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No-fives subgroup temperaments: Difference between revisions

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→Temperaments with a 2.3.11 gene: -duplicate data; normalize mappings and generators; +link
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[[Comma list]]: 33/32
[[Comma list]]: 33/32


{{Mapping|legend=2| 1 1 4 | 0 1 -1 }}
{{Mapping|legend=2| 1 0 5 | 0 1 -1 }}


: mapping generators: ~2/1, ~3/2
: mapping generators: ~2, ~3


[[Optimal tuning]] ([[CTE]]): ~2/1 = 1\1, ~3/2 = 692.713
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 692.713


{{Optimal ET sequence|legend=1| 2, 5, 7, 12e }}
{{Optimal ET sequence|legend=1| 2, 5, 7, 12e }}
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[[Comma list]]: [[4096/3993]]
[[Comma list]]: [[4096/3993]]


{{Mapping|legend=2|1 0 4|0 3 -1}}
{{Mapping|legend=2| 1 0 4 | 0 3 -1 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1/1, ~[[16/11]] = 634.320
[[Optimal tuning]] ([[CTE]]): ~2 = 1/1, ~[[16/11]] = 634.320


{{Optimal ET sequence|legend=1|11b, 13, 15, 17 }}
{{Optimal ET sequence|legend=1| 11b, 13, 15, 17 }}


[[Tp tuning #T2 tuning|RMS error]]: 1.237 cents
[[Tp tuning #T2 tuning|RMS error]]: 1.237 cents


=== Neutral ===
=== Neutral ===
Neutral can be thought of as the 2.3.11 version of either [[mohajira]] or [[neutrominant]], as well as suhajira and ringo. Among other things, it is the temperament optimizing the [[neutral tetrad]].
See [[Rastmic clan #Neutral]]
 
Subgroup: 2.3.11
 
[[Comma]]: 243/242
 
[[Gencom]]: [2 11/9; 243/242]
 
[[Gencom|Gencom mapping]]: [{{val|1 1 0 0 2}}, {{val|0 2 0 0 5}}]
 
[[Mapping|Sval mapping]]: [{{val|1 1 2}}, {{val|0 2 5}}]
 
[[Tp tuning|POL2 generator]]: ~11/9 = 350.525
 
{{Optimal ET sequence|legend=1| 7, 10, 17, 24, 41, 65, 89, 202, 291, 380 }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.3021 cents
 
; Scales
* [[neutraltet7|Seven note albitonic scale]]
* [[neutraltet10|Ten note chromatic scale]]
* [[neutraltet17|Seventeen note mega chromatic scale]]


==== Namo ====
==== Namo ====
Subgroup: 2.3.11.13
See [[Rastmic clan #Namo]]


[[Comma list]]: 144/143, 243/242
=== Huxley ===
 
{{Main| Huxley }}
[[Gencom]]: [2 11/9; 144/143 243/242]
 
[[Gencom|Gencom mapping]]: [{{val|1 1 0 0 2 4}}, {{val|0 2 0 0 5 -1}}]
 
[[Mapping|Sval mapping]]: [{{val|1 1 2 4}}, {{val|0 2 5 -1}}]
 
[[Tp tuning|POL2 generator]]: ~11/9 = 351.488
 
{{Optimal ET sequence|legend=1| 7, 10, 17, 24, 41 }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.7038 cents


=== Huxley ===
Huxley, the 4 & 13 temperament in the 2.3.11.13 subgroup, extends [[lovecraft]]. Specifically it tunes the ~13/8 to exactly half of ~8/3.  
Huxley, the 4 & 13 temperament in the 2.3.11.13 subgroup, extends [[lovecraft]]. Specifically it tunes the ~13/8 to exactly half of ~8/3.  


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[[Comma list]]: 363/361, 729/704
[[Comma list]]: 363/361, 729/704


[[Mapping]]: [{{val|1 0 -6 -6}}, {{val|0 2 12 13}}]
{{Mapping|legend=2| 1 0 -6 -6 | 0 2 12 13 }}


[[POTE generator]]: ~[[19/11]] = 945.4
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~19/11 = 945.4


{{Optimal ET sequence|legend=1| 9eehh, 14, 19, 33 }}
{{Optimal ET sequence|legend=1| 9eehh, 14, 19, 33 }}
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[[Comma list]]: 49/48, 77/76, 729/704
[[Comma list]]: 49/48, 77/76, 729/704


[[Mapping]]: [{{val|1 0 2 -6 -6}}, {{val|0 2 1 12 13}}]
{{Mapping|legend=2| 1 0 2 -6 -6 | 0 2 1 12 13 }}


[[POTE generator]]: ~[[7/4]] = 944.667
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/4 = 944.667


{{Optimal ET sequence|legend=1| 9eehh, 14, 33d, 47deh }}
{{Optimal ET sequence|legend=1| 9eehh, 14, 33d, 47deh }}
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