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No-fives subgroup temperaments: Difference between revisions

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== Temperaments with a 2.3.7 gene ==
== Temperaments with a 2.3.7 gene ==
=== [[Semaphore and Godzilla|Semaphore]] ===
=== Semaphore ===
Subgroup: 2.3.7
See [[Semaphoresmic clan #Semaphore]].  


[[Comma]]: 49/48
=== Bleu ===
 
Bleu can be described as the 9 & 17 temperament in the no-5 13-limit.  
[[Gencom]]: [2 8/7; 49/48]
 
[[Gencom|Gencom mapping]]: [{{val|1 2 0 3}}, {{val|0 -2 0 -1}}]
 
[[Mapping|Sval mapping]]: [{{val|1 2 3}}, {{val|0 -2 -1}}]
 
[[Tp tuning|POL2 generator]]: ~7/6 = 250.385
 
{{Optimal ET sequence|legend=1| 5, 14, 19, 24, 67d, 91d }}
 
[[Tp tuning #T2 tuning|RMS error]]: 2.523 cents


=== Bleu ===
[[Subgroup]]: 2.3.7
Subgroup: 2.3.7


[[Comma]]: 17496/16807
[[Comma list]]: 17496/16807


[[Gencom]]: [2 54/49; 17496/16807]
{{Mapping|legend=2| 1 1 2 | 0 5 7 }}


[[Gencom|Gencom mapping]]: [{{val|1 1 0 2}}, {{val|0 5 0 7}}]
{{Mapping|legend=3| 1 1 0 2 | 0 5 0 7 }}


[[Mapping|Sval mapping]]: [{{val|1 1 2}}, {{val|0 5 7}}]
: [[gencom]]: [2 54/49; 17496/16807]


[[Tp tuning|POL2 generator]]: ~54/49 = 139.848
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~54/49 = 139.848


{{Optimal ET sequence|legend=1| 9, 17, 43, 60d }}
{{Optimal ET sequence|legend=1| 9, 17, 43, 60d }}
Line 36: Line 24:
[[Tp tuning #T2 tuning|RMS error]]: 1.917 cents
[[Tp tuning #T2 tuning|RMS error]]: 1.917 cents


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


[[Comma list]]: 99/98, 864/847
Comma list: 99/98, 864/847


[[Gencom]]: [2 12/11; 99/98 864/847]
Sval mapping: {{mapping| 1 1 2 3 | 0 5 7 4 }}


[[Gencom|Gencom mapping]]: [{{val|1 1 0 2 3}}, {{val|0 5 0 7 4}}]
Gencom mapping: {{mapping| 1 1 0 2 3 | 0 5 0 7 4 }}


[[Mapping|Sval mapping]]: [{{val|1 1 2 3}}, {{val|0 5 7 4}}]
: gencom: [2 12/11; 99/98 864/847]


[[Tp tuning|POL2 generator]]: ~12/11 = 140.005
Optimal tuning]] (POTE): ~2 = 1\1, ~12/11 = 140.005


{{Optimal ET sequence|legend=1| 9, 17, 43, 60d }}
Optimal ET sequence: {{Optimal ET sequence| 9, 17, 43, 60d }}


[[Tp tuning #T2 tuning|RMS error]]: 1.829 cents
RMS error: 1.829 cents


==== 2.3.7.11.13 ====
==== 2.3.7.11.13 subgroup ====
Subgroup: 2.3.7.11.13
Subgroup: 2.3.7.11.13


[[Comma list]]: 78/77, 99/98, 144/143
Comma list: 78/77, 99/98, 144/143


[[Gencom]]: [2 12/11; 78/77 99/98 144/143]
Sval mapping: {{mapping| 1 1 2 3 3 | 0 5 7 4 6 }}


[[Gencom|Gencom mapping]]: [{{val|1 1 0 2 3 3}}, {{val|0 5 0 7 4 6}}]
Gencom mapping: {{mapping| 1 1 0 2 3 3 | 0 5 0 7 4 6 }}


[[Mapping|Sval mapping]]: [{{val|1 1 2 3 3}}, {{val|0 5 7 4 6}}]
: gencom: [2 13/12; 78/77 99/98 144/143]


[[Tp tuning|POL2 generator]]: ~12/11 = 139.990
Optimal tuning (POTE): ~2 = 1\1, ~13/12 = 139.990


{{Optimal ET sequence|legend=1| 17, 43, 60d }}
Optimal ET sequence: {{Optimal ET sequence| 17, 43, 60c }}


[[Tp tuning #T2 tuning|RMS error]]: 1.752 cents
RMS error: 1.752 cents


=== Archy ===
=== Archy ===
Archy (properly pronounced "arky", after the Greek theorist Archytas) can be thought of as "no-fives [[Dominant (temperament)|dominant]]" or "no-fives [[superpyth]]". The name comes from the fact that it tempers out 64/63, the Archytas comma.
See [[Archytas clan #Archy]]
 
Subgroup: 2.3.7
 
[[Comma]]: 64/63
 
[[Gencom]]: [2 3/2; 64/63]
 
