Alphatricot family: Difference between revisions

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The generator for '''tricot temperament''' is the real cube root of third harmonic, 3<sup>1/3</sup>, tuned between 63/44 and 13/9. Tricot temperament can be described as 53&amp;70 temperament, tempering out the [[tricot comma]], {{monzo| 39 -29 3 }} in the 5-limit. There are some mappings for 7-limit extension of this temperament: trimot (53&amp;70) and trillium (53&amp;441). Tempering out [[5120/5103|hemifamity comma]] (5120/5103) leads trimot (supported by 53edo and 70edo), and tempering out [[4375/4374|ragisma]] (4375/4374) leads trillium (supported by 53, 441, 494, 935, and 1376 edos).
The generator for '''tricot temperament''' is the real cube root of third harmonic, 3<sup>1/3</sup>, tuned between 63/44 and 13/9. Tricot temperament can be described as 53&amp;70 temperament, tempering out the [[tricot comma]], {{monzo| 39 -29 3 }} in the 5-limit. There are some mappings for 7-limit extension of this temperament: trimot (53&amp;70), trident (53&amp;229) and trillium (53&amp;441). Tempering out [[5120/5103|hemifamity comma]] (5120/5103) leads trimot (supported by 53edo and 70edo), [[6144/6125|hemiwürmity comma]] (6144/6125) leads trident (supported by 53, 176, 229, 282, and 511 edos), and [[4375/4374|ragisma]] (4375/4374) leads trillium (supported by 53, 441, 494, 935, and 1376 edos).


See [[Hemifamity_temperaments#Tricot|Hemifamity temperaments]] for more infomation.
See [[Hemifamity_temperaments#Tricot|Hemifamity temperaments]] for more infomation.


== 5-limit Tricot ==
== Tricot ==
Comma: {{monzo | 39 -29 3 }} = 68719476736000/68630377364883
Comma: {{monzo | 39 -29 3 }} = 68719476736000/68630377364883


Line 36: Line 36:
Map: [&lt;1 0 -13 -3 -5|, &lt;0 3 29 11 16|]
Map: [&lt;1 0 -13 -3 -5|, &lt;0 3 29 11 16|]


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


Badness: 0.0561
Badness: 0.0561
Line 47: Line 47:
Map: [&lt;1 0 -13 -3 -5 0|, &lt;0 3 29 11 16 7|]
Map: [&lt;1 0 -13 -3 -5 0|, &lt;0 3 29 11 16 7|]


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


Badness: 0.0321
Badness: 0.0321
Line 63: Line 63:


Badness: 0.1017
Badness: 0.1017
=== 11-limit ===
Commas: 3388/3375, 6144/6125, 8019/8000
POTE generator: ~231/160 = 634.0669
Map: [&lt;1 0 -13 25 -33|, &lt;0 3 29 -42 69|]
EDOs: {{EDOs| 53, 176, 229 }}
Badness: 0.0743
=== 13-limit ===
Commas: 351/350, 2080/2079, 2197/2187, 3146/3125
POTE generator: ~13/9 = 634.0652
Map: [&lt;1 0 -13 25 -33 0|, &lt;0 3 29 -42 69 7|]
EDOs: {{EDOs| 53, 176, 229 }}
Badness: 0.0466


== Trillium (53&amp;441) ==
== Trillium (53&amp;441) ==
Line 77: Line 99:
Badness: 0.0309
Badness: 0.0309


=== 11-limit 53&amp;388 ===
=== 11-limit ===
Commas: 4375/4374, 131072/130977, 759375/758912
 
POTE generator: ~3888/2695 = 634.0094
 
Map: [&lt;1 0 -13 53 -89|, &lt;0 3 29 -95 175|]
 
EDOs: {{EDOs| 53, 441, 494, 935, 1429 }}
 
Badness: 0.0468
 
=== 13-limit ===
Commas: 2080/2079, 4096/4095, 4375/4374, 78125/78078
 
POTE generator: ~75/52 = 634.0095
 
Map: [&lt;1 0 -13 53 -89 -28|, &lt;0 3 29 -95 175 60|]
 
EDOs: {{EDOs| 53, 441, 494, 935, 1429 }}
 
Badness: 0.0194
 
=== Pseudotrillium (53&amp;388) ===
Commas: 4375/4374, 5632/5625, 4108797/4096000
Commas: 4375/4374, 5632/5625, 4108797/4096000


POTE generator: ~1125/704 = 634.0190
POTE generator: ~231/160 = 634.0190


Map: [&lt;1 0 -13 53 -61|, &lt;0 3 29 -95 122|]
Map: [&lt;1 0 -13 53 -61|, &lt;0 3 29 -95 122|]


