Alphatricot family: Difference between revisions

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


POTE generator: ~59049/40960 = 634.012
[[Mapping]]: [<1 0 -13|, <0 3 29|]


Map: [<1 0 -13|, <0 3 29|]
[[Wedgie]]: <<3 29 39||


Wedgie: <<3 29 39||
[[POTE tuning|POTE generator]]: ~59049/40960 = 634.012


EDOs: {{EDOs| 53, 229, 282, 335, 388, 441, 1376, 1817, 2258 }}
{{Val list|legend=1| 53, 229, 282, 335, 388, 441, 1376, 1817, 2258 }}


Badness: 0.0461
[[Badness]]: 0.046093


= Trimot (53&70) =
= Trimot =
Commas: 2430/2401, 5120/5103
{{see also|Hemifamity temperaments}}


POTE generator: ~81/56 = 634.0259
[[Comma list]]: 2430/2401, 5120/5103


Map: [<1 0 -13 -3|, <0 3 29 11|]
[[Mapping]]: [<1 0 -13 -3|, <0 3 29 11|]


Wedgie: <<3 29 11 39 9 -56||
[[Wedgie]]: <<3 29 11 39 9 -56||


EDOs: {{EDOs| 17c, 36c, 53, 70, 229dd, 282dd }}
[[POTE tuning|POTE generator]]: ~81/56 = 634.0259


Badness: 0.1001
{{Val list|legend=1| 17c, 36c, 53, 70, 229dd, 282dd }}
 
[[Badness]]: 0.100127


== 11-limit ==
== 11-limit ==
Commas: 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|]


POTE generator: ~63/44 = 634.0273
POTE generator: ~63/44 = 634.0273


Map: [<1 0 -13 -3 -5|, <0 3 29 11 16|]
Vals: {{Val list| 17c, 36ce, 53, 70, 123de }}


EDOs: {{EDOs| 17c, 36ce, 53, 70, 123de }}
Badness: 0.056134


Badness: 0.0561
== 13-limit ==
Comma list: 99/98, 121/120, 169/168, 352/351


== 13-limit ==
Mapping: [<1 0 -13 -3 -5 0|, <0 3 29 11 16 7|]
Commas: 99/98, 121/120, 169/168, 352/351


POTE generator: ~13/9 = 634.0115
POTE generator: ~13/9 = 634.0115


Map: [<1 0 -13 -3 -5 0|, <0 3 29 11 16 7|]
Vals: {{Val list| 17c, 36ce, 53, 70, 123de }}


EDOs: {{EDOs| 17c, 36ce, 53, 70, 123de }}
Badness: 0.032102


Badness: 0.0321
= Trident =
[[Comma list]]: 6144/6125, 14348907/14336000


= Trident (53&229) =
[[Mapping]]: [<1 0 -13 25|, <0 3 29 -42|]
Commas: 6144/6125, 14348907/14336000


POTE generator: ~4096/2835 = 634.0480
[[Wedgie]]: <<3 29 -42 39 -75 -179||


Map: [<1 0 -13 25|, <0 3 29 -42|]
[[POTE tuning|POTE generator]]: ~4096/2835 = 634.0480


Wedgie: <<3 29 -42 39 -75 -179||
{{Val list|legend=1| 53, 176, 229, 282, 511 }}


EDOs: {{EDOs| 53, 176, 229, 282, 511 }}
[[Badness]]: 0.101694


Badness: 0.1017
== 11-limit ==
Comma list: 3388/3375, 6144/6125, 8019/8000


== 11-limit ==
Mapping: [<1 0 -13 25 -33|, <0 3 29 -42 69|]
Commas: 3388/3375, 6144/6125, 8019/8000


POTE generator: ~231/160 = 634.0669
POTE generator: ~231/160 = 634.0669


Map: [<1 0 -13 25 -33|, <0 3 29 -42 69|]
Vals: {{Val list| 53, 176, 229 }}


EDOs: {{EDOs| 53, 176, 229 }}
Badness: 0.074272


Badness: 0.0743
== 13-limit ==
Comma list: 351/350, 2080/2079, 2197/2187, 3146/3125


== 13-limit ==
Mapping: [<1 0 -13 25 -33 0|, <0 3 29 -42 69 7|]
Commas: 351/350, 2080/2079, 2197/2187, 3146/3125


POTE generator: ~13/9 = 634.0652
POTE generator: ~13/9 = 634.0652


Map: [<1 0 -13 25 -33 0|, <0 3 29 -42 69 7|]
Vals: {{Val list| 53, 176, 229 }}


EDOs: {{EDOs| 53, 176, 229 }}
Badness: 0.046593


Badness: 0.0466
= Trillium =
[[Comma list]]: 4375/4374, 1099511627776/1098337086315


= Trillium (53&441) =
[[Mapping]]: [<1 0 -13 53|, <0 3 29 -95|]
Commas: 4375/4374, 1099511627776/1098337086315


POTE generator: ~23625/16384 = 634.0118
[[Wedgie]]: <<3 29 -95 39 -159 -302||


Map: [<1 0 -13 53|, <0 3 29 -95|]
[[POTE tuning|POTE generator]]: ~23625/16384 = 634.0118


Wedgie: <<3 29 -95 39 -159 -302||
{{Val list|legend=1| 53, 441, 494, 935, 1376, 3193, 4569 }}


EDOs: {{EDOs| 53, 441, 494, 935, 1376, 3193, 4569 }}
[[Badness]]: 0.030852


Badness: 0.0309
== 11-limit ==
Comma list: 4375/4374, 131072/130977, 759375/758912


