Dicot family: Difference between revisions

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=Dicot=
=Dicot=
Comma: 25/24
[[Comma]]: 25/24


POTE generator: ~5/4 = 348.594
[[POTE tuning|POTE generator]]: ~5/4 = 348.594


Map: [<1 1 2|, <0 2 1|]
[[Map]]: [<1 1 2|, <0 2 1|]


EDOs: [[3edo|3]], [[4edo|4]], [[7edo|7]], [[10edo|10]], [[13edo|13]], [[17edo|17]], [[23edo|23b]], [[24edo|24c]], [[27edo|27c]], [[31edo|31c]]
{{Vals|legend=1| 3, 4, 7, 17, 24c, 31c }}


Badness: 0.0130
[[Badness]]: 0.013028


==7-limit==
==7-limit==
[[Comma]]s: 15/14, 25/24
[[Comma list]]: 15/14, 25/24


[[POTE_tuning|POTE generator]]: ~5/4 = 336.381
[[POTE tuning|POTE generator]]: ~5/4 = 336.381


Map: [<1 1 2 2|, <0 2 1 3|]
[[Map]]: [<1 1 2 2|, <0 2 1 3|]


Wedgie: <<2 1 3 -3 -1 4||
Wedgie: <<2 1 3 -3 -1 4||


EDOs: 3d, 4, 7, [[11edo|11c]], [[18edo|18bc]], [[25edo|25bccd]]
{{Vals|legend=1| 3d, 4, 7, 18bc, 25bccd }}


Badness: 0.0199
[[Badness]]: 0.019935


==11-limit==
==11-limit==
Commas: 15/14, 22/21, 25/24
Comma list: 15/14, 22/21, 25/24


POTE generator: ~5/4 = 342.125
POTE generator: ~5/4 = 342.125
Line 35: Line 35:
Map: [<1 1 2 2 2|, <0 2 1 3 5|]
Map: [<1 1 2 2 2|, <0 2 1 3 5|]


EDOs: 3de, 4e, 7
Vals: {{Vals| 3de, 4e, 7 }}


Badness: 0.0199
Badness: 0.019854


==Eudicot==
==Eudicot==
Commas: 15/14, 25/24, 33/32
Comma list: 15/14, 25/24, 33/32


POTE generator: ~5/4 = 336.051
POTE generator: ~5/4 = 336.051
Line 46: Line 46:
Map: [<1 1 2 2 4|, <0 2 1 3 -2|]
Map: [<1 1 2 2 4|, <0 2 1 3 -2|]


EDOs: 3d, 4, 7, 11c, 18bc, 25bccd
Vals: {{Vals| 3d, 4, 7, 18bc, 25bccd }}


Badness: 0.0271
Badness: 0.027114


===13-limit===
===13-limit===
Commas: 15/14, 25/24, 33/32, 40/39
Comma list: 15/14, 25/24, 33/32, 40/39


POTE generator: ~5/4 = 338.846
POTE generator: ~5/4 = 338.846
Line 57: Line 57:
Map: [<1 1 2 2 4 4|, <0 2 1 3 -2 -1|]
Map: [<1 1 2 2 4 4|, <0 2 1 3 -2 -1|]


EDOs: 3d, 4, 7, 11c, 18bc, 25bccd
Vals: {{Vals| 3d, 4, 7, 25bccd, 32bccddef, 39bcccdddef }}


Badness: 0.0238
Badness: 0.023828


=Flat=
=Flat=
Commas: 21/20, 25/24
[[Comma list]]: 21/20, 25/24


POTE generator: ~5/4 = 331.916
[[POTE tuning|POTE generator]]: ~5/4 = 331.916


Map: [<1 1 2 3|, <0 2 1 -1|]
[[Map]]: [<1 1 2 3|, <0 2 1 -1|]


