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The '''alphatricot family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[alphatricot comma]] ({{monzo|legend=1| 39 -29 3 }}, [[ratio]]: 68 719 476 736 000 / 68 630 377 364 883).  
The '''alphatricot family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[alphatricot comma]] ({{monzo|legend=1| 39 -29 3 }}, [[ratio]]: 68 719 476 736 000 / 68 630 377 364 883).  


Strong 7-limit extensions of this temperament include alphatrimot (53 & 70), alphatrident (53 & 229) and alphatrillium (53 & 441). Tempering out [[5120/5103|hemifamity comma]] (5120/5103) leads to alphatrimot, [[6144/6125|porwell comma]] (6144/6125) leads to alphatrident, and [[4375/4374|ragisma]] (4375/4374) leads to alphatrillium.
Strong 7-limit extensions of this temperament include alphatrimot ({{nowrap| 53 & 70 }}), alphatrident ({{nowrap| 53 & 229 }}) and alphatrillium ({{nowrap| 53 & 441 }}). Tempering out [[5120/5103|hemifamity comma]] (5120/5103) leads to alphatrimot, [[6144/6125|porwell comma]] (6144/6125) leads to alphatrident, and [[4375/4374|ragisma]] (4375/4374) leads to alphatrillium.


== Alphatricot ==
== Alphatricot ==
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{{Mapping|legend=1| 1 0 -13 | 0 3 29 }}
{{Mapping|legend=1| 1 0 -13 | 0 3 29 }}
: mapping generators: ~2, ~59049/40960
: mapping generators: ~2, ~59049/40960


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.0000, ~59049/40960 = 634.0102
* [[WE]]: ~2 = 1199.9762{{c}}, ~59049/40960 = 633.9998{{c}}
: [[error map]]: {{val| 0.0000 +0.0757 -0.0168 }}
: [[error map]]: {{val| -0.024 +0.044 -0.010 }}
* [[POTE]]: ~2 = 1200.0000, ~59049/40960 = 634.0124
* [[CWE]]: ~2 = 1200.0000{{c}}, ~59049/40960 = 634.0116{{c}}
: error map: {{val| 0.0000 +0.0821 +0.0454 }}
: error map: {{val| 0.000 +0.080 +0.022 }}


{{Optimal ET sequence|legend=1| 53, 229, 282, 335, 388, 441, 1376, 1817, 2258, 15365bbc, 17632bbc }}
{{Optimal ET sequence|legend=1| 53, 229, 282, 335, 388, 441, 1376, 1817, 2258, 15365bbc, 17632bbc }}


[[Badness]] (Smith): 0.046093
[[Badness]] (Sintel): 1.08


; Scales
; Scales
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* [[Alphatricot19]] – improper [[17L 2s]]
* [[Alphatricot19]] – improper [[17L 2s]]


=== 2.3.5.13 subgroup ===
=== Alphatrimot (2.3.5.13 subgroup) ===
{{See also| No-fives subgroup temperaments #Threedic }}
{{See also| No-fives subgroup temperaments #Threedic }}


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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~13/9 = 634.0179
* WE: ~2 = 1200.2092{{c}}, ~13/9 = 634.1076{{c}}
* POTE: ~2 = 1200.000, ~13/9 = 633.9970
* CWE: ~2 = 1200.0000{{c}}, ~13/9 = 634.0032{{c}}


{{Optimal ET sequence|legend=0| 17c, 36c, 53 }}
{{Optimal ET sequence|legend=0| 17c, 36c, 53, 335f, 388f, …, 653ff }}


Badness (Sintel): 1.262
Badness (Sintel): 1.26


=== Catatricot ===
=== Alphatrillium (2.3.5.13 subgroup) ===
However, alphatricot in the 5-limit is far more accurate than threedic. Catatricot interprets the generator as ~[[75/52]] instead of 13/9, making the tempering of [[140625/140608]], the catasma, instead of the threedie. It also tempers out [[256000/255879]], the phaotisma.
However, alphatricot in the 5-limit is far more accurate than threedic. Alphatrillium interprets the generator as ~[[75/52]] instead of 13/9, making the tempering of [[140625/140608]], the catasma, instead of the threedie. It also tempers out [[256000/255879]], the phaotisma.