[[Gencom|Gencom mapping]]: [{{val|1 1 0 4}}, {{val|0 1 0 -2}}]
 
[[Mapping|Sval mapping]]: [{{val|1 2 2}}, {{val|0 -1 2}}]
 
[[Tp tuning|POL2 generator]]: ~3/2 = 709.321
 
{{Optimal ET sequence|legend=1| 5, 12, 17, 22, 27, 137bd }}
 
[[Tp tuning #T2 tuning|RMS error]]: 1.856 cents


==== Supra ====
==== Supra ====
Subgroup: 2.3.7.11
See [[Archytas clan #Supra]]
 
[[Comma list]]: 64/63, 99/98
 
[[Gencom]]: [2 3/2; 64/63 99/98]
 
[[Gencom|Gencom mapping]]: [{{val|1 1 0 4 7}}, {{val|0 1 0 -2 -6}}]
 
[[Mapping|Sval mapping]]: [{{val|1 0 6 13}}, {{val|0 1 -2 -6}}]
 
[[Tp tuning|POL2 generator]]: ~3/2 = 707.192
 
{{Optimal ET sequence|legend=1| 5, 12, 17, 39d, 56d }}
 
[[Tp tuning #T2 tuning|RMS error]]: 1.977 cents


===== Supraphon =====
===== Supraphon =====
Subgroup: 2.3.7.11.13
See [[Archytas clan #Supraphon]]
 
[[Comma list]]: 64/63, 78/77, 99/98
 
[[Gencom]]: [2 3/2; 64/63 78/77 99/98]
 
[[Gencom|Gencom mapping]]: [{{val|1 1 0 4 7 9}}, {{val|0 1 0 -2 -6 -9}}]
 
[[Mapping|Sval mapping]]: [{{val|1 0 6 13 18}}, {{val|0 1 -2 -6 -9}}]
 
[[Tp tuning|POL2 generator]]: ~3/2 = 706.137
 
{{Optimal ET sequence|legend=1| 5f, 12f, 17, 22, 39d, 56d }}
 
[[Tp tuning #T2 tuning|RMS error]]: 2.095 cents


==== Suhajira ====
==== Suhajira ====
Subgroup: 2.3.7.11
See [[Rastmic clan #Suhajira]]
 
[[Comma list]]: 64/63, 243/242
 
[[Gencom]]: [2 11/9; 64/63 243/242]
 
[[Gencom|Gencom mapping]]: [{{val|1 1 0 4 2}}, {{val|0 2 0 -4 5}}]
 
[[Mapping|Sval mapping]]: [{{val|1 1 4 2}}, {{val|0 2 -4 5}}]
 
[[Tp tuning|POL2 generator]]: ~11/9 = 353.958
 
{{Optimal ET sequence|legend=1| 7, 10, 17, 44e, 61de, 78de }}
 
[[Tp tuning #T2 tuning|RMS error]]: 1.968 cents
 
===== 2.3.7.11.13 =====
Subgroup: 2.3.7.11.13
 
[[Comma list]]: 64/63, 78/77, 144/143
 
[[Gencom]]: [2 11/9; 64/63 78/77 144/143]
 
[[Gencom|Gencom mapping]]: [{{val|1 1 0 4 2 4}}, {{val|0 2 0 -4 5 -1}}]
 
[[Mapping|Sval mapping]]: [{{val|1 1 4 2 4}}, {{val|0 2 -4 5 -1}}]
 
[[Tp tuning|POL2 generator]]: ~11/9 = 353.775
 
{{Optimal ET sequence|legend=1| 7, 10, 17, 44e, 61de, 78de }}
 
[[Tp tuning #T2 tuning|RMS error]]: 1.953 cents


==== Flutterpyth ====
==== Flutterpyth ====
Line 169: Line 82:


=== Skwares ===
=== Skwares ===
Subgroup: 2.3.7
Skwares is the no-5 restriction of [[squares]].
 
[[Subgroup]]: 2.3.7


[[Comma]]: 19683/19208
[[Comma list]]: 19683/19208


[[Gencom]]: [2 9/7; 19683/19208]
{{Mapping|legend=2| 1 3 6 | 0 -4 -9 }}


[[Gencom|Gencom mapping]]: [{{val|1 3 6}}, {{val|0 -4 -9}}]
{{Mapping|legend=3| 1 3 0 6 | 0 -4 0 -9 }}


[[Mapping|Sval mapping]]: [{{val|1 3 6}}, {{val|0 -4 -9}}]
: [[gencom]]: [2 9/7; 19683/19208]


[[Tp tuning|POL2 generator]]: ~9/7 = 425.365
[[Optimal tuning]] ([[POTE]]): ~9/7 = 425.365


{{Optimal ET sequence|legend=1| 14, 17, 31, 48, 79, 189b, 268bd, 347bd }}
{{Optimal ET sequence|legend=1| 14, 17, 31, 48, 79, 189b, 268bd, 347bd }}
Line 190: Line 105:
Subgroup: 2.3.7.11
Subgroup: 2.3.7.11


