Xenharmonic Wiki

Aberschismic temperaments: Difference between revisions

← Older editNewer edit →
VisualWikitext
Update trimot and remove its 5-limit (discussed in tricot family)
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
5,035 edits
No edit summary
Line 367: Line 367:
Badness: 0.0348
Badness: 0.0348


= Trimot =
= Tricot (aka Trimot) =
{{see also|Tricot family #Trimot }}
{{see also|Tricot family}}


The generator for trimot is the real cube root of third harmonic, 3<sup>1/3</sup>, tuned between 63/44 and 13/9. Trimot can be described as 53&amp;70 temperament, tempering out the [[Tricot|tricot comma]], {{monzo| 39 -29 3 }} in the 5-limit, 2430/2401 (nuwell comma) and 5120/5103 in the 7-limit, 99/98 and 121/120 in the 11-limit, 169/168, 352/351, 640/637, and 729/728 in the 13-limit.
The generator for tricot is the real cube root of third harmonic, 3<sup>1/3</sup>, tuned between 63/44 and 13/9. Tricot can be described as 53&amp;70 temperament (also known as ''trimot''), tempering out the [[tricot comma]], {{monzo| 39 -29 3 }} in the 5-limit, 2430/2401 (nuwell comma) and 5120/5103 in the 7-limit, 99/98 and 121/120 in the 11-limit, 169/168, 352/351, 640/637, and 729/728 in the 13-limit.


Commas: 2430/2401, 5120/5103
[[Comma list]]: 2430/2401, 5120/5103


POTE generator: ~81/56 = 634.026
[[Mapping]]: [&lt;1 0 -13 -3|, &lt;0 3 29 11|]


Map: [&lt;1 0 -13 -3|, &lt;0 3 29 11|]
[[Wedgie]]: &lt;&lt;3 29 11 39 9 -56||


Wedgie: &lt;&lt;3 29 11 39 9 -56||
[[POTE tuning|POTE generator]]: ~81/56 = 634.026


EDOs: {{EDOs| 17c, 36c, 53, 229dd, 282dd }}
{{Val list|legend=1| 17c, 36c, 53, 229dd, 282dd }}


Badness: 0.1001
[[Badness]]: 0.100127


== 11-limit ==
== 11-limit ==
Commas: 99/98, 121/120, 5120/5103
Comma list: 99/98, 121/120, 5120/5103
 
Mapping: [&lt;1 0 -13 -3 -5|, &lt;0 3 29 11 16|]


POTE generator: ~63/44 = 634.027
POTE generator: ~63/44 = 634.027


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


EDOs: {{EDOs| 17c, 36ce, 53, 176de }}
Badness: 0.056134


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


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


POTE generator: ~13/9 = 634.012
POTE generator: ~13/9 = 634.012


Map: [&lt;1 0 -13 -3 -5 0|, &lt;0 3 29 11 16 7|]
Vals: {{Val list| 17c, 36ce, 53, 70, 123de }}
 
Badness: 0.032102


EDOs: {{EDOs| 17c, 36ce, 53 }}
= Ketchup =
[[Comma list]]: 5120/5103, 1071875/1062882


Badness: 0.0321
[[Mapping]]: [&lt;2 3 4 6|, &lt;0 4 15 -9|]


=Ketchup=
[[Wedgie]]: &lt;&lt;8 30 -18 29 -51 -126||
Commas: 5120/5103, 1071875/1062882


POTE generator: ~64/63 = ~81/80 = 25.719
[[POTE tuning|POTE generator]]: ~64/63 = ~81/80 = 25.719


Map: [&lt;2 3 4 6|, &lt;0 4 15 -9|]
{{Val list|legend=1| 46, 94, 140 }}


EDOS: 46, 94, 140
[[Badness]]: 0.084538


Badness: 0.0845
== 11-limit ==
Comma list: 385/384, 1331/1323, 2200/2187


==11-limit==
Mapping: [&lt;2 3 4 6 7|, &lt;0 4 15 -9 -2|]
Commas: 385/384, 1331/1323, 2200/2187


POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.693
POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.693


Map: [&lt;2 3 4 6 7|, &lt;0 4 15 -9 -2|]
Vals: {{Val list| 46, 94, 140 }}


EDOs: 46, 94, 140
Badness: 0.039555


Badness: 0.0396
== 13-limit ==
Comma list: 325/324, 352/351, 847/845, 1331/1323


==13-limit==
Mapping: [&lt;2 3 4 6 7 8|, &lt;0 4 15 -9 -2 -14|]
Commas: 325/324, 352/351, 847/845, 1331/1323


POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.697
POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.697


Map: [&lt;2 3 4 6 7 8|, &lt;0 4 15 -9 -2 -14|]
Vals: {{Val list| 46, 94, 140 }}


EDOs: 46, 94, 140
Badness: 0.024824


Badness: 0.0248
== 17-limit ==
Comma list: 289/288, 325/324, 352/351, 385/384, 561/560


==17-limit==
Map: [&lt;2 3 4 6 7 8 8|, &lt;0 4 15 -9 -2 -14 4|]
Commas: 289/288, 325/324, 352/351, 385/384, 561/560


POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.701
POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.701


Map: [&lt;2 3 4 6 7 8 8|, &lt;0 4 15 -9 -2 -14 4|]
Vals: {{Val list| 46, 94, 140 }}


EDOs: 46, 94, 140
Badness: 0.016591


Badness: 0.0166
== 19-limit ==
Comma list: 190/189, 209/208, 289/288, 352/351, 385/384, 561/560


==19-limit==
Mapping: [&lt;2 3 4 6 7 8 8 9|, &lt;0 4 15 -9 -2 -14 4 -12|]
Commas: 190/189, 209/208, 289/288, 352/351, 385/384, 561/560


POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.660
POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.660


Map: [&lt;2 3 4 6 7 8 8 9|, &lt;0 4 15 -9 -2 -14 4 -12|]
Vals: {{Val list| 46, 94, 140h, 234eh }}


EDOs: 46, 94, 140h, 234eh
Badness: 0.018170


Badness: 0.0182
== 23-limit ==
Commas: 190/189, 209/208, 253/252, 289/288, 323/322, 352/351, 385/384


==23-limit==
Mapping: [&lt;2 3 4 6 7 8 8 9 9|, &lt;0 4 15 -9 -2 -14 4 -12 1|]
Commas: 190/189, 209/208, 253/252, 289/288, 323/322, 352/351, 385/384


POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.661
POTE generator: ~55/54 = ~64/63 = ~81/80 = 25.661


Map: [&lt;2 3 4 6 7 8 8 9 9|, &lt;0 4 15 -9 -2 -14 4 -12 1|]
Vals: {{Val list| 46, 94, 140h, 234ehi }}
 
EDOs: 46, 94, 140h, 234ehi


Badness: 0.0140
Badness: 0.014033


[[Category:Temperament]]
[[Category:Temperament]]
[[Category:Hemifamity]]
[[Category:Hemifamity]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Aberschismic_temperaments"