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Hemifamity temperaments: Difference between revisions

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The hemifamity temperaments temper out the hemifamity comma, {{monzo| 10 -6 1 -1 }} = [[5120/5103]], dividing an exact or approximate septimal diesis, {{monzo| 2 2 -1 -1 }} = [[36/35]] into two equal steps.


The hemifamity temperaments temper out the hemifamity comma, {{monzo| 10 -6 1 -1 }} = [[5120/5103]], dividing an exact or approximate septimal diesis, {{monzo| 2 2 -1 -1 }} = [[36/35]] into two equal steps. Belonging to it and considered below are buzzard, undecental, leapday, mystery, quanic and ketchup. Other hemifamity temperaments are [[Meantone family #Dominant|dominant]], [[Schismatic family #Garibaldi|garibaldi]], [[Breedsmic temperaments #Hemififths|hemififths]], [[Ragismic microtemperaments #Amity|amity]], [[Hemimean clan #Misty|misty]], [[Gamelismic clan #Rodan|rodan]], [[Kleismic family #Countercata|countercata]] and [[Mirkwai clan #Kwai|kwai]].
Belonging to it and considered below are buzzard, undecental, leapday, mystery, quanic and ketchup. Other hemifamity temperaments are [[Meantone family #Dominant|dominant]], [[Schismatic family #Garibaldi|garibaldi]], [[Breedsmic temperaments #Hemififths|hemififths]], [[Ragismic microtemperaments #Amity|amity]], [[Hemimean clan #Misty|misty]], [[Gamelismic clan #Rodan|rodan]], [[Kleismic family #Countercata|countercata]] and [[Mirkwai clan #Kwai|kwai]].


= Buzzard =
= Buzzard =
{{see also| Vulture family }}
Subgroup: 2.3.5.7
[[Comma list]]: 1728/1715, 5120/5103
[[Comma list]]: 1728/1715, 5120/5103


[[Mapping]]: [<1 0 -6 4|, <0 4 21 -3|]
[[Mapping]]: [{{val| 1 0 -6 4 }}, {{val| 0 4 21 -3 }}]


[[Wedgie]]: <<4 21 -3 24 -16 -66||
{{Multival|legend=1| 4 21 -3 24 -16 -66 }}


[[POTE_tuning|POTE generator]]: ~21/16 = 475.636
[[POTE generator]]: ~21/16 = 475.636


{{Val list|legend=1| 5, 43c, 48, 53, 111, 164d, 275d }}
{{Val list|legend=1| 5, 43c, 48, 53, 111, 164d, 275d }}
Line 17: Line 21:


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 176/175, 540/539, 5120/5103
Comma list: 176/175, 540/539, 5120/5103


Mapping: [<1 0 -6 4 -12|, <0 4 21 -3 39|]
Mapping: [{{val| 1 0 -6 4 -12 }}, {{val| 0 4 21 -3 39 }}]


POTE generator: ~21/16 = 475.700
POTE generator: ~21/16 = 475.700
2, 3, 5, 53, 58, 111, 391,
 
Vals: {{Val list| 53, 58, 111, 280cd, 391cd }}
Vals: {{Val list| 53, 58, 111, 280cd, 391cd }}


Badness: 0.034484
Badness: 0.034484


== 13-limit ==
=== 13-limit ===
 
Subgroup: 2.3.5.7.11.13
 
Comma list: 176/175, 351/350, 540/539, 676/675
Comma list: 176/175, 351/350, 540/539, 676/675


Mapping: [<1 0 -6 4 -12 -7|, <0 4 21 -3 39 27|]
Mapping: [{{val| 1 0 -6 4 -12 -7 }}, {{val| 0 4 21 -3 39 27 }}]


POTE generator: ~21/16 = 475.697
POTE generator: ~21/16 = 475.697
Line 38: Line 48:
Badness: 0.018842
Badness: 0.018842


== 17-limit ==
=== 17-limit ===
 
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 176/175, 256/255, 351/350, 442/441, 540/539
Comma list: 176/175, 256/255, 351/350, 442/441, 540/539


Mapping: [<1 0 -6 4 -12 -7 14|, <0 4 21 -3 39 27 -25|]
Mapping: [{{val| 1 0 -6 4 -12 -7 14 }}, {{val| 0 4 21 -3 39 27 -25 }}]


POTE generator: ~21/16 = 475.692
POTE generator: ~21/16 = 475.692
Line 49: Line 62:
Badness: 0.018403
Badness: 0.018403


== 19-limit ==
=== 19-limit ===
 
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 176/175, 256/255, 286/285, 324/323, 351/350, 540/539
Comma list: 176/175, 256/255, 286/285, 324/323, 351/350, 540/539


Mapping: [<1 0 -6 4 -12 -7 14 -12|, <0 4 21 -3 39 27 -25 41|]
Mapping: [{{val| 1 0 -6 4 -12 -7 14 -12 }}, {{val| 0 4 21 -3 39 27 -25 41 }}]


POTE generator: ~21/16 = 475.679
POTE generator: ~21/16 = 475.679
Line 61: Line 77:


== Buteo ==
== Buteo ==
Subgroup: 2.3.5.7.11
Comma list: 99/98, 385/384, 2200/2187
Comma list: 99/98, 385/384, 2200/2187


Mapping: [<1 0 -6 4 9|, <0 4 21 -3 -14|]
Mapping: [{{val| 1 0 -6 4 9 }}, {{val| 0 4 21 -3 -14 }}]


POTE generator: ~21/16 = 475.436
POTE generator: ~21/16 = 475.436
Line 72: Line 91:


