Hemimean clan: Difference between revisions

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= Semisept =
= Semisept =
= 5-limit =
== 5-limit ==
[[Comma list]]: 782757789696/762939453125
[[Comma list]]: 782757789696/762939453125


Line 182: Line 182:
Badness: 0.0284
Badness: 0.0284


=Sengagen=
= Sengagen =
Commas: 3136/3125, 420175/419904
[[Comma list]]: 3136/3125, 420175/419904


POTE generator: ~686/675 = 24.217
[[Mapping]]: [{{val| 1 1 2 2 }}, {{val| 0 29 16 40 }}]


Map: [<1 1 2 2|, <0 29 16 40|]
{{Multival|legend=1| 29 16 40 -42 -18 48 }}


Wedgie: <<29 16 40 -42 -18 48||
[[POTE generator]]: ~686/675 = 24.217


EDOs: 49, 50, 99, 248, 347, 446
{{Val list|legend=1| 49, 50, 99, 248, 347, 446 }}


Badness: 0.0580
[[Badness]]: 0.0580


=Subpental=
= Subpental =
Commas: 3136/3125, 19683/19600
[[Comma list]]: 3136/3125, 19683/19600


POTE generator: ~56/45 = 378.467
[[Mapping]]: [{{val| 1 6 8 17 }}, {{val| 0 -14 -18 -45 }}]


Map: [<1 6 8 17|, <0 -14 -18 -45|]
{{Multival|legend=1| 14 18 45 -4 32 54 }}


Wedgie: <<14 18 45 -4 32 54||
[[POTE generator]]: ~56/45 = 378.467


EDOs: 19, 111, 130, 929c, 1059c, 1189bc, 1319bc
{{Val list|legend=1| 19, 111, 130, 929c, 1059c, 1189bc, 1319bc }}


Badness: 0.0543
[[Badness]]: 0.0543


==11-limit==
== 11-limit ==
Commas: 540/539, 3136/3125, 8019/8000
Comma list: 540/539, 3136/3125, 8019/8000
 
Mapping: [{{val| 1 6 8 17 -6 }}, {{val| 0 -14 -18 -45 30 }}]


POTE generator: ~56/45 = 378.440
POTE generator: ~56/45 = 378.440


Map: [<1 6 8 17 -6|, <0 -14 -18 -45 30|]
{{Val list|legend=1| 19, 111, 130, 241, 371ce, 501cde, 872cde }}


EDOs: 19, 111, 130, 241, 371ce, 501cde, 872cde
Badness: 0.0453


Badness: 0.0453
== 13-limit ==
Comma list: 351/350, 540/539, 676/675, 3136/3125


==13-limit==
Mapping: [{{val| 1 6 8 17 -6 16 }}, {{val| 0 -14 -18 -45 30 -39 }}]
Commas: 351/350, 540/539, 676/675, 3136/3125


POTE generator: ~56/45 = 378.437
POTE generator: ~56/45 = 378.437


Map: [<1 6 8 17 -6 16|, <0 -14 -18 -45 30 -39|]
{{Val list|legend=1| 19, 111, 130, 241, 371ce }}


EDOs: 19, 111, 130, 241, 371ce
Badness: 0.0239


Badness: 0.0239
= Arch =
[[Comma list]]: 3136/3125, 5250987/5242880


=Arch=
[[Mapping]]: [{{val| 1 2 2 2 }}, {{val| 0 -18 14 35 }}]
Commas: 3136/3125, 5250987/5242880


POTE generator: ~64/63 = 27.668
{{Multival|legend=1| 18 -14 -35 -64 -106 -42 }}


Map: [<1 2 2 2|, <0 -18 14 35|]
[[POTE generator]]: ~64/63 = 27.668


Wedgie: <<18 -14 -35 -64 -106 -42||
{{Val list|legend=1| 43, 87, 130, 217, 347, 824c, 1171c, 1518cd }}


EDOs: 43, 87, 130, 217, 347, 824c, 1171c, 1518cd
[[Badness]]: 0.0943


Badness: 0.0943
== 11-limit ==
Comma list: 441/440, 3136/3125, 4000/3993


==11-limit==
Mapping: [{{val| 1 2 2 2 3 }}, {{val| 0 -18 14 35 20 }}]
Commas: 441/440, 3136/3125, 4000/3993


POTE generator: ~64/63 = 27.663
POTE generator: ~64/63 = 27.663


Map: [<1 2 2 2 3|, <0 -18 14 35 20|]
{{Val list|legend=1| 43, 87, 130, 217, 347e, 911cde }}


EDOs: 43, 87, 130, 217, 347e, 911cde
Badness: 0.0365


Badness: 0.0365
== 13-limit ==
Comma list: 364/363, 441/440, 676/675, 3136/3125


==13-limit==
Mapping: [{{val| 1 2 2 2 3 4 }}, {{val| 0 -18 14 35 20 -13 }}]
Commas: 364/363, 441/440, 676/675, 3136/3125


