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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|tricot comma]], {{monzo| 39 -29 3 }} in the 5-limit. There are some mappings for 7-limit extension of this temperament: septimal tricot (53&amp;70, also known as ''trimot''), trident (53&amp;229) and trillium (53&amp;441). Tempering out [[5120/5103|hemifamity comma]] (5120/5103) leads septimal tricot (supported by 53EDO and 70EDO), [[6144/6125|porwell comma]] (6144/6125) leads trident (supported by 53, 176, and 229 EDOs), and [[4375/4374|ragisma]] (4375/4374) leads trillium (supported by 53, 441, 494, 935, and 1429 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: septimal tricot (53&amp;70, also known as ''trimot''), trident (53&amp;229) and trillium (53&amp;441). Tempering out [[5120/5103|hemifamity comma]] (5120/5103) leads to septimal tricot, [[6144/6125|porwell comma]] (6144/6125) leads to trident, and [[4375/4374|ragisma]] (4375/4374) leads to trillium.


== Tricot ==
== Tricot ==
[[Comma]]: {{monzo | 39 -29 3 }} = 68719476736000/68630377364883
Subgroup: 2.3.5


[[Mapping]]: [{{val|1 0 -13}}, {{val|0 3 29}}]
[[Comma list]]: {{monzo | 39 -29 3 }} = 68719476736000/68630377364883


{{Multival|legend=1|3 29 39}}
[[Mapping]]: [{{val| 1 0 -13 }}, {{val| 0 3 29 }}]


[[POTE tuning|POTE generator]]: ~59049/40960 = 634.012
Mapping generators: ~2, ~59049/40960
 
{{Multival|legend=1| 3 29 39 }}
 
[[POTE generator]]: ~59049/40960 = 634.012


{{Val list|legend=1| 53, 229, 282, 335, 388, 441, 1376, 1817, 2258 }}
{{Val list|legend=1| 53, 229, 282, 335, 388, 441, 1376, 1817, 2258 }}
Line 14: Line 18:
[[Badness]]: 0.046093
[[Badness]]: 0.046093


=== 7-limit (Trimot) ===
== Septimal tricot (aka trimot) ==
{{see also|Hemifamity temperaments #Tricot}}
{{see also| Hemifamity temperaments #Tricot (aka trimot) }}


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
Line 21: Line 25:
[[Comma list]]: 2430/2401, 5120/5103
[[Comma list]]: 2430/2401, 5120/5103


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


{{Multival|legend=1|3 29 11 39 9 -56}}
{{Multival|legend=1| 3 29 11 39 9 -56 }}


[[POTE tuning|POTE generator]]: ~81/56 = 634.0259
[[POTE generator]]: ~81/56 = 634.0259


{{Val list|legend=1| 17c, 36c, 53, 70, 229dd, 282dd }}
{{Val list|legend=1| 17c, 36c, 53, 70, 229dd, 282dd }}
Line 36: Line 40:
Comma list: 99/98, 121/120, 5120/5103
Comma list: 99/98, 121/120, 5120/5103


Mapping: [{{val|1 0 -13 -3 -5}}, {{val|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 49: Line 53:
Comma list: 99/98, 121/120, 169/168, 352/351
Comma list: 99/98, 121/120, 169/168, 352/351


Mapping: [{{val|1 0 -13 -3 -5 0}}, {{val|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 62: Line 66:
[[Comma list]]: 6144/6125, 14348907/14336000
[[Comma list]]: 6144/6125, 14348907/14336000


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


{{Multival|legend=1|3 29 -42 39 -75 -179}}
{{Multival|legend=1| 3 29 -42 39 -75 -179 }}


[[POTE tuning|POTE generator]]: ~4096/2835 = 634.0480
[[POTE generator]]: ~4096/2835 = 634.0480


{{Val list|legend=1| 53, 176, 229, 282, 511 }}
{{Val list|legend=1| 53, 176, 229, 282, 511 }}
Line 77: Line 81:
Comma list: 3388/3375, 6144/6125, 8019/8000
Comma list: 3388/3375, 6144/6125, 8019/8000


Mapping: [{{val|1 0 -13 25 -33}}, {{val|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 90: Line 94:
Comma list: 351/350, 2080/2079, 2197/2187, 3146/3125
Comma list: 351/350, 2080/2079, 2197/2187, 3146/3125


Mapping: [{{val|1 0 -13 25 -33 0}}, {{val|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 103: Line 107:
[[Comma list]]: 4375/4374, 1099511627776/1098337086315
[[Comma list]]: 4375/4374, 1099511627776/1098337086315


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


{{Multival|legend=1|3 29 -95 39 -159 -302}}
{{Multival|legend=1| 3 29 -95 39 -159 -302 }}


[[POTE tuning|POTE generator]]: ~23625/16384 = 634.0118
[[POTE generator]]: ~23625/16384 = 634.0118


{{Val list|legend=1| 53, 441, 494, 935, 1376, 3193, 4569 }}
{{Val list|legend=1| 53, 441, 494, 935, 1376, 3193, 4569 }}
Line 118: Line 122:
Comma list: 4375/4374, 131072/130977, 759375/758912
Comma list: 4375/4374, 131072/130977, 759375/758912


Mapping: [{{val|1 0 -13 53 -89}}, {{val|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 131: Line 135:
Comma list: 2080/2079, 4096/4095, 4375/4374, 78125/78078
Comma list: 2080/2079, 4096/4095, 4375/4374, 78125/78078


Mapping: [{{val|1 0 -13 53 -89 -28}}, {{val|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 144: Line 148:
Comma list: 4375/4374, 5632/5625, 4108797/4096000
Comma list: 4375/4374, 5632/5625, 4108797/4096000


Mapping: [{{val|1 0 -13 53 -61}}, {{val|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 157: Line 161:
Comma list: 847/845, 1001/1000, 4096/4095, 4375/4374
Comma list: 847/845, 1001/1000, 4096/4095, 4375/4374


Mapping: [{{val|1 0 -13 53 -61 -28}}, {{val|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 170: Line 174:
[[Comma list]]: 250047/250000, 11785390260224/11767897353375
[[Comma list]]: 250047/250000, 11785390260224/11767897353375


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


{{Multival|legend=1|9 87 156 117 222 118}}
{{Multival|legend=1| 9 87 156 117 222 118 }}


[[POTE tuning|POTE generator]]: ~100352/91125 = 165.9837
[[POTE generator]]: ~100352/91125 = 165.9837


{{Val list|legend=1| 159, 282, 441, 2487, 2928, 3369 }}
{{Val list|legend=1| 159, 282, 441, 2487, 2928, 3369 }}
Line 185: Line 189:
Comma list: 4000/3993, 166698/166375, 200704/200475
Comma list: 4000/3993, 166698/166375, 200704/200475


Mapping: [{{val|3 6 19 30 22}}, {{val|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 198: Line 202:
Comma list: 1575/1573, 2080/2079, 34398/34375, 43904/43875
Comma list: 1575/1573, 2080/2079, 34398/34375, 43904/43875


Mapping: [{{val|3 6 19 30 22 36}}, {{val|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 211: Line 215:
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: [{{val|3 6 19 30 22 36 16}}, {{val|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 222: Line 226:
[[Category:Temperament family]]
[[Category:Temperament family]]
[[Category:Tricot family| ]] <!-- main article -->
[[Category:Tricot family| ]] <!-- main article -->
[[Category:Rank 2]]
[[Category:Tricot]]
[[Category:Tricot]]
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