Wedgie: <<2 1 -1 -3 -7 -5||
Wedgie: <<2 1 -1 -3 -7 -5||


EDOs: 3, 4, 7d, 11cd
{{Vals|legend=1| 3, 4, 7d, 11cd, 18bcddd }}


Badness: 0.0254
[[Badness]]: 0.025381


==11-limit==
==11-limit==
Commas: 21/20, 25/24, 33/32
Comma list: 21/20, 25/24, 33/32


POTE generator: ~5/4 = 337.532
POTE generator: ~5/4 = 337.532
Line 81: Line 81:
Map: [<1 1 2 3 4|, <0 2 1 -1 -2|]
Map: [<1 1 2 3 4|, <0 2 1 -1 -2|]


EDOs: 3, 4, 7d, 11cd
Vals: {{Vals| 3, 4, 7d }}


Badness: 0.0250
Badness: 0.024988


==13-limit==
==13-limit==
Commas: 14/13, 21/20, 25/24, 33/32
Comma list: 14/13, 21/20, 25/24, 33/32


POTE generator: ~5/4 = 341.023
POTE generator: ~5/4 = 341.023
Line 92: Line 92:
Map: [<1 1 2 3 4 4|, <0 2 1 -1 -2 -1|]
Map: [<1 1 2 3 4 4|, <0 2 1 -1 -2 -1|]


EDOs: 3, 4, 7d, 11cd
Vals: {{Vals| 3, 4, 7d }}


Badness: 0.0234
Badness: 0.023420


=Sharp=
=Sharp=
Commas: 25/24, 28/27
[[Comma list]]: 25/24, 28/27


[[POTE_tuning|POTE generator]]: ~5/4 = 357.938
[[POTE tuning|POTE generator]]: ~5/4 = 357.938


Map: [<1 1 2 1|, <0 2 1 6|]
[[Map]]: [<1 1 2 1|, <0 2 1 6|]


EDOs: 3d, 7d, [[10edo|10]], 17d, [[57edo|57bccdd]]
{{Vals|legend=1| 3d, 7d, 10, 37cd, 47bccd, 57bccdd }}


Badness: 0.0289
[[Badness]]: 0.028942


==11-limit==
==11-limit==
Commas: 25/24, 28/27, 35/33
Comma list: 25/24, 28/27, 35/33


POTE generator: ~5/4 = 356.106
POTE generator: ~5/4 = 356.106
Line 114: Line 114:
Map: [<1 1 2 1 2|, <0 2 1 6 5|]
Map: [<1 1 2 1 2|, <0 2 1 6 5|]


EDOs: 3de, 7d, 10, 17d, 27cde
Vals: {{Vals| 3de, 7d, 10, 17d, 27cde }}


Badness: 0.0224
Badness: 0.022366


=Decimal=
=Decimal=
Commas: 25/24, 49/48
[[Comma list]]: 25/24, 49/48


[[POTE_tuning|POTE generator]]: ~7/6 = 251.557
[[POTE tuning|POTE generator]]: ~7/6 = 251.557


Map: [<2 0 3 4|, <0 2 1 1|]
[[Map]]: [<2 0 3 4|, <0 2 1 1|]


Wedgie: <<4 2 2 -6 -8 -1||
Wedgie: <<4 2 2 -6 -8 -1||


EDOs: [[10edo|10]], [[14edo|14c]], [[24edo|24c]], [[38edo|38cd]]
{{Vals|legend=1| 4, 10, 14c, 24c, 38ccd, 62cccdd }}


Badness: 0.0283
[[Badness]]: 0.028334


==11-limit==
==11-limit==
Commas: 25/24, 45/44, 49/48
Comma list: 25/24, 45/44, 49/48


[[POTE_tuning|POTE generator]]: ~7/6 = 253.493
POTE generator: ~7/6 = 253.493


Map: [<2 0 3 4 -1|, <0 2 1 1 5|]
Map: [<2 0 3 4 -1|, <0 2 1 1 5|]