POTE generator: ~64/63 = 27.660
POTE generator: ~64/63 = 27.660


Map: [<1 2 2 2 3 4|, <0 -18 14 35 20 -13|]
{{Val list|legend=1| 43, 87, 130, 217, 347e, 564e }}


EDOs: 43, 87, 130, 217, 347e, 564e
Badness: 0.0195


Badness: 0.0195
= Emka =
[[Comma list]]: 3136/3125, 84035/82944


=Emka=
[[Mapping]]: [{{val| 1 14 6 12 }}, {{val| 0 -27 -8 -20 }}]
Commas: 3136/3125, 84035/82944


POTE generator: ~48/35 = 551.782
[[POTE generator]]: ~48/35 = 551.782


Map: [<1 14 6 12|, <0 -27 -8 -20|]
{{Val list|legend=1| 37, 50, 87, 137d, 224d }}


EDOs: 37, 50, 87, 137d, 224d
[[Badness]]: 0.1443


Badness: 0.1443
== 11-limit ==
Comma list: 385/384, 2401/2376, 3136/3125


==11-limit==
Mapping: [{{val| 1 14 6 12 3 }}, {{val| 0 -27 -8 -20 1 }}]
Commas: 385/384, 2401/2376, 3136/3125


POTE generator: ~11/8 = 551.765
POTE generator: ~11/8 = 551.765


Map: [<1 14 6 12 3|, <0 -27 -8 -20 1|]
{{Val list|legend=1| 37, 50, 87, 224d, 311d }}


EDOs: 37, 50, 87, 224d, 311d
Badness: 0.0547


Badness: 0.0547
== 13-limit ==
Comma list: 196/195, 364/363, 385/384, 625/624


==13-limit==
Mapping: [{{val| 1 14 6 12 3 6 }}, {{val| 0 -27 -8 -20 1 -5 }}]
Commas: 196/195, 364/363, 385/384, 625/624


POTE generator: ~11/8 = 551.758
POTE generator: ~11/8 = 551.758


Map: [<1 14 6 12 3 6|, <0 -27 -8 -20 1 -5|]
{{Val list|legend=1| 37, 50, 87, 224d, 311d, 398d }}
 
EDOs: 37, 50, 87, 224d, 311d, 398d


Badness: 0.0297
Badness: 0.0297

Revision as of 17:51, 5 April 2021

The hemimean clan, tempering out the no-threes hemimean comma 3136/3125, contains the temperaments misty and semisept, considered below, as well as meantone, hemiwürschmidt, parakleismic, hemithirds, clyde, bischismic, passion, hexe and sycamore considered elsewhere.

Didacus

Subgroup: 2.5.7

Comma list: 3136/3125

Sval mapping: [⟨1 0 -3], ⟨0 2 5]]

Mapping generators: ~2, ~28/25

Gencom mapping: [⟨1 0 0 -3], ⟨0 0 2 5]]

Gencom: [2 28/25; 3136/3125]

POTE generator: ~28/25 = 193.772

Template:Val list

Misty

See also: Misty family

Comma list: 3136/3125, 5120/5103

Mapping: [⟨3 0 26 56], ⟨0 1 -4 -10]]

Wedgie: ⟨⟨ 3 -12 -30 -26 -56 -36 ]]

POTE generator: ~3/2 = 703.021

Template:Val list

11-limit

Comma list: 441/440, 3136/3125, 4375/4356

Mapping: [⟨3 0 26 56 77], ⟨0 1 -4 -10 -14]]

POTE generator: ~3/2 = 703.210

Template:Val list

13-limit

Comma list: 196/195, 352/351, 364/363, 625/624

Mapping: [⟨3 0 26 56 77 92], ⟨0 1 -4 -10 -14 -17]]

POTE generator: ~3/2 = 703.303

Template:Val list

17-limit

Comma list: 196/195, 352/351, 364/363, 375/374, 595/594

Mapping: [⟨3 0 26 56 77 92 -2], ⟨0 1 -4 -10 -14 -17 3]]

POTE generator: ~3/2 = 703.233

Template:Val list

19-limit

Comma list: 196/195, 210/209, 352/351, 364/363, 375/374, 595/594

Mapping: [⟨3 0 26 56 77 92 -2 8], ⟨0 1 -4 -10 -14 -17 3 1]]

POTE generator: ~3/2 = 703.253

Template:Val list

Mystic

Comma list: 325/324, 441/440, 896/891, 1001/1000

Mapping: [⟨3 0 26 56 77 -46], ⟨0 1 -4 -10 -14 12]]

POTE generator: ~3/2 = 703.311

Template:Val list

Hemimist

Comma list: 3136/3125, 5120/5103, 3025/3024

Mapping: [⟨3 0 26 56 8], ⟨0 2 -8 -20 1]]

POTE generator: ~11/8 = 551.527

Template:Val list

Badness: 0.0474

13-limit

Comma list: 352/351, 676/675, 847/845, 3025/3024

Mapping: [⟨3 0 26 56 8 23], ⟨0 2 -8 -20 1 -5]]

