
: error map: {{val| 0.000 -0.794 +1.682 +1.162 }}


{{Optimal ET sequence|legend=1| 50, 111, 161, 272 }}
{{Optimal ET sequence|legend=1| 50, 111, 161, 272 }}


[[Badness]]: 0.179925
[[Badness]] (Sintel): 4.55


=== 11-limit ===
=== 11-limit ===
Line 896: Line 932:
{{Mapping|legend=0| 1 -4 -2 -8 4 | 0 31 24 60 -3 }}
{{Mapping|legend=0| 1 -4 -2 -8 4 | 0 31 24 60 -3 }}


Optimal tuning (POTE): ~2 = 1\1, ~112/99 = 216.168
Optimal tunings:
* WE: ~2 = 1199.8503{{c}}, ~112/99 = 216.1406{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~112/99 = 216.1652{{c}}


{{Optimal ET sequence|legend=1| 50, 111, 161, 272, 433c }}
{{Optimal ET sequence|legend=0| 50, 111, 161, 272, 433c }}


Badness: 0.068825
Badness (Sintel): 2.28


=== 13-limit ===
=== 13-limit ===
Line 909: Line 947:
{{Mapping|legend=0| 1 -4 -2 -8 4 1 | 0 31 24 60 -3 15 }}
{{Mapping|legend=0| 1 -4 -2 -8 4 1 | 0 31 24 60 -3 15 }}


Optimal tuning (POTE): ~2 = 1\1, ~112/99 = 216.172
Optimal tunings:
* WE: ~2 = 1199.7479{{c}}, ~112/99 = 216.1263{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~112/99 = 216.1681{{c}}


{{Optimal ET sequence|legend=1| 50, 111, 161, 272 }}
{{Optimal ET sequence|legend=0| 50, 111, 161, 272 }}


Badness: 0.036070
Badness (Sintel): 1.49


=== 17-limit ===
=== 17-limit ===
Line 922: Line 962:
{{Mapping|legend=0| 1 -4 -2 -8 4 1 -6 | 0 31 24 60 -3 15 56 }}
{{Mapping|legend=0| 1 -4 -2 -8 4 1 -6 | 0 31 24 60 -3 15 56 }}


Optimal tuning (POTE): ~2 = 1\1, ~17/15 = 216.172
Optimal tunings:
* WE: ~2 = 1199.7537{{c}}, ~17/15 = 216.1281{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~17/15 = 216.1688{{c}}


{{Optimal ET sequence|legend=1| 50, 111, 161, 272 }}
{{Optimal ET sequence|legend=0| 50, 111, 161, 272 }}


Badness: 0.022528
Badness (Sintel): 1.15


=== 19-limit ===
=== 19-limit ===
Line 935: Line 977:
{{Mapping|legend=0| 1 -4 -2 -8 4 1 -6 -8 | 0 31 24 60 -3 15 56 68 }}
{{Mapping|legend=0| 1 -4 -2 -8 4 1 -6 -8 | 0 31 24 60 -3 15 56 68 }}


Optimal tuning (POTE): ~2 = 1\1, ~17/15 = 216.170
Optimal tunings:
* WE: ~2 = 1199.7496{{c}}, ~17/15 = 216.1244{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~17/15 = 216.1658{{c}}


{{Optimal ET sequence|legend=1| 50, 111, 161, 272h, 433cfh, 705ccdffhh }}
{{Optimal ET sequence|legend=0| 50, 111, 161, 272h, 433cfh }}


Badness: 0.016900
Badness (Sintel): 1.03


== Undetrita ==
== Undetrita ==
Retrieved from "https://en.xen.wiki/w/Hemimean_clan"