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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. 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]].
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]].


=Buzzard=
= Buzzard =
Commas: 1728/1715, 5120/5103
[[Comma list]]: 1728/1715, 5120/5103


[[POTE_tuning|POTE generator]]: ~320/243 = 475.636
[[Mapping]]: [<1 0 -6 4|, <0 4 21 -3|]


Map: [<1 0 -6 4|, <0 4 21 -3|]
[[Wedgie]]: <<4 21 -3 24 -16 -66||


Wedgie: <<4 21 -3 24 -16 -66||
[[POTE_tuning|POTE generator]]: ~21/16 = 475.636


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


Badness: 0.0480
[[Badness]]: 0.047963


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


[[POTE_tuning|POTE generator]]: ~320/243 = 475.700
Mapping: [<1 0 -6 4 -12|, <0 4 21 -3 39|]


Map: [<1 0 -6 4 -12|, <0 4 21 -3 39|]
POTE generator: ~21/16 = 475.700
2, 3, 5, 53, 58, 111, 391,
Vals: {{Val list| 53, 58, 111, 280cd, 391cd }}


EDOs: 53, 58, 111, 280cd, 391cd
Badness: 0.034484


Badness: 0.0345
== 13-limit ==
Comma list: 176/175, 351/350, 540/539, 676/675


==13-limit==
Mapping: [<1 0 -6 4 -12 -7|, <0 4 21 -3 39 27|]
Commas: 176/175, 351/350, 540/539, 676/675


[[POTE_tuning|POTE generator]]: ~320/243 = 475.697
POTE generator: ~21/16 = 475.697


Map: [<1 0 -6 4 -12 -7|, <0 4 21 -3 39 27|]
Vals: {{Val list| 53, 58, 111, 280cdf, 391cdf }}


EDOs: 53, 58, 111, 280cdf, 391cdf
Badness: 0.018842


Badness: 0.0188
== 17-limit ==
Comma list: 176/175, 256/255, 351/350, 442/441, 540/539


==17-limit==
Mapping: [<1 0 -6 4 -12 -7 14|, <0 4 21 -3 39 27 -25|]
Commas: 176/175, 256/255, 351/350, 442/441, 540/539


[[POTE_tuning|POTE generator]]: ~320/243 = 475.692
POTE generator: ~21/16 = 475.692


Map: [<1 0 -6 4 -12 -7 14|, <0 4 21 -3 39 27 -25|]
Vals: {{Val list| 53, 58, 111, 321cdfg }}


EDOs: 53, 58, 111, 321cdfg
Badness: 0.018403


Badness: 0.0184
== 19-limit ==
Comma list: 176/175, 256/255, 286/285, 324/323, 351/350, 540/539


==19-limit==
Mapping: [<1 0 -6 4 -12 -7 14 -12|, <0 4 21 -3 39 27 -25 41|]
Commas: 176/175, 256/255, 286/285, 324/323, 351/350, 540/539


[[POTE_tuning|POTE generator]]: ~320/243 = 475.679
POTE generator: ~21/16 = 475.679


Map: [<1 0 -6 4 -12 -7 14 -12|, <0 4 21 -3 39 27 -25 41|]
Vals: {{Val list| 53, 58h, 111 }}


EDOs: 53, 58h, 111
Badness: 0.015649


Badness: 0.0156
== Buteo ==
Comma list: 99/98, 385/384, 2200/2187


==Buteo==
Mapping: [<1 0 -6 4 9|, <0 4 21 -3 -14|]
Commas: 99/98, 385/384, 2200/2187


POTE generator: ~21/16 = 475.436
POTE generator: ~21/16 = 475.436


Map: [<1 0 -6 4 9|, <0 4 21 -3 -14|]
Vals: {{Val list| 5, 48, 53 }}


EDOs: 5, 48, 53
Badness: 0.060238


Badness: 0.0602
=== 13-limit ===
Comma list: 99/98, 275/273, 385/384, 572/567


===13-limit===
Mapping: [<1 0 -6 4 9 -7|, <0 4 21 -3 -14 27|]
Commas: 99/98, 275/273, 385/384, 572/567


POTE generator: ~21/16 = 475.464
POTE generator: ~21/16 = 475.464


Map: [<1 0 -6 4 9 -7|, <0 4 21 -3 -14 27|]
Vals: {{Val list| 5, 48f, 53 }}


EDOs: 5, 53
Badness: 0.039854
 
Badness: 0.0390


= Undecental =
= Undecental =
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