POTE generator: ~11/8 = 551.525

Template:Val list

Badness: 0.0229

Semisept

5-limit

Comma list: 782757789696/762939453125

Mapping: [⟨1 12 6], ⟨0 -17 -6]]

POTE generator: ~192/125 = 735.146

Template:Val list

Badness: 0.6306

7-limit

Comma list: 3136/3125, 1728/1715

Mapping: [⟨1 12 6 12], ⟨0 -17 -6 -15]]

Wedgie: ⟨⟨ 17 6 15 -30 -24 18 ]]

POTE generator: ~75/49 = 735.155

Template:Val list

11-limit

Comma list: 176/175, 540/539, 1331/1323

Mapping: [⟨1 12 6 12 20], ⟨0 -17 -6 -15 -27]]

POTE generator: ~55/36 = 735.125

Template:Val list

Badness: 0.0225

13-limit

Comma list: 176/175, 351/350, 540/539, 1375/1372

Mapping: [⟨1 12 6 12 20 -11], ⟨0 -17 -6 -15 -27 24]]

POTE generator: ~55/36 = 735.126

Template:Val list

Badness: 0.0252

17-limit

Comma list: 176/175, 256/255, 351/350, 640/637, 715/714

Mapping: [⟨1 12 6 12 20 -11 -10], ⟨0 -17 -6 -15 -27 24 23]]

POTE generator: ~26/17 = 735.125

Template:Val list

19-limit

Comma list: 176/175, 286/285, 351/350, 476/475, 540/539, 1331/1323

Mapping: [⟨1 12 6 12 20 -11 -10 -8], ⟨0 -17 -6 -15 -27 24 23 20]]

POTE generator: ~26/17 = 735.116

Template:Val list

23-limit

Comma list: 176/175, 253/252, 286/285, 345/343, 351/350, 391/390, 460/459

Mapping: [{{val| 1 12 6 12 20 -11 -10 -8 18|, ⟨0 -17 -6 -15 -27 24 23 20 -22]]

POTE generator: ~26/17 = 735.106

Template:Val list

Semishly

Comma list: 144/143, 176/175, 196/195, 275/273

Mapping: [⟨1 12 6 12 20 8], ⟨0 -17 -6 -15 -27 -7]]

POTE generator: ~13/10 = 464.980

Template:Val list

Badness: 0.0284

Sengagen

Comma list: 3136/3125, 420175/419904

Mapping: [⟨1 1 2 2], ⟨0 29 16 40]]

Wedgie: ⟨⟨ 29 16 40 -42 -18 48 ]]

POTE generator: ~686/675 = 24.217

Template:Val list

Badness: 0.0580

Subpental

Comma list: 3136/3125, 19683/19600

Mapping: [⟨1 6 8 17], ⟨0 -14 -18 -45]]

Wedgie: ⟨⟨ 14 18 45 -4 32 54 ]]

POTE generator: ~56/45 = 378.467

Template:Val list

Badness: 0.0543

11-limit

Comma list: 540/539, 3136/3125, 8019/8000

Mapping: [⟨1 6 8 17 -6], ⟨0 -14 -18 -45 30]]

POTE generator: ~56/45 = 378.440

Template:Val list

Badness: 0.0453

13-limit

Comma list: 351/350, 540/539, 676/675, 3136/3125

Mapping: [⟨1 6 8 17 -6 16], ⟨0 -14 -18 -45 30 -39]]

POTE generator: ~56/45 = 378.437

Template:Val list

Badness: 0.0239

Arch

Comma list: 3136/3125, 5250987/5242880

Mapping: [⟨1 2 2 2], ⟨0 -18 14 35]]

Wedgie: ⟨⟨ 18 -14 -35 -64 -106 -42 ]]

POTE generator: ~64/63 = 27.668

Template:Val list

Badness: 0.0943

11-limit

Comma list: 441/440, 3136/3125, 4000/3993

Mapping: [⟨1 2 2 2 3], ⟨0 -18 14 35 20]]

POTE generator: ~64/63 = 27.663

Template:Val list

Badness: 0.0365

13-limit

Comma list: 364/363, 441/440, 676/675, 3136/3125

Mapping: [⟨1 2 2 2 3 4], ⟨0 -18 14 35 20 -13]]

POTE generator: ~64/63 = 27.660

Template:Val list

Badness: 0.0195

Emka

Comma list: 3136/3125, 84035/82944

Mapping: [⟨1 14 6 12], ⟨0 -27 -8 -20]]

POTE generator: ~48/35 = 551.782

Template:Val list

Badness: 0.1443

11-limit

Comma list: 385/384, 2401/2376, 3136/3125

Mapping: [⟨1 14 6 12 3], ⟨0 -27 -8 -20 1]]

POTE generator: ~11/8 = 551.765

Template:Val list

Badness: 0.0547

13-limit

Comma list: 196/195, 364/363, 385/384, 625/624

Mapping: [⟨1 14 6 12 3 6], ⟨0 -27 -8 -20 1 -5]]

POTE generator: ~11/8 = 551.758

Template:Val list

Badness: 0.0297

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