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 99/98, 275/273, 385/384, 572/567
Comma list: 99/98, 275/273, 385/384, 572/567


Mapping: [<1 0 -6 4 9 -7|, <0 4 21 -3 -14 27|]
Mapping: [{{val| 1 0 -6 4 9 -7 }}, {{val| 0 4 21 -3 -14 27 }}]


POTE generator: ~21/16 = 475.464
POTE generator: ~21/16 = 475.464
Line 83: Line 105:


= Undecental =
= Undecental =
Subgroup: 2.3.5.7
[[Comma list]]: 5120/5103, 235298/234375
[[Comma list]]: 5120/5103, 235298/234375


[[Mapping]]: [<1 0 61 71|, <0 1 -37 -43|]
[[Mapping]]: [{{val| 1 0 61 71 }}, {{val| 0 1 -37 -43 }}]


[[Wedgie]]: <<1 -37 -43 -61 -71 4||
{{Multival|legend=1| 1 -37 -43 -61 -71 4 }}


[[POTE_tuning|POTE generator]]: ~3/2 = 703.039
[[POTE generator]]: ~3/2 = 703.039


{{Val list|legend=1| 29, 70, 99, 722bc, 821bc, 920bc, 1019bc, 1118bbcc, 1217bbcc, 1316bbccd }}
{{Val list|legend=1| 29, 70, 99, 722bc, 821bc, 920bc, 1019bc, 1118bbcc, 1217bbcc, 1316bbccd }}


Badness: 0.094603
[[Badness]]: 0.094603


= Leapday =
= Leapday =
[[Comma]]: 10737418240/10460353203 (trisayo comma)


[[Mapping]]: [<1 0 -31|, <0 1 21|]
Subgroup: 2.3.5


[[POTE tuning|POTE generator]]: ~3/2 = 704.179
[[Comma list]]: 10737418240/10460353203
 
[[Mapping]]: [{{val| 1 0 -31 }}, {{val| 0 1 21 }}]
 
[[POTE generator]]: ~3/2 = 704.179


{{Val list|legend=1| 29, 46, 121, 167, 455bc, 622bbc }}
{{Val list|legend=1| 29, 46, 121, 167, 455bc, 622bbc }}
Line 107: Line 135:


== 7-limit ==
== 7-limit ==
Subgroup: 2.3.5.7
[[Comma list]]: 686/675, 5120/5103
[[Comma list]]: 686/675, 5120/5103


[[Mapping]]: [<1 0 -31 -21|, <0 1 21 15|]
[[Mapping]]: [{{val| 1 0 -31 -21 }}, {{val| 0 1 21 15 }}]


[[Wedgie]]: <<1 21 15 31 21 -24||
{{Multival|legend=1| 1 21 15 31 21 -24 }}


[[POTE tuning|POTE generator]]: ~3/2 = 704.263
[[POTE generator]]: ~3/2 = 704.263


{{Val list|legend=1| 17c, 29, 46, 167d, 213d, 259cdd, 305bcdd }}
{{Val list|legend=1| 17c, 29, 46, 167d, 213d, 259cdd, 305bcdd }}
Line 120: Line 151:


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 121/120, 441/440, 686/675
Comma list: 121/120, 441/440, 686/675


Mapping: [<1 0 -31 -21 -14|, <0 1 21 15 11|]
Mapping: [{{val| 1 0 -31 -21 -14 }}, {{val| 0 1 21 15 11 }}]


POTE generator: ~3/2 = 704.250
POTE generator: ~3/2 = 704.250
Line 131: Line 165:


== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 121/120, 169/168, 352/351
Comma list: 91/90, 121/120, 169/168, 352/351


Mapping: [<1 0 -31 -21 -14 -9|, <0 1 21 15 11 8|]
Mapping: [{{val| 1 0 -31 -21 -14 -9 }}, {{val| 0 1 21 15 11 8 }}]


POTE generator: ~3/2 = 704.214
POTE generator: ~3/2 = 704.214
Line 142: Line 179:


== 17-limit ==
== 17-limit ==
Subgroup: 2.3.5.7.11.13.17
Comma list: 91/90, 121/120, 136/135, 154/153, 169/168
Comma list: 91/90, 121/120, 136/135, 154/153, 169/168


Mapping: [<1 0 -31 -21 -14 -9 -34|, <0 1 21 15 11 8 24|]
Mapping: [{{val| 1 0 -31 -21 -14 -9 -34 }}, {{val| 0 1 21 15 11 8 24 }}]


POTE generator: ~3/2 = 704.229
POTE generator: ~3/2 = 704.229
Line 152: Line 192:
Badness: 0.017863
Badness: 0.017863


== 19-limit ==
=== 19-limit ===
 
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 91/90, 121/120, 133/132, 136/135, 154/153, 169/168
Comma list: 91/90, 121/120, 133/132, 136/135, 154/153, 169/168


Mapping: [<1 0 -31 -21 -14 -9 -34 9|, <0 1 21 15 11 8 24 -3|]
Mapping: [{{val| 1 0 -31 -21 -14 -9 -34 9 }}, {{val| 0 1 21 15 11 8 24 -3 }}]


POTE generator: ~3/2 = 704.135
POTE generator: ~3/2 = 704.135
Line 163: Line 206:
Badness: 0.017356
Badness: 0.017356


== Leapling ==
=== Leapling ===
 
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 77/76, 91/90, 121/120, 136/135, 153/152, 169/168
Comma list: 77/76, 91/90, 121/120, 136/135, 153/152, 169/168


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