EDOs: 10, 14c, 24c, 38cd
Vals: {{Vals| 10, 14c, 24c, 38ccd, 52cccde }}


Badness: 0.0267
Badness: 0.026712


==Decimated==
==Decimated==
Commas: 25/24, 33/32, 49/48
Comma list: 25/24, 33/32, 49/48


[[POTE_tuning|POTE generator]]: ~7/6 = 255.066
POTE generator: ~7/6 = 255.066


Map: [<2 0 3 4 10|, <0 2 1 1 -2|]
Map: [<2 0 3 4 10|, <0 2 1 1 -2|]


EDOs: 4, 10e, 14c
Vals: {{Vals| 4, 10e, 14c }}


Badness: 0.0315
Badness: 0.031456


==Decibel==
==Decibel==
Commas: 25/24, 35/33, 49/48
Comma list: 25/24, 35/33, 49/48


POTE generator: ~8/7 = 243.493
POTE generator: ~8/7 = 243.493
Line 160: Line 160:
Map: [<2 0 3 4 7|, <0 2 1 1 0|]
Map: [<2 0 3 4 7|, <0 2 1 1 0|]


EDOs: 4, 6, 10
Vals: {{Vals| 4, 6, 10 }}


Badness: 0.0324
Badness: 0.032385


=Dichotic=
=Dichotic=
Commas: 25/24, 64/63
[[Comma list]]: 25/24, 64/63


POTE generator: ~5/4 = 356.264
[[POTE tuning|POTE generator]]: ~5/4 = 356.264


Map: [<1 1 2 4|, <0 2 1 -4|]
[[Map]]: [<1 1 2 4|, <0 2 1 -4|]


Wedgie: <<2 1 -4 -3 -12 -12||
Wedgie: <<2 1 -4 -3 -12 -12||


EDOs: 7, 10, 17, 27c, 37c
{{Vals|legend=1| 3, 7, 10, 17, 27c, 37c, 64bccc }}


Badness: 0.0376
[[Badness]]: 0.037565


==11-limit==
==11-limit==
Commas: 25/24, 45/44, 64/63
Comma list: 25/24, 45/44, 64/63


POTE generator: ~5/4 = 354.262
POTE generator: ~5/4 = 354.262
Line 184: Line 184:
Map: [<1 1 2 4 2|, <0 2 1 -4 5|]
Map: [<1 1 2 4 2|, <0 2 1 -4 5|]


EDOs: 7, 10, 17, 27ce, 44ce
Vals: {{Vals| 7, 10, 17, 27ce, 44cce }}


Badness: 0.0307
Badness: 0.030680


==Dichosis==
==Dichosis==
Commas: 25/24, 35/33, 64/63
Comma list: 25/24, 35/33, 64/63


POTE generator: ~5/4 = 360.659
POTE generator: ~5/4 = 360.659
Line 195: Line 195:
Map: [<1 1 2 4 5|, <0 2 1 -4 -5|]
Map: [<1 1 2 4 5|, <0 2 1 -4 -5|]


EDOs: 3, 10
Vals: {{Vals| 3, 7e, 10 }}


Badness: 0.0414
Badness: 0.041361


=Jamesbond=
=Jamesbond=
Commas: 25/24, 81/80
[[Comma list]]: 25/24, 81/80


[[POTE_tuning|POTE generator]]: ~8/7 = 258.139
[[POTE tuning|POTE generator]]: ~8/7 = 258.139


Map: [<7 11 16 0|, <0 0 0 1|]
[[Map]]: [<7 11 16 0|, <0 0 0 1|]


EDOs: 7, [[14edo|14c]]
{{Vals|legend=1| 7, 14c }}
 
[[Badness]]: 0.041714


==11-limit==
==11-limit==
11-limit jamesbond is called "septimal" on the Regular Temperament Finder.
Comma list: 25/24, 33/32, 45/44
 
