Alphatricot family: Difference between revisions

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Line 4: Line 4:
[[Comma]]: {{monzo | 39 -29 3 }} = 68719476736000/68630377364883
[[Comma]]: {{monzo | 39 -29 3 }} = 68719476736000/68630377364883


[[Mapping]]: [<1 0 -13|, <0 3 29|]
[[Mapping]]: [{{val|1 0 -13}}, {{val|0 3 29}}]


[[Wedgie]]: <<3 29 39||
{{Multival|legend=1|3 29 39}}


[[POTE tuning|POTE generator]]: ~59049/40960 = 634.012
[[POTE tuning|POTE generator]]: ~59049/40960 = 634.012
Line 19: Line 19:
[[Comma list]]: 2430/2401, 5120/5103
[[Comma list]]: 2430/2401, 5120/5103


[[Mapping]]: [<1 0 -13 -3|, <0 3 29 11|]
[[Mapping]]: [{{val|1 0 -13 -3}}, {{val|0 3 29 11}}]


[[Wedgie]]: <<3 29 11 39 9 -56||
{{Multival|legend=1|3 29 11 39 9 -56}}


[[POTE tuning|POTE generator]]: ~81/56 = 634.0259
[[POTE tuning|POTE generator]]: ~81/56 = 634.0259
Line 32: Line 32:
Comma list: 99/98, 121/120, 5120/5103
Comma list: 99/98, 121/120, 5120/5103


Mapping: [<1 0 -13 -3 -5|, <0 3 29 11 16|]
Mapping: [{{val|1 0 -13 -3 -5}}, {{val|0 3 29 11 16}}]


POTE generator: ~63/44 = 634.0273
POTE generator: ~63/44 = 634.0273
Line 43: Line 43:
Comma list: 99/98, 121/120, 169/168, 352/351
Comma list: 99/98, 121/120, 169/168, 352/351


Mapping: [<1 0 -13 -3 -5 0|, <0 3 29 11 16 7|]
Mapping: [{{val|1 0 -13 -3 -5 0}}, {{val|0 3 29 11 16 7}}]


POTE generator: ~13/9 = 634.0115
POTE generator: ~13/9 = 634.0115
Line 54: Line 54:
[[Comma list]]: 6144/6125, 14348907/14336000
[[Comma list]]: 6144/6125, 14348907/14336000


[[Mapping]]: [<1 0 -13 25|, <0 3 29 -42|]
[[Mapping]]: [{{val|1 0 -13 25}}, {{val|0 3 29 -42}}]


[[Wedgie]]: <<3 29 -42 39 -75 -179||
{{Multival|legend=1|3 29 -42 39 -75 -179}}


[[POTE tuning|POTE generator]]: ~4096/2835 = 634.0480
[[POTE tuning|POTE generator]]: ~4096/2835 = 634.0480
Line 67: Line 67:
Comma list: 3388/3375, 6144/6125, 8019/8000
Comma list: 3388/3375, 6144/6125, 8019/8000


Mapping: [<1 0 -13 25 -33|, <0 3 29 -42 69|]
Mapping: [{{val|1 0 -13 25 -33}}, {{val|0 3 29 -42 69}}]


POTE generator: ~231/160 = 634.0669
POTE generator: ~231/160 = 634.0669
Line 78: Line 78:
Comma list: 351/350, 2080/2079, 2197/2187, 3146/3125
Comma list: 351/350, 2080/2079, 2197/2187, 3146/3125


Mapping: [<1 0 -13 25 -33 0|, <0 3 29 -42 69 7|]
Mapping: [{{val|1 0 -13 25 -33 0}}, {{val|0 3 29 -42 69 7}}]


POTE generator: ~13/9 = 634.0652
POTE generator: ~13/9 = 634.0652
Line 89: Line 89:
[[Comma list]]: 4375/4374, 1099511627776/1098337086315
[[Comma list]]: 4375/4374, 1099511627776/1098337086315


[[Mapping]]: [<1 0 -13 53|, <0 3 29 -95|]
[[Mapping]]: [{{val|1 0 -13 53}}, {{val|0 3 29 -95}}]


[[Wedgie]]: <<3 29 -95 39 -159 -302||
{{Multival|legend=1|3 29 -95 39 -159 -302}}


[[POTE tuning|POTE generator]]: ~23625/16384 = 634.0118
[[POTE tuning|POTE generator]]: ~23625/16384 = 634.0118
Line 102: Line 102:
Comma list: 4375/4374, 131072/130977, 759375/758912
Comma list: 4375/4374, 131072/130977, 759375/758912


Mapping: [<1 0 -13 53 -89|, <0 3 29 -95 175|]
Mapping: [{{val|1 0 -13 53 -89}}, {{val|0 3 29 -95 175}}]