[[Comma list]]: 99/98, 243/242
Comma list: 99/98, 243/242


[[Gencom]]: [2 9/7; 99/98 243/242]
Sval mapping: {{mapping| 1 3 6 7 | 0 -4 -9 -10 }}


[[Gencom|Gencom mapping]]: [{{val|1 3 0 6 7}}, {{val|0 -4 0 -9 -10}}]
Gencom mapping: {{mapping| 1 3 0 6 7 | 0 -4 0 -9 -10 }}


[[Mapping|Sval mapping]]: [{{val|1 3 6 7}}, {{val|0 -4 -9 -10}}]
: gencom: [2 9/7; 99/98 243/242]


[[Tp tuning|POL2 generator]]: ~9/7 = 425.244
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 425.244


{{Optimal ET sequence|legend=1| 14, 17, 31, 48, 79, 127, 206bde }}
Optimal ET sequence: {{Optimal ET sequence| 5, 8, 11, 14, 17, 31, 48, 79, 127, 206bcd }}


[[Tp tuning #T2 tuning|RMS error]]: 1.099 cents
RMS error: 1.099 cents


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


[[Comma list]]: 78/77, 99/98, 243/242
Comma list: 78/77, 99/98, 243/242


[[Gencom]]: [2 9/7; 78/77, 99/98, 243/242]
Sval mapping: {{mapping| 1 3 6 7 9 | 0 -4 -9 -10 -15 }}


[[Gencom|Gencom mapping]]: [{{val|1 3 0 6 7 9}}, {{val|0 -4 0 -9 -10 -15}}]
Gencom mapping: {{mapping| 1 3 0 6 7 9 | 0 -4 0 -9 -10 -15}}


[[Mapping|Sval mapping]]: [{{val|1 3 6 7 9}}, {{val|0 -4 -9 -10 -15}}]
: gencom: [2 9/7; 78/77, 99/98, 243/242]


[[Tp tuning|POL2 generator]]: ~9/7 = 424.457
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 424.457


{{Optimal ET sequence|legend=1| 17, 48f, 65ef, 82d, 147df }}
Optimal ET sequence: {{Optimal ET sequence| 17, 48f, 65ef, 82d, 147df }}


[[Tp tuning #T2 tuning|RMS error]]: 1.769 cents
RMS error: 1.769 cents


===== Skwairs =====
===== Skwairs =====
Subgroup: 2.3.7.11.13
Subgroup: 2.3.7.11.13


[[Comma list]]: 99/98, 144/143, 243/242
Comma list: 99/98, 144/143, 243/242


[[Gencom]]: [2 9/7; 99/98, 144/143, 243/242]
Sval mapping: {{mapping| 1 3 6 7 3 | 0 -4 -9 -10 2 }}


[[Gencom|Gencom mapping]]: [{{val|1 3 0 6 7 3}}, {{val|0 -4 0 -9 -10 2}}]
Gencom mapping: {{mapping| 1 3 0 6 7 3 | 0 -4 0 -9 -10 2 }}


[[Mapping|Sval mapping]]: [{{val|1 3 6 7 3}}, {{val|0 -4 -9 -10 2}}]
: gencom: [2 9/7; 99/98, 144/143, 243/242]


[[Tp tuning|POL2 generator]]: ~9/7 = 424.702
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 424.702


{{Optimal ET sequence|legend=1| 14, 17, 31 }}
Optimal ET sequence: {{Optimal ET sequence| 14, 17, 31 }}


[[Tp tuning #T2 tuning|RMS error]]: 1.290 cents
RMS error: 1.290 cents


===== Byhearted =====
===== Byhearted =====
: <small>''For the full 19-limit version of this temperament, see [[Tetracot family #Byhearted]].''</small>
: ''For the full 19-limit version of this temperament, see [[Tetracot family #Byhearted]].''


Subgroup: 2.3.7.11.19
Subgroup: 2.3.7.11.19


[[Comma list]]: 99/98, 243/242, 363/361
Comma list: 99/98, 243/242, 363/361


[[Gencom]]: [209/147 21/19; 99/98 243/242 363/361]
Sval mapping: {{mapping| 2 2 3 4 5 | 0 4 9 10 12 }}


[[Mapping|Sval mapping]]: [{{val|2 2 3 4 5}}, {{val|0 4 9 10 12}}]
: gencom: [209/147 21/19; 99/98 243/242 363/361]


[[Tp tuning|POL2 generator]]: ~21/19 = 174.735
Optimal tuning (POTE): ~2 = 1\1, ~21/19 = 174.735


{{Optimal ET sequence|legend=1| 14, 34dh, 48, 110e, 158e }}
Optimal ET sequence: {{Optimal ET sequence| 14, 34dh, 48, 110e, 158e }}


[[Tp tuning #T2 tuning|RMS error]]: 0.8727 cents
RMS error: 0.8727 cents


=== Harrison ===
=== Harrison ===
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