Commas: 25/24, 33/32, 45/44


POTE generator: ~8/7 = 258.910
POTE generator: ~8/7 = 258.910
Line 217: Line 217:
Map: [<7 11 16 0 24|, <0 0 0 1 0|]
Map: [<7 11 16 0 24|, <0 0 0 1 0|]


EDOs: 7, 14c
Vals: {{Vals| 7, 14c }}


Badness: 0.0235
Badness: 0.023524


==13-limit==
==13-limit==
Commas: 25/24 27/26 33/32 45/44
Comma list: 25/24, 27/26, 33/32, 40/39


POTE generator: ~8/7 = 250.764
POTE generator: ~8/7 = 250.764
Line 228: Line 228:
Map: [<7 11 16 0 24 26|, <0 0 0 1 0 0|]
Map: [<7 11 16 0 24 26|, <0 0 0 1 0 0|]


EDOs: 7, 14c
Vals: {{Vals| 7, 14c }}


Badness: 0.0230
Badness: 0.023003


==Septimal==
==Septimal==
Commas: 25/24, 33/32, 45/44, 65/63
Comma list: 25/24, 33/32, 45/44, 65/63


POTE generator: ~8/7 = 247.447
POTE generator: ~8/7 = 247.445


Map: [<7 11 16 0 24 6|, <0 0 0 1 0 1|]
Map: [<7 11 16 0 24 6|, <0 0 0 1 0 1|]


EDOs: 7, 14cf
Vals: {{Vals| 7, 14cf }}


Badness: 0.0226
Badness: 0.022569


=Sidi=
=Sidi=
Commas: 25/24, 245/243
[[Comma list]]: 25/24, 245/243


[[POTE_tuning|POTE generator]]: ~9/7 = 427.208
[[POTE tuning|POTE generator]]: ~9/7 = 427.208


Map: [<1 3 3 6|, <0 -4 -2 -9|]
[[Map]]: [<1 3 3 6|, <0 -4 -2 -9|]


EDOs: [[14edo|14c]], [[45edo|45c]], <59 93 135 165|
{{Vals|legend=1| 14c, 45c, 59bccd }}


Badness: 0.0566
[[Badness]]: 0.0566


==11-limit==
==11-limit==
Commas: 25/24, 45/44, 99/98
Comma list: 25/24, 45/44, 99/98


POTE generator: ~9/7 = 427.273
POTE generator: ~9/7 = 427.273
Line 261: Line 261:
Map: [<1 3 3 6 7|, <0 -4 -2 -9 -10|]
Map: [<1 3 3 6 7|, <0 -4 -2 -9 -10|]


EDOs: 14c, 17, 45ce, 59bccde
Vals: {{Vals| 14c, 17, 45ce, 59bccde }}


Badness: 0.0330
Badness: 0.0330


=Quad=
=Quad=
Commas: 9/8, 25/24
[[Comma list]]: 9/8, 25/24


POTE generator: ~5/4 = 324.482
[[POTE tuning|POTE generator]]: ~5/4 = 324.482


Map: [<4 6 9 0|, <0 0 0 1|]
[[Map]]: [<4 6 9 0|, <0 0 0 1|]


Wedgie: <<0 0 4 0 6 9||
Wedgie: <<0 0 4 0 6 9||


EDOs: 4, 12bcd
{{Vals|legend=1| 4, 12bcd }}


Badness: 0.0460
[[Badness]]: 0.0460


[[Category:Theory]]
[[Category:Theory]]
[[Category:Temperament family]]
[[Category:Temperament family]]
[[Category:Dicot]]
[[Category:Dicot]]

Revision as of 08:14, 4 April 2021

The 5-limit parent comma for the dicot family is 25/24, the chromatic semitone. Its monzo is |-3 -1 2>, and flipping that yields <<2 1 -3|| for the wedgie. This tells us the generator is a third (major and minor mean the same thing), and that two thirds gives a fifth. In fact, (5/4)^2 = 3/2 * 25/24. Possible tunings for dicot are 7edo, 24edo using the val <24 38 55| (24c) and 31edo using the val <31 49 71| (31c). In a sense, what dicot is all about is using neutral thirds and pretending that's 5-limit, and like any temperament which seems to involve pretending, dicot is at the edge of what can sensibly be called a temperament at all.

