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No-fives subgroup temperaments: Difference between revisions

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=== Hemif ===
=== Hemif ===
Subgroup: 2.3.7
Related temperaments: [[hemififths]], [[namo]]


[[Comma]]: 1605632/1594323
[[Subgroup]]: 2.3.7


[[Gencom]]: [2 2187/1792; 1605632/1594323]
[[Comma list]]: 1605632/1594323


[[Gencom|Gencom mapping]]: [{{val|1 1 0 -1}}, {{val|0 2 0 13}}]
{{Mapping|legend=2| 1 1 -1 | 0 2 13 }}


[[Mapping|Sval mapping]]: [{{val|1 1 -1}}, {{val|0 2 13}}]
{{Mapping|legend=3| 1 1 0 -1 | 0 2 0 13 }}


[[Tp tuning|POL2 generator]]: ~2187/1792 = 351.485
: [[gencom]]: [2 2187/1792; 1605632/1594323]
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~2187/1792 = 351.485


{{Optimal ET sequence|legend=1| 7, 17, 41, 58, 99 }}
{{Optimal ET sequence|legend=1| 7, 17, 41, 58, 99 }}


[[Tp tuning #T2 tuning|RMS error]]: 0.2344 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.2344 cents
Related temperaments: [[Breedsmic temperaments #Hemififths|hemififths]], namo


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


[[Comma list]]: 243/242, 896/891
Comma list: 243/242, 896/891


[[Gencom]]: [2 11/9; 243/242 896/891]
Sval mapping: {{mapping| 1 1 -1 2 | 0 2 13 5 }}


[[Gencom|Gencom mapping]]: [{{val|1 1 0 -1 2}}, {{val|0 2 0 13 5}}]
Gencom mapping: {{mapping| 1 1 0 -1 2 | 0 2 0 13 5 }}


[[Mapping|Sval mapping]]: [{{val|1 1 -1 2}}, {{val|0 2 13 5}}]
: gencom: [2 11/9; 243/242 896/891]


[[Tp tuning|POL2 generator]]: ~11/9 = 351.535
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 351.535


{{Optimal ET sequence|legend=1| 7, 17, 41, 58, 99e }}
Optimal ET sequence: {{Optimal ET sequence| 7, 17, 41, 58, 99e }}


[[Tp tuning #T2 tuning|RMS error]]: 0.6108 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.6108 cents
Line 626: Line 626:
Subgroup: 2.3.7.11.13
Subgroup: 2.3.7.11.13


[[Comma list]]: 144/143, 243/242, 364/363
Comma list: 144/143, 243/242, 364/363


[[Gencom]]: [2 11/9; 144/143 243/242 364/363]
Sval mapping: {{mapping| 1 1 -1 2 4 | 0 2 13 5 -1 }}


[[Gencom|Gencom mapping]]: [{{val|1 1 0 -1 2 4}}, {{val|0 2 0 13 5 -1}}]
Gencom mapping: {{mapping| 1 1 0 -1 2 4 | 0 2 0 13 5 -1 }}


[[Mapping|Sval mapping]]: [{{val|1 1 -1 2 4}}, {{val|0 2 13 5 -1}}]
: gencom: [2 11/9; 144/143 243/242 364/363]


[[Tp tuning|POL2 generator]]: ~11/9 = 351.691
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 351.691


{{Optimal ET sequence|legend=1| 7, 10, 17, 24, 41, 58 }}
Optimal ET sequence: {{Optimal ET sequence| 7, 10, 17, 24, 41, 58 }}


[[Tp tuning #T2 tuning|RMS error]]: 0.7167 cents
RMS error: 0.7167 cents


===== Heartful =====
===== Heartful =====
{{see also|Heartland}}
{{See also| Heartland }}
 
Related temperaments: [[bunya]]


Subgroup: 2.3.7.11.19
Subgroup: 2.3.7.11.19


[[Comma list]]: 243/242, 896/891, 1083/1078
Comma list: 243/242, 896/891, 1083/1078
 
[[Gencom]]: [2 21/19; 243/242 896/891 1083/1078]


[[Mapping|Sval mapping]]: [{{val|1 1 -1 2 0}}, {{val|0 4 26 10 29}}]
Sval mapping: {{mapping| 1 1 -1 2 0 | 0 4 26 10 29 }}


[[Tp tuning|POL2 generator]]: ~21/19 = 175.804
: gencom: [2 21/19; 243/242 896/891 1083/1078]


{{Optimal ET sequence|legend=1| 34dh, 41, 116e, 157e }}
Optimal tuning (POTE): ~2 = 1\1, ~21/19 = 175.804


[[Tp tuning #T2 tuning|RMS error]]: 0.5360 cents
Optimal ET sequence: {{Optimal ET sequence| 34dh, 41, 116e, 157e }}


Related temperaments: [[Tetracot family|bunya]]
RMS error: 0.5360 cents


=== Hearts ===
=== Hearts ===
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