Subgroup: 2.3.5.13
Subgroup: 2.3.5.13
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~75/52 = 634.009
* WE: ~2 = 1199.9796{{c}}, ~75/52 = 634.0000{{c}}
* POTE: ~2 = 1200.000, ~75/52 = 634.0108
* CWE: ~2 = 1200.0000{{c}}, ~75/52 = 634.0103{{c}}


{{Optimal ET sequence|legend=1| 17cff, 36cff, 53, 282, 335, 388, 441, 494, 935 }}
{{Optimal ET sequence|legend=1| 17cff, 36cff, 53, 282, 335, 388, 441, 494, 935, 6051f, 6986f, …, 10726bff }}


Badness (Sintel): 0.181
Badness (Sintel): 0.181


== Alphatrillium ==
== Alphatrillium ==
Alphatrillium, named by [[Xenllium]] in 2021 as ''trillium'' but renamed following the specifications of ploidacot, can be described as the {{nowrap| 53 & 441 }} temperament, tempering out the [[ragisma]] aside from the alphatricot comma. [[441edo]] is a good tuning for this temperament, with generator 233\441. The harmonic 7 is found at -95 generator steps, so that the smallest [[mos scale]] is the 123-tone one. For much simpler mappings of 7 at the cost of higher errors, you could try [[#Alphatrident|alphatrident]] and [[#Alphatrimot|alphatrimot]].  
Alphatrillium, named by [[Xenllium]] in 2021 as ''trillium'' but renamed following the specifications of ploidacot, can be described as the {{nowrap| 53 & 441 }} temperament, tempering out the [[ragisma]] aside from the alphatricot comma. [[441edo]] is a good tuning for this temperament, with generator 233\441. The harmonic 7 is found at -95 generator steps, so that the smallest [[mos scale]] that contains it is the 123-note one, though otonal and utonal tetrads don't occur until the 176-note mos due to 7/5 being mapped to -124 generators. For much simpler mappings of 7 at the cost of higher errors, you could try [[#Alphatrident|alphatrident]] and [[#Alphatrimot|alphatrimot]].  


It can be extended to the 11-limit by tempering out [[131072/130977]], and to the 13-limit by tempering out [[2080/2079]], [[4096/4095]] and [[4225/4224]]. The optimal tunings in the 11- and 13-limit lean towards [[494edo]]; [[935edo]] and especially [[1429edo]] are recommendable tunings.  
It can be extended to the 11-limit by tempering out [[131072/130977]], and to the 13-limit by tempering out [[2080/2079]], [[4096/4095]] and [[4225/4224]]. The optimal tunings in the 11- and 13-limit lean towards [[494edo]]; [[935edo]] and especially [[1429edo]] are recommendable tunings.  
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[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 4375/4374, 1099511627776/1098337086315
[[Comma list]]: 4375/4374, {{monzo| 40 -22 -1 -1 }}


{{Mapping|legend=1| 1 0 -13 53 | 0 3 29 -95 }}
{{Mapping|legend=1| 1 0 -13 53 | 0 3 29 -95 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.0000, ~23625/16384 = 634.0121
* [[WE]]: ~2 = 1199.9795{{c}}, ~59049/40960 = 634.0010{{c}}
: [[error map]]: {{val| 0.0000 +0.0813 +0.0372 +0.0247 }}
: [[error map]]: {{val| -0.021 +0.048 -0.019 -0.004 }}
* [[POTE]]: ~2 = 1200.0000, ~23625/16384 = 634.0118
* [[CWE]]: ~2 = 1200.0000{{c}}, ~59049/40960 = 634.0119{{c}}
: error map: {{val| 0.0000 +0.0804 +0.0283 +0.0537 }}
: error map: {{val| 0.000 +0.081 +0.030 +0.048 }}


{{Optimal ET sequence|legend=1| 53, …, 335, 388, 441, 935, 1376, 3193, 4569, 5945, 10514b }}
{{Optimal ET sequence|legend=1| 53, …, 335, 388, 441, 935, 1376, 3193, 4569, 5945, 10514b }}


[[Badness]] (Smith): 0.030852
[[Badness]] (Sintel): 0.781


=== 11-limit ===
=== 11-limit ===
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.0000, ~3888/2695 = 634.0091
* WE: ~2 = 1199.9551{{c}}, ~3888/2695 = 633.9857{{c}}
* POTE: ~2 = 1200.0000, ~3888/2695 = 634.0094
* CWE: ~2 = 1200.0000{{c}}, ~3888/2695 = 634.0094{{c}}


{{Optimal ET sequence|legend=0| 53, 388e, 441, 494, 935, 1429, 1923e }}
{{Optimal ET sequence|legend=0| 53, 388e, 441, 494, 935, 1429, 1923e }}


Badness (Smith): 0.046758
Badness (Sintel): 1.55


==== 13-limit ====
==== 13-limit ====
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.0000, ~75/52 = 634.0091
* WE: ~2 = 1199.9603{{c}}, ~75/52 = 633.9885{{c}}
* POTE: ~2 = 1200.0000, ~75/52 = 634.0095
* CWE: ~2 = 1200.0000{{c}}, ~75/52 = 634.0094{{c}}