Seven limit children

The second comma of the normal comma list defines which 7-limit family member we are looking at. Septimal dicot, with wedgie <<2 1 3 -3 -1 4|| adds 36/35, sharp with wedgie <<2 1 6 -3 4 11|| adds 28/27, and dichotic with wedgie <<2 1 -4 -3 -12 -12|| ads 64/63, all retaining the same period and generator. Decimal with wedgie <<4 2 2 -6 -8 -1|| adds 49/48, sidi with wedgie <<4 2 9 -3 6 15|| adds 245/243, and jamesbond with wedgie <<0 0 7 0 11 16|| adds 81/80. Here decimal divides the period to 1/2 octave, and sidi uses 9/7 as a generator, with two of them making up the combined 5/3 and 8/5 neutral sixth. Jamesbond has a period of 1/7 octave, and uses an approximate 15/14 as generator.

Dicot

Comma: 25/24

POTE generator: ~5/4 = 348.594

Map: [<1 1 2|, <0 2 1|]

Optimal ET sequence: 3, 4, 7, 17, 24c, 31c

Badness: 0.013028

7-limit

Comma list: 15/14, 25/24

POTE generator: ~5/4 = 336.381

Map: [<1 1 2 2|, <0 2 1 3|]

Wedgie: <<2 1 3 -3 -1 4||

Optimal ET sequence: 3d, 4, 7, 18bc, 25bccd

Badness: 0.019935

11-limit

Comma list: 15/14, 22/21, 25/24

POTE generator: ~5/4 = 342.125

Map: [<1 1 2 2 2|, <0 2 1 3 5|]

Vals: 3de, 4e, 7

Badness: 0.019854

Eudicot

Comma list: 15/14, 25/24, 33/32

POTE generator: ~5/4 = 336.051

Map: [<1 1 2 2 4|, <0 2 1 3 -2|]

Vals: 3d, 4, 7, 18bc, 25bccd

Badness: 0.027114

13-limit

Comma list: 15/14, 25/24, 33/32, 40/39

POTE generator: ~5/4 = 338.846

Map: [<1 1 2 2 4 4|, <0 2 1 3 -2 -1|]

Vals: 3d, 4, 7, 25bccd, 32bccddef, 39bcccdddef

Badness: 0.023828

Flat

Comma list: 21/20, 25/24

POTE generator: ~5/4 = 331.916

Map: [<1 1 2 3|, <0 2 1 -1|]

Wedgie: <<2 1 -1 -3 -7 -5||

Optimal ET sequence: 3, 4, 7d, 11cd, 18bcddd

Badness: 0.025381

11-limit

Comma list: 21/20, 25/24, 33/32

POTE generator: ~5/4 = 337.532

Map: [<1 1 2 3 4|, <0 2 1 -1 -2|]

Vals: 3, 4, 7d

Badness: 0.024988

13-limit

Comma list: 14/13, 21/20, 25/24, 33/32

POTE generator: ~5/4 = 341.023

Map: [<1 1 2 3 4 4|, <0 2 1 -1 -2 -1|]

Vals: 3, 4, 7d

Badness: 0.023420

Sharp

Comma list: 25/24, 28/27

POTE generator: ~5/4 = 357.938

Map: [<1 1 2 1|, <0 2 1 6|]

Optimal ET sequence: 3d, 7d, 10, 37cd, 47bccd, 57bccdd

Badness: 0.028942

11-limit

Comma list: 25/24, 28/27, 35/33

POTE generator: ~5/4 = 356.106

Map: [<1 1 2 1 2|, <0 2 1 6 5|]

