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No-fives subgroup temperaments: Difference between revisions

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Switch to Sintel's badness, WE & CWE tunings (3/)
Switch to Sintel's badness, WE & CWE tunings (4/)
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{{See also| Heartland }}
{{See also| Heartland }}


Subgroup: 2.3.7
This temperament is the no-5 [[restriction]] of [[octacot]].
 
[[Subgroup]]: 2.3.7


[[Comma list]]: 5764801/5668704
[[Comma list]]: 5764801/5668704


[[Gencom]]: [2 343/324; 5764801/5668704]
{{Mapping|legend=2| 1 1 2 | 0 8 11 }}
 
: mapping generators: ~2, ~343/342
[[Mapping|Sval mapping]]: [{{val|1 1 2}}, {{val|0 8 11}}]


[[Tp tuning|POL2 generator]]: ~343/324 = 87.8304
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.0000{{c}}, ~343/324 = 87.8431{{c}}
: [[error map]]: {{val| +0.174 +0.964 -2.204 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~343/324 = 87.8492{{c}}
: error map: {{val| 0.000 +0.838 -2.485 }}


{{Optimal ET sequence|legend=1| 14, 27, 41 }}
{{Optimal ET sequence|legend=1| 14, 27, 41 }}


[[Tp tuning #T2 tuning|RMS error]]: 0.5041 cents
[[Badness]] (Sintel): 2.62
 
Related temperaments: [[octacot]]


==== 2.3.7.11 ====
==== 2.3.7.11 ====
Subgroup: 2.3.7.11
Subgroup: 2.3.7.11


[[Comma list]]: 243/242, 2401/2376
Comma list: 243/242, 2401/2376


[[Gencom]]: [2 22/21; 243/242 2401/2376]
Subgroup-val mapping: {{mapping| 1 1 2 2 | 0 8 11 20 }}


[[Mapping|Sval mapping]]: [{{val|1 1 2 2}}, {{val|0 8 11 20}}]
Optimal tunings:  
* WE: ~2 = 1200.4071{{c}}, ~22/21 = 87.6809{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/21 = 87.6902{{c}}


[[Tp tuning|POL2 generator]]: ~22/21 = 87.6512
{{Optimal ET sequence|legend=0| 14, 27e, 41, 96d, 137d, 178d }}


{{Optimal ET sequence|legend=1| 14, 27e, 41, 96d, 137d, 178d }}
Badness (Sintel): 0.815
 
[[Tp tuning #T2 tuning|RMS error]]: 0.7147 cents
 
Related temperaments: [[octacot]]


==== 2.3.7.11.19 ====
==== 2.3.7.11.19 ====
Subgroup: 2.3.7.11.19
Subgroup: 2.3.7.11.19


[[Comma list]]: 133/132, 243/242, 343/342
Comma list: 133/132, 243/242, 343/342


[[Gencom]]: [2 19/18; 133/132 243/242 343/342]
Subgroup-val mapping: {{mapping| 1 1 2 2 3 | 0 8 11 20 17 }}


[[Mapping|Sval mapping]]: [{{val|1 1 2 2 3}}, {{val|0 8 11 20 17}}]
Optimal tunings:  
* WE: ~2 = 1200.6100{{c}}, ~19/18 = 87.7129{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~19/18 = 87.7285{{c}}


[[Tp tuning|POL2 generator]]: ~19/18 = 87.6684
{{Optimal ET sequence|legend=0| 14, 27e, 41, 137dh }}


{{Optimal ET sequence|legend=1| 14, 27e, 41 }}
Badness (Sintel): 0.560


[[Tp tuning #T2 tuning|RMS error]]: 0.7065 cents
=== Magi ===
This temperament is the no-5 [[restriction]] of [[magic]], tempering out the [[septimagic comma]].  