== 11-limit ==
Mapping: [<1 0 -13 53 -89|, <0 3 29 -95 175|]
Commas: 4375/4374, 131072/130977, 759375/758912


POTE generator: ~3888/2695 = 634.0094
POTE generator: ~3888/2695 = 634.0094


Map: [<1 0 -13 53 -89|, <0 3 29 -95 175|]
Vals: {{Val list| 53, 441, 494, 935, 1429 }}


EDOs: {{EDOs| 53, 441, 494, 935, 1429 }}
Badness: 0.046758


Badness: 0.0468
== 13-limit ==
Comma list: 2080/2079, 4096/4095, 4375/4374, 78125/78078


== 13-limit ==
Mapping: [<1 0 -13 53 -89 -28|, <0 3 29 -95 175 60|]
Commas: 2080/2079, 4096/4095, 4375/4374, 78125/78078


POTE generator: ~75/52 = 634.0095
POTE generator: ~75/52 = 634.0095


Map: [<1 0 -13 53 -89 -28|, <0 3 29 -95 175 60|]
Vals: {{Val list| 53, 441, 494, 935, 1429 }}


EDOs: {{EDOs| 53, 441, 494, 935, 1429 }}
Badness: 0.019393


Badness: 0.0194
== Pseudotrillium ==
Comma list: 4375/4374, 5632/5625, 4108797/4096000


== Pseudotrillium (53&388) ==
Mapping: [<1 0 -13 53 -61|, <0 3 29 -95 122|]
Commas: 4375/4374, 5632/5625, 4108797/4096000


POTE generator: ~231/160 = 634.0190
POTE generator: ~231/160 = 634.0190


Map: [<1 0 -13 53 -61|, <0 3 29 -95 122|]
Vals: {{Val list| 53, 335, 388 }}


EDOs: {{EDOs| 53, 335, 388 }}
Badness: 0.111931


Badness: 0.1119
=== 13-limit ===
Comma list: 847/845, 1001/1000, 4096/4095, 4375/4374


=== 13-limit ===
Mapping: [<1 0 -13 53 -61 -28|, <0 3 29 -95 122 60|]
Commas: 847/845, 1001/1000, 4096/4095, 4375/4374


POTE generator: ~75/52 = 634.0181
POTE generator: ~75/52 = 634.0181


Map: [<1 0 -13 53 -61 -28|, <0 3 29 -95 122 60|]
Vals: {{Val list| 53, 335, 388 }}


EDOs: {{EDOs| 53, 335, 388 }}
Badness: 0.054837


Badness: 0.0548
= Tritricot =
[[Comma list]]: 250047/250000, 11785390260224/11767897353375


= Tritricot (159&282) =
[[Mapping]]: [<3 6 19 30|, <0 -3 -29 -52|]
Commas: 250047/250000, 11785390260224/11767897353375


POTE generator: ~100352/91125 = 165.9837
[[Wedgie]]: <<9 87 156 117 222 118||


Map: [<3 6 19 30|, <0 -3 -29 -52|]
[[POTE tuning|POTE generator]]: ~100352/91125 = 165.9837


Wedgie: <<9 87 156 117 222 118||
{{Val list|legend=1| 159, 282, 441, 2487, 2928, 3369 }}


EDOs: {{EDOs| 159, 282, 441, 2487, 2928, 3369 }}
[[Badness]]: 0.086081


Badness: 0.0861
== 11-limit ==
Comma list: 4000/3993, 166698/166375, 200704/200475


== 11-limit ==
Mapping: [<3 6 19 30 22|, <0 -3 -29 -52 -28|]
Commas: 4000/3993, 166698/166375, 200704/200475


POTE generator: ~11/10 = 165.9835
POTE generator: ~11/10 = 165.9835


Map: [<3 6 19 30 22|, <0 -3 -29 -52 -28|]
Vals: {{Val list| 159, 282, 441 }}


EDOs: {{EDOs| 159, 282, 441 }}
Badness: 0.074002


Badness: 0.0740
== 13-limit ==
Comma list: 1575/1573, 2080/2079, 34398/34375, 43904/43875


== 13-limit ==
Mapping: [<3 6 19 30 22 36|, <0 -3 -29 -52 -28 -60|]
Commas: 1575/1573, 2080/2079, 34398/34375, 43904/43875


POTE generator: ~11/10 = 165.9842
POTE generator: ~11/10 = 165.9842


Map: [<3 6 19 30 22 36|, <0 -3 -29 -52 -28 -60|]
Vals: {{Val list| 159, 282, 441 }}


EDOs: {{EDOs| 159, 282, 441 }}
Badness: 0.035641


Badness: 0.0356
== 17-limit ==
Comma list: 936/935, 1575/1573, 1701/1700, 2025/2023, 8624/8619


== 17-limit ==
Mapping: [<3 6 19 30 22 36 16|, <0 -3 -29 -52 -28 -60 -9|]
Commas: 936/935, 1575/1573, 1701/1700, 2025/2023, 8624/8619


POTE generator: ~11/10 = 165.9805
POTE generator: ~11/10 = 165.9805


Map: [<3 6 19 30 22 36 16|, <0 -3 -29 -52 -28 -60 -9|]
Vals: {{Val list| 159, 282, 441 }}
 
EDOs: {{EDOs| 159, 282, 441 }}


Badness: 0.0260
Badness: 0.025972


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

Revision as of 10:13, 12 April 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: trimot (53&70), trident (53&229) and trillium (53&441). Tempering out hemifamity comma (5120/5103) leads trimot (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

Trimot

See also: Hemifamity temperaments

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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