Vals: 3de, 7d, 10, 17d, 27cde

Badness: 0.022366

Decimal

Comma list: 25/24, 49/48

POTE generator: ~7/6 = 251.557

Map: [<2 0 3 4|, <0 2 1 1|]

Wedgie: <<4 2 2 -6 -8 -1||

Optimal ET sequence: 4, 10, 14c, 24c, 38ccd, 62cccdd

Badness: 0.028334

11-limit

Comma list: 25/24, 45/44, 49/48

POTE generator: ~7/6 = 253.493

Map: [<2 0 3 4 -1|, <0 2 1 1 5|]

Vals: 10, 14c, 24c, 38ccd, 52cccde

Badness: 0.026712

Decimated

Comma list: 25/24, 33/32, 49/48

POTE generator: ~7/6 = 255.066

Map: [<2 0 3 4 10|, <0 2 1 1 -2|]

Vals: 4, 10e, 14c

Badness: 0.031456

Decibel

Comma list: 25/24, 35/33, 49/48

POTE generator: ~8/7 = 243.493

Map: [<2 0 3 4 7|, <0 2 1 1 0|]

Vals: 4, 6, 10

Badness: 0.032385

Dichotic

Comma list: 25/24, 64/63

POTE generator: ~5/4 = 356.264

Map: [<1 1 2 4|, <0 2 1 -4|]

Wedgie: <<2 1 -4 -3 -12 -12||

Optimal ET sequence: 3, 7, 10, 17, 27c, 37c, 64bccc

Badness: 0.037565

11-limit

Comma list: 25/24, 45/44, 64/63

POTE generator: ~5/4 = 354.262

Map: [<1 1 2 4 2|, <0 2 1 -4 5|]

Vals: 7, 10, 17, 27ce, 44cce

Badness: 0.030680

Dichosis

Comma list: 25/24, 35/33, 64/63

POTE generator: ~5/4 = 360.659

Map: [<1 1 2 4 5|, <0 2 1 -4 -5|]

Vals: 3, 7e, 10

Badness: 0.041361

Jamesbond

Comma list: 25/24, 81/80

POTE generator: ~8/7 = 258.139

Map: [<7 11 16 0|, <0 0 0 1|]

Optimal ET sequence: 7, 14c

Badness: 0.041714

11-limit

Comma list: 25/24, 33/32, 45/44

POTE generator: ~8/7 = 258.910

Map: [<7 11 16 0 24|, <0 0 0 1 0|]

Vals: 7, 14c

Badness: 0.023524

13-limit

Comma list: 25/24, 27/26, 33/32, 40/39

POTE generator: ~8/7 = 250.764

Map: [<7 11 16 0 24 26|, <0 0 0 1 0 0|]

Vals: 7, 14c

Badness: 0.023003

Septimal

Comma list: 25/24, 33/32, 45/44, 65/63

POTE generator: ~8/7 = 247.445

Map: [<7 11 16 0 24 6|, <0 0 0 1 0 1|]

Vals: 7, 14cf

Badness: 0.022569

Sidi

Comma list: 25/24, 245/243

POTE generator: ~9/7 = 427.208

Map: [<1 3 3 6|, <0 -4 -2 -9|]

Optimal ET sequence: 14c, 45c, 59bccd

Badness: 0.0566

11-limit

Comma list: 25/24, 45/44, 99/98

POTE generator: ~9/7 = 427.273

Map: [<1 3 3 6 7|, <0 -4 -2 -9 -10|]

Vals: 14c, 17, 45ce, 59bccde

Badness: 0.0330

Quad

Comma list: 9/8, 25/24

POTE generator: ~5/4 = 324.482

Map: [<4 6 9 0|, <0 0 0 1|]

Wedgie: <<0 0 4 0 6 9||

Optimal ET sequence: 4, 12bcd

Badness: 0.0460

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