EDOs: {{EDOs| 53, 323, 388 }}
EDOs: {{EDOs| 53, 335, 388 }}


Badness: 0.1119
Badness: 0.1119


=== 11-limit 53&amp;494 ===
==== 13-limit ====
Commas: 4375/4374, 131072/130977, 759375/758912
Commas: 847/845, 1001/1000, 4096/4095, 4375/4374


POTE generator: ~3888/2695 = 634.0094
POTE generator: ~75/52 = 634.0181


Map: [&lt;1 0 -13 53 89|, &lt;0 3 29 -95 175|]
Map: [&lt;1 0 -13 53 -61 -28|, &lt;0 3 29 -95 122 60|]


EDOs: {{EDOs| 53, 441, 494, 935, 1429 }}
EDOs: {{EDOs| 53, 335, 388 }}


Badness: 0.0468
Badness: 0.0548


[[Category:Temperament]]
[[Category:Temperament]]

Revision as of 01:27, 14 March 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), hemiwürmity comma (6144/6125) leads trident (supported by 53, 176, 229, 282, and 511 edos), and ragisma (4375/4374) leads trillium (supported by 53, 441, 494, 935, and 1376 edos).

See Hemifamity temperaments for more infomation.

Tricot

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

POTE generator: ~59049/40960 = 634.012

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

Wedgie: <<3 29 39||

EDOs: 53, 229, 282, 335, 388, 441, 1376, 1817, 2258

Badness: 0.0461

Trimot (53&70)

Commas: 2430/2401, 5120/5103

POTE generator: ~81/56 = 634.0259

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

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

EDOs: 17c, 36c, 53, 70, 229dd, 282dd

Badness: 0.1001

11-limit

Commas: 99/98, 121/120, 5120/5103

POTE generator: ~63/44 = 634.0273

Map: [<1 0 -13 -3 -5|, <0 3 29 11 16|]

EDOs: 17c, 36ce, 53, 70, 123de

Badness: 0.0561

13-limit

Commas: 99/98, 121/120, 169/168, 352/351

POTE generator: ~13/9 = 634.0115

Map: [<1 0 -13 -3 -5 0|, <0 3 29 11 16 7|]

EDOs: 17c, 36ce, 53, 70, 123de

Badness: 0.0321

Trident (53&229)

Commas: 6144/6125, 14348907/14336000

POTE generator: ~4096/2835 = 634.0480

Map: [<1 0 -13 25|, <0 3 29 -42|]

Wedgie: <<3 29 -42 39 -75 -179||

EDOs: 53, 176, 229, 282, 511

Badness: 0.1017

11-limit

Commas: 3388/3375, 6144/6125, 8019/8000

POTE generator: ~231/160 = 634.0669

Map: [<1 0 -13 25 -33|, <0 3 29 -42 69|]

EDOs: 53, 176, 229

Badness: 0.0743

13-limit

Commas: 351/350, 2080/2079, 2197/2187, 3146/3125

POTE generator: ~13/9 = 634.0652

Map: [<1 0 -13 25 -33 0|, <0 3 29 -42 69 7|]

EDOs: 53, 176, 229

Badness: 0.0466

Trillium (53&441)

Commas: 4375/4374, 1099511627776/1098337086315

POTE generator: ~23625/16384 = 634.0118

Map: [<1 0 -13 53|, <0 3 29 -95|]

Wedgie: <<3 29 -95 39 -159 -302||

EDOs: 53, 441, 494, 935, 1376, 3193, 4569

Badness: 0.0309

11-limit

Commas: 4375/4374, 131072/130977, 759375/758912

POTE generator: ~3888/2695 = 634.0094

Map: [<1 0 -13 53 -89|, <0 3 29 -95 175|]

EDOs: 53, 441, 494, 935, 1429

Badness: 0.0468

13-limit

Commas: 2080/2079, 4096/4095, 4375/4374, 78125/78078

POTE generator: ~75/52 = 634.0095

Map: [<1 0 -13 53 -89 -28|, <0 3 29 -95 175 60|]

EDOs: 53, 441, 494, 935, 1429

Badness: 0.0194

Pseudotrillium (53&388)

Commas: 4375/4374, 5632/5625, 4108797/4096000

POTE generator: ~231/160 = 634.0190

Map: [<1 0 -13 53 -61|, <0 3 29 -95 122|]

EDOs: 53, 335, 388

Badness: 0.1119

13-limit

Commas: 847/845, 1001/1000, 4096/4095, 4375/4374

POTE generator: ~75/52 = 634.0181

Map: [<1 0 -13 53 -61 -28|, <0 3 29 -95 122 60|]

EDOs: 53, 335, 388

Badness: 0.0548

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