Related temperaments: [[octacot]]
[[Subgroup]]: 2.3.7
 
=== Magi ===
Subgroup: 2.3.7


[[Comma list]]: 537824/531441
[[Comma list]]: 537824/531441


[[Gencom]]: [2 243/196; 537824/531441]
{{Mapping|legend=2| 1 0 -1 | 0 5 12 }}
: mapping generators: ~2, ~243/196


[[Mapping|Sval mapping]]: [{{val|1 0 -1}}, {{val|0 5 12}}]
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1199.8224{{c}}, ~243/196 = 380.6043{{c}}
: [[error map]]: {{val| -0.178 +1.066 -1.397 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~243/196 = 380.6378{{c}}
: error map: {{val| 0.000 +1.234 -1.173 }}


[[Tp tuning|POL2 generator]]: ~243/196 = 380.661
{{Optimal ET sequence|legend=1| 19, 22, 41, 104, 145, 186, 331 }}


{{Optimal ET sequence|legend=1| 19, 22, 41, 104, 145, 186 }}
[[Badness]] (Sintel): 1.30
 
[[Tp tuning #T2 tuning|RMS error]]: 0.4277 cents


==== 2.3.7.11 ====
==== 2.3.7.11 ====
Subgroup: 2.3.7.11
Subgroup: 2.3.7.11


[[Comma list]]: 896/891, 26411/26244
Comma list: 896/891, 26411/26244


[[Gencom]]: [2 96/77; 896/891 26411/26244]
Subgroup-val mapping: {{mapping| 1 0 -1 6 | 0 5 12 -8 }}


[[Mapping|Sval mapping]]: [{{val|1 0 -1 6}}, {{val|0 5 12 -8}}]
Optimal tunings:  
* WE: ~2 = 1199.4843{{c}}, ~96/77 = 380.6040{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~96/77 = 380.7490{{c}}


[[Tp tuning|POL2 generator]]: ~96/77 = 380.768
{{Optimal ET sequence|legend=0| 19, 22, 41, 63, 104 }}


{{Optimal ET sequence|legend=1| 19, 22, 41, 63, 104 }}
Badness (Sintel): 0.661


[[Tp tuning #T2 tuning|RMS error]]: 0.4262 cents
===== Caspar =====
 
===== Balthazar =====
Subgroup: 2.3.7.11.13
Subgroup: 2.3.7.11.13


[[Comma list]]: 169/168, 896/891, 26411/26244
Comma list: 144/143, 343/338, 729/728


[[Gencom]]: [2 143/128; 169/168 896/891 26411/26244]
Subgroup-val mapping: {{mapping| 1 0 -1 6 -2 | 0 5 12 -8 18 }}


[[Mapping|Sval mapping]]: [{{val|1 0 -1 6 1}}, {{val|0 10 24 -16 17}}]
Optimal tunings:  
* WE: ~2 = 1199.3353{{c}}, ~26/21 = 380.3206{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~26/21 = 380.5041{{c}}


[[Tp tuning|POL2 generator]]: ~143/128 = 190.407
{{Optimal ET sequence|legend=0| 19, 22f, 41 }}


{{Optimal ET sequence|legend=1| 19, 44, 63, 145f }}
Badness (Sintel): 1.09


[[Tp tuning #T2 tuning|RMS error]]: 0.6937 cents
====== Twenothology ======
Subgroup: 2.3.7.11.13.29


===== Caspar =====
Comma list: 144/143, 232/231, 343/338, 729/728
Subgroup: 2.3.7.11.13
 
[[Comma list]]: 144/143, 343/338, 729/728
 
[[Gencom]]: [2 26/21; 144/143 343/338 729/728]


[[Mapping|Sval mapping]]: [{{val|1 0 -1 6 -2}}, {{val|0 5 12 -8 18}}]
Subgroup-val mapping: {{mapping| 1 0 -1 6 -2 2 | 0 5 12 -8 18 9 }}


[[Tp tuning|POL2 generator]]: ~26/21 = 380.531
Optimal tunings:  
* WE: ~2 = 1199.6175{{c}}, ~26/21 = 380.4049{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~26/21 = 380.5103{{c}}


{{Optimal ET sequence|legend=1| 19, 22f, 41 }}
{{Optimal ET sequence|legend=0| 19, 22f, 41 }}


[[Tp tuning #T2 tuning|RMS error]]: 1.032 cents
Badness (Sintel): 0.964


===== Melchior =====
===== Melchior =====
Subgroup: 2.3.7.11.13
Subgroup: 2.3.7.11.13


[[Comma list]]: 352/351, 364/363, 26411/26244
Comma list: 352/351, 364/363, 26411/26244


[[Gencom]]: [2 96/77; 352/351 364/363 26411/26244]
Subgroup-val mapping: {{mapping| 1 0 -1 6 11 | 0 5 12 -8 -23 }}