{{Optimal ET sequence|legend=0| 53, 388e, 441, 494, 935, 1429, 1923e, 3352de }}
{{Optimal ET sequence|legend=0| 53, 388e, 441, 494, 935, 1429, 1923e, 3352de }}


Badness (Smith): 0.019393
Badness (Sintel): 0.801


=== Pseudotrillium ===
=== Pseudotrillium ===
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.0000, ~231/160 = 634.0195
* WE: ~2 = 1200.0692{{c}}, ~231/160 = 634.0556{{c}}
* POTE: ~2 = 1200.0000, ~231/160 = 634.0190
* CWE: ~2 = 1200.0000{{c}}, ~231/160 = 634.0191{{c}}


{{Optimal ET sequence|legend=0| 53, 335, 388 }}
{{Optimal ET sequence|legend=0| 53, 335, 388 }}


Badness (Smith): 0.111931
Badness (Sintel): 3.70


==== 13-limit ====
==== 13-limit ====
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.0000, ~75/52 = 634.0185
* WE: ~2 = 1200.0351{{c}}, ~75/52 = 634.0366{{c}}
* POTE: ~2 = 1200.0000, ~75/52 = 634.0181
* CWE: ~2 = 1200.0000{{c}}, ~75/52 = 634.0181{{c}}


{{Optimal ET sequence|legend=0| 53, 335, 388 }}
{{Optimal ET sequence|legend=0| 53, 335, 388 }}


Badness (Smith): 0.054837
Badness (Sintel): 2.27


== Alphatrident ==
== Alphatrident ==
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.0000, ~4096/2835 = 634.0484
* [[WE]]: ~2 = 1199.7509{{c}}, ~4096/2835 = 633.9164{{c}}
: [[error map]]: {{val| 0.0000 +0.1901 +1.0893 +1.1421 }}
: [[error map]]: {{val| -0.249 -0.206 +0.500 +0.458 }}
* [[POTE]]: ~2 = 1200.0000, ~4096/2835 = 634.0480
* [[CWE]]: ~2 = 1200.0000{{c}}, ~4096/2835 = 634.0481{{c}}
: error map: {{val| 0.0000 +0.1890 +1.0784 +1.1579 }}
: error map: {{val| 0.000 +0.189 +1.081 +1.155 }}


{{Optimal ET sequence|legend=1| 53, 176, 229, 282, 511, 793cd }}
{{Optimal ET sequence|legend=1| 53, 176, 229, 282, 511, 793cd }}


[[Badness]] (Smith): 0.101694
[[Badness]] (Sintel): 2.57


=== 11-limit ===
=== 11-limit ===
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.0000, ~231/160 = 634.0630
* WE: ~2 = 1199.8432{{c}}, ~231/160 = 633.9840{{c}}
* POTE: ~2 = 1200.0000, ~231/160 = 634.0669
* CWE: ~2 = 1200.0000{{c}}, ~231/160 = 634.0662{{c}}


{{Optimal ET sequence|legend=0| 53, 123, 176, 229 }}
{{Optimal ET sequence|legend=0| 53, 123, 176, 229 }}


Badness (Smith): 0.074272
Badness (Sintel): 2.46


=== 13-limit ===
=== 13-limit ===
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.0000, ~13/9 = 634.0643
* WE: ~2 = 1199.9675{{c}}, ~13/9 = 634.0480{{c}}
* POTE: ~2 = 1200.0000, ~13/9 = 634.0652
* CWE: ~2 = 1200.0000{{c}}, ~13/9 = 634.0651{{c}}


{{Optimal ET sequence|legend=0| 53, 123, 176, 229 }}
{{Optimal ET sequence|legend=0| 53, 123, 176, 229 }}


Badness (Smith): 0.046593
Badness (Sintel): 1.93


== Alphatrimot ==
== Alphatrimot ==
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.0000, ~81/56 = 633.9681
* [[WE]]: ~2 = 1199.4448{{c}}, ~81/56 = 633.7326{{c}}
: [[error map]]: {{val| 0.0000 -0.0508 -1.2400 +4.8227 }}
: [[error map]]: {{val| -0.555 -0.757 +0.851 +3.898 }}
* [[POTE]]: ~2 = 1200.0000, ~81/56 = 634.0259
* [[CWE]]: ~2 = 1200.0000{{c}}, ~81/56 = 634.0071{{c}}
: error map: {{val| 0.0000 +0.1228 +0.4387 +5.4595 }}
: error map: {{val| 0.000 +0.066 -0.108 +5.252 }}


{{Optimal ET sequence|legend=1| 17c, 36c, 53, 229dd, 282dd }}
{{Optimal ET sequence|legend=1| 17c, 36c, 53, 229dd, 282dd }}


[[Badness]] (Smith): 0.100127