POTE generator: ~3888/2695 = 634.0094
POTE generator: ~3888/2695 = 634.0094
Line 113: Line 113:
Comma list: 2080/2079, 4096/4095, 4375/4374, 78125/78078
Comma list: 2080/2079, 4096/4095, 4375/4374, 78125/78078


Mapping: [<1 0 -13 53 -89 -28|, <0 3 29 -95 175 60|]
Mapping: [{{val|1 0 -13 53 -89 -28}}, {{val|0 3 29 -95 175 60}}]


POTE generator: ~75/52 = 634.0095
POTE generator: ~75/52 = 634.0095
Line 124: Line 124:
Comma list: 4375/4374, 5632/5625, 4108797/4096000
Comma list: 4375/4374, 5632/5625, 4108797/4096000


Mapping: [<1 0 -13 53 -61|, <0 3 29 -95 122|]
Mapping: [{{val|1 0 -13 53 -61}}, {{val|0 3 29 -95 122}}]


POTE generator: ~231/160 = 634.0190
POTE generator: ~231/160 = 634.0190
Line 135: Line 135:
Comma list: 847/845, 1001/1000, 4096/4095, 4375/4374
Comma list: 847/845, 1001/1000, 4096/4095, 4375/4374


Mapping: [<1 0 -13 53 -61 -28|, <0 3 29 -95 122 60|]
Mapping: [{{val|1 0 -13 53 -61 -28}}, {{val|0 3 29 -95 122 60}}]


POTE generator: ~75/52 = 634.0181
POTE generator: ~75/52 = 634.0181
Line 146: Line 146:
[[Comma list]]: 250047/250000, 11785390260224/11767897353375
[[Comma list]]: 250047/250000, 11785390260224/11767897353375


[[Mapping]]: [<3 6 19 30|, <0 -3 -29 -52|]
[[Mapping]]: [{{val|3 6 19 30}}, {{val|0 -3 -29 -52}}]


[[Wedgie]]: <<9 87 156 117 222 118||
{{Multival|legend=1|9 87 156 117 222 118}}


[[POTE tuning|POTE generator]]: ~100352/91125 = 165.9837
[[POTE tuning|POTE generator]]: ~100352/91125 = 165.9837
Line 159: Line 159:
Comma list: 4000/3993, 166698/166375, 200704/200475
Comma list: 4000/3993, 166698/166375, 200704/200475


Mapping: [<3 6 19 30 22|, <0 -3 -29 -52 -28|]
Mapping: [{{val|3 6 19 30 22}}, {{val|0 -3 -29 -52 -28}}]


POTE generator: ~11/10 = 165.9835
POTE generator: ~11/10 = 165.9835
Line 170: Line 170:
Comma list: 1575/1573, 2080/2079, 34398/34375, 43904/43875
Comma list: 1575/1573, 2080/2079, 34398/34375, 43904/43875


Mapping: [<3 6 19 30 22 36|, <0 -3 -29 -52 -28 -60|]
Mapping: [{{val|3 6 19 30 22 36}}, {{val|0 -3 -29 -52 -28 -60}}]


POTE generator: ~11/10 = 165.9842
POTE generator: ~11/10 = 165.9842
Line 181: Line 181:
Comma list: 936/935, 1575/1573, 1701/1700, 2025/2023, 8624/8619
Comma list: 936/935, 1575/1573, 1701/1700, 2025/2023, 8624/8619


Mapping: [<3 6 19 30 22 36 16|, <0 -3 -29 -52 -28 -60 -9|]
Mapping: [{{val|3 6 19 30 22 36 16}}, {{val|0 -3 -29 -52 -28 -60 -9}}]


POTE generator: ~11/10 = 165.9805
POTE generator: ~11/10 = 165.9805
Line 191: Line 191:
[[Category:Temperament family]]
[[Category:Temperament family]]
[[Category:Theory]]
[[Category:Theory]]
[[Category:Tricot]]

Revision as of 02:06, 22 May 2021

The generator for tricot temperament is the real cube root of third harmonic, 31/3, tuned between 63/44 and 13/9. Tricot temperament can be described as 53&70 temperament, tempering out the tricot comma, [39 -29 3⟩ in the 5-limit. There are some mappings for 7-limit extension of this temperament: septimal tricot (53&70, also known as trimot), trident (53&229) and trillium (53&441). Tempering out hemifamity comma (5120/5103) leads septimal tricot (supported by 53edo and 70edo), porwell comma (6144/6125) leads trident (supported by 53, 176, and 229 edos), and ragisma (4375/4374) leads trillium (supported by 53, 441, 494, 935, and 1429 edos).

Tricot

Comma: [39 -29 3⟩ = 68719476736000/68630377364883

Mapping: [⟨1 0 -13], ⟨0 3 29]]

Wedgie: ⟨⟨ 3 29 39 ]]

POTE generator: ~59049/40960 = 634.012

Template:Val list

Badness: 0.046093

7-limit (aka Trimot)

See also: Hemifamity temperaments § Tricot

Comma list: 2430/2401, 5120/5103

Mapping: [⟨1 0 -13 -3], ⟨0 3 29 11]]

Wedgie: ⟨⟨ 3 29 11 39 9 -56 ]]

POTE generator: ~81/56 = 634.0259

Template:Val list

Badness: 0.100127

11-limit

Comma list: 99/98, 121/120, 5120/5103

Mapping: [⟨1 0 -13 -3 -5], ⟨0 3 29 11 16]]

POTE generator: ~63/44 = 634.0273

Vals: Template:Val list

Badness: 0.056134

13-limit

Comma list: 99/98, 121/120, 169/168, 352/351

Mapping: [⟨1 0 -13 -3 -5 0], ⟨0 3 29 11 16 7]]

POTE generator: ~13/9 = 634.0115

Vals: Template:Val list

Badness: 0.032102

Trident

Comma list: 6144/6125, 14348907/14336000

Mapping: [⟨1 0 -13 25], ⟨0 3 29 -42]]

Wedgie: ⟨⟨ 3 29 -42 39 -75 -179 ]]

POTE generator: ~4096/2835 = 634.0480

Template:Val list

Badness: 0.101694

11-limit

Comma list: 3388/3375, 6144/6125, 8019/8000

Mapping: [⟨1 0 -13 25 -33], ⟨0 3 29 -42 69]]

POTE generator: ~231/160 = 634.0669

Vals: Template:Val list

Badness: 0.074272

13-limit

Comma list: 351/350, 2080/2079, 2197/2187, 3146/3125

Mapping: [⟨1 0 -13 25 -33 0], ⟨0 3 29 -42 69 7]]

POTE generator: ~13/9 = 634.0652

Vals: Template:Val list

Badness: 0.046593

Trillium

Comma list: 4375/4374, 1099511627776/1098337086315

Mapping: [⟨1 0 -13 53], ⟨0 3 29 -95]]

Wedgie: ⟨⟨ 3 29 -95 39 -159 -302 ]]

POTE generator: ~23625/16384 = 634.0118

Template:Val list

Badness: 0.030852

11-limit

Comma list: 4375/4374, 131072/130977, 759375/758912

Mapping: [⟨1 0 -13 53 -89], ⟨0 3 29 -95 175]]

POTE generator: ~3888/2695 = 634.0094

Vals: Template:Val list

Badness: 0.046758

13-limit

Comma list: 2080/2079, 4096/4095, 4375/4374, 78125/78078

Mapping: [⟨1 0 -13 53 -89 -28], ⟨0 3 29 -95 175 60]]

POTE generator: ~75/52 = 634.0095

Vals: Template:Val list

Badness: 0.019393

Pseudotrillium

Comma list: 4375/4374, 5632/5625, 4108797/4096000

Mapping: [⟨1 0 -13 53 -61], ⟨0 3 29 -95 122]]

POTE generator: ~231/160 = 634.0190

Vals: Template:Val list

Badness: 0.111931

13-limit

Comma list: 847/845, 1001/1000, 4096/4095, 4375/4374

Mapping: [⟨1 0 -13 53 -61 -28], ⟨0 3 29 -95 122 60]]

POTE generator: ~75/52 = 634.0181

Vals: Template:Val list

Badness: 0.054837

Tritricot

Comma list: 250047/250000, 11785390260224/11767897353375

Mapping: [⟨3 6 19 30], ⟨0 -3 -29 -52]]

Wedgie: ⟨⟨ 9 87 156 117 222 118 ]]

POTE generator: ~100352/91125 = 165.9837

Template:Val list

Badness: 0.086081

11-limit

Comma list: 4000/3993, 166698/166375, 200704/200475

Mapping: [⟨3 6 19 30 22], ⟨0 -3 -29 -52 -28]]

POTE generator: ~11/10 = 165.9835

Vals: Template:Val list

Badness: 0.074002

13-limit

Comma list: 1575/1573, 2080/2079, 34398/34375, 43904/43875

Mapping: [⟨3 6 19 30 22 36], ⟨0 -3 -29 -52 -28 -60]]

POTE generator: ~11/10 = 165.9842

Vals: Template:Val list

Badness: 0.035641

17-limit

Comma list: 936/935, 1575/1573, 1701/1700, 2025/2023, 8624/8619

Mapping: [⟨3 6 19 30 22 36 16], ⟨0 -3 -29 -52 -28 -60 -9]]

POTE generator: ~11/10 = 165.9805

Vals: Template:Val list

Badness: 0.025972

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