[[Mapping|Sval mapping]]: [{{val|1 0 -1 6 11}}, {{val|0 5 12 -8 -23}}]
Optimal tunings:  
* WE: ~2 = 1199.4887{{c}}, ~96/77 = 380.6034{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~96/77 = 380.7669{{c}}


[[Tp tuning|POL2 generator]]: ~96/77 = 380.766
{{Optimal ET sequence|legend=0| 19f, 22, 41, 63, 104 }}


{{Optimal ET sequence|legend=1| 19f, 22, 41, 63, 104 }}
Badness (Sintel): 0.710


[[Tp tuning #T2 tuning|RMS error]]: 0.3891 cents
===== Balthazar =====
Subgroup: 2.3.7.11.13


==== Hogwarts ====
Comma list: 169/168, 896/891, 26411/26244
Subgroup: 2.3.7.29


[[Comma list]]: 784/783, 5887/5832
Subgroup-val mapping: {{mapping| 1 0 -1 6 1 | 0 10 24 -16 17 }}
: mapping generators: ~2, ~143/128


[[Gencom]]: [2 36/29; 784/783 5887/5832]
Optimal tunings:  
* WE: ~2 = 1199.7322{{c}}, ~143/128 = 190.3647{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~143/128 = 190.4016{{c}}


[[Mapping|Sval mapping]]: [{{val|1 0 -1 2}}, {{val|0 5 12 9}}]
{{Optimal ET sequence|legend=0| 19, 44, 63, 145f }}


[[Tp tuning|POL2 generator]]: ~36/29 = 380.618
Badness (Sintel): 1.82


{{Optimal ET sequence|legend=1| 19, 22, 41, 145, 186j, 227j }}
==== Hogwarts ====
Subgroup: 2.3.7.29


===== Twenothology =====
Comma list: 784/783, 5887/5832
Subgroup: 2.3.7.11.13.29


[[Comma list]]: 144/143, 232/231, 343/338, 729/728
Subgroup-val mapping: {{mapping| 1 0 -1 2 | 0 5 12 9 }}


[[Mapping|Sval mapping]]: [{{val|1 0 -1 6 -2 2}}, {{val|0 5 12 -8 18 9}}]
Optimal tunings:  
* WE: ~2 = 1200.1518{{c}}, ~36/29 = 380.6661{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~36/29 = 380.6375{{c}}


[[Tp tuning|POL2 generator]]: ~26/21 = 380.526
{{Optimal ET sequence|legend=0| 19, 22, 41, 145, 186j, 227j }}


{{Optimal ET sequence|legend=1| 19, 22f, 41 }}
Badness (Sintel): 0.424


=== Lee ===
=== Lee ===
Subgroup: 2.3.7
[[Subgroup]]: 2.3.7
 
[[Comma]]: 177147/175616


[[Gencom]]: [2 81/56; 177147/175616]
[[Comma list]]: 177147/175616


[[Gencom|Gencom mapping]]: [{{val|1 0 0 -3}}, {{val|0 3 0 11}}]
{{Mapping|legend=2| 1 0 -3 | 0 3 11 }}


[[Mapping|Sval mapping]]: [{{val|1 0 -3}}, {{val|0 3 11}}]
{{Mapping|legend=3| 1 0 0 -3 | 0 3 0 11 }}
: mapping generators: ~2, ~81/56


[[Tp tuning|POL2 generator]]: ~81/56 = 633.525
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.2962{{c}}, ~81/56 = 633.6812{{c}}
: [[error map]]: {{val| +0.296 -0.912 +0.778 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~81/56 = 633.5658{{c}}
: error map: {{val| 0.000 -1.258 +0.398 }}


{{Optimal ET sequence|legend=1| 17, 36, 89, 125, 161, 358, 519b }}
{{Optimal ET sequence|legend=1| 17, 36, 89, 125, 161, 358, 519b }}


[[Tp tuning #T2 tuning|RMS error]]: 0.3519 cents
[[Badness]] (Sintel): 0.741


=== Buzzard ===
=== Buzzard ===
{{main|Buzzardsmic clan #Buzzard}}
See [[Buzzardsmic clan #Buzzard]].


=== [[Slendric]] ===
=== Slendric ===
{{main|Gamelismic clan #Slendric}}
See [[Gamelismic clan #Slendric]].


=== Hemif ===
=== Hemif ===
Retrieved from "https://en.xen.wiki/w/No-fives_subgroup_temperaments"