Subgroup temperaments: Difference between revisions

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Line 18: Line 18:
[[Tp tuning|POL2 generator]]: ~11/10 = 164.078
[[Tp tuning|POL2 generator]]: ~11/10 = 164.078


{{Val list|legend=1| 7, 15, 22, 37, 73cd, 95cd, 117bcd ]}
{{Val list|legend=1| 7, 15, 22, 37, 73cd, 95cd, 117bcd }}


[[Tp tuning #T2 tuning|RMS error]]: 2.287 cents
[[Tp tuning #T2 tuning|RMS error]]: 2.287 cents
Line 51: Line 51:
[[Gencom]]: [2 40/27; 243/242 4000/3993]
[[Gencom]]: [2 40/27; 243/242 4000/3993]


[[Gencom|Gencom mapping]]: [<1 5 12 0 12|, <0 -6 -17 0 -15|]
[[Gencom|Gencom mapping]]: [{{val|1 5 12 0 12}}, {{val|0 -6 -17 0 -15}}]


[[Mapping|Sval mapping]]: [<1 5 12 12|, <0 -6 -17 -15|]
[[Mapping|Sval mapping]]: [{{val|1 5 12 12}}, {{val|0 -6 -17 -15}}]


[[Tp tuning|POL2 generator]]: ~40/27 = 683.166
[[Tp tuning|POL2 generator]]: ~40/27 = 683.166
Line 282: Line 282:
[[Gencom]]: [2 9/7; 78/77, 99/98, 243/242]
[[Gencom]]: [2 9/7; 78/77, 99/98, 243/242]


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


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


[[Tp tuning|POL2 generator]]: ~9/7 = 424.457
[[Tp tuning|POL2 generator]]: ~9/7 = 424.457
Line 422: Line 422:
[[Tp tuning #T2 tuning|RMS error]]: 0.5391 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.5391 cents


==Rainy==
== Rainy ==
Three generators make an [[8/7]]; five generators make a [[5/4]]. This is the no-threes version of [[tertiaseptal]].
Three generators make an [[8/7]]; five generators make a [[5/4]]. This is the no-threes version of [[tertiaseptal]].


Line 560: Line 560:
[[Mapping|Sval mapping]]: [{{val|1 2 4}}, {{val|0 3 1}}]
[[Mapping|Sval mapping]]: [{{val|1 2 4}}, {{val|0 3 1}}]


[[Tp tuning|POL2 generator]]: ~17/13 = 467.375
[[Tp tuning|POL2 generator]]: ~21/16 = 467.375


{{Val list|legend=1| 5, 13, 18, 41, 59, 77, 95 }}
{{Val list|legend=1| 5, 13, 18, 41, 59, 77, 95 }}
Line 566: Line 566:
[[Tp tuning #T2 tuning|RMS error]]: 0.3202 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.3202 cents


= 2.3.7/5.11/5.13/5 subgroup =
= Miscellaneous subgroup temperaments =


== Historical ==
== Historical ==
Subgroup: 2.3.7/5.11/5.13/5
Subgroup: 2.3.7/5.11/5.13/5


Commas: 364/363, 441/440, 1001/1000
[[Comma list]]: 364/363, 441/440, 1001/1000


[[Lp_tuning|POL2 generator]]: ~21/20 = 83.016
[[Mapping|Sval mapping]]: [{{val|1 2 0 1 2}}, {{val|0 -6 7 2 -9}}]


[[Gencom]]: [2 21/20; 364/363 441/440 1001/1000]
[[Tp tuning|POL2 generator]]: ~21/20 = 83.016


Gencom map: [<1 2 -3/4 -3/4 1/4 5/4|, <0 -6 0 7 2 -9|]
{{Val list|legend=1| 14, 29, 72, 101, 130, 159 }}


Sval map: [<1 2 0 1 2|, <0 -6 7 2 -9|]
[[Tp tuning #T2 tuning|RMS error]]: 0.2562 cents
 
EDOs: 14, 29, 72, 101, 130, 159
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.2562 cents
 
= 2.3.7.11/5.13 subgroup =


== Hypnosis ==
== Hypnosis ==
Subgroup: 2.3.7.11/5.13
Subgroup: 2.3.7.11/5.13


Commas: 169/168, 540/539, 729/728
[[Comma list]]: 169/168, 540/539, 729/728


Related temperament: [[Swetismic temperaments #Hypnos|hypnos]], [[Hemifamity temperaments #Tricot|tricot]]
Related temperament: [[Swetismic temperaments #Hypnos|hypnos]], [[Hemifamity temperaments #Tricot|tricot]]


[[Gencom]]: [2 13/9; 169/168, 540/539, 729/728]
[[Mapping|Sval mapping]]: [{{val|1 0 -3 8 0}}, {{val|0 3 11 -13 7}}]


Gencom map: [<1 0 -4 -3 4 0|, <0 3 13/2 11 -13/2 7|]
[[Tp tuning|POL2 generator]]: ~13/9 = 633.518


Sval map: [<1 0 -3 8 0|, <0 3 11 -13 7|]
{{Val list|legend=1| 17, 36, 118e, 125e, 161e, 197e }}


EDOs: 17, 36, 118e, 125e, 161e, 197e
[[Tp tuning #T2 tuning|RMS error]]: 0.5379 cents
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.5379 cents


[[Category:Regular temperament theory]]
[[Category:Regular temperament theory]]
[[Category:Temperament clan]]
[[Category:Temperament clan]]
[[Category:Subgroup]]
[[Category:Subgroup]]
{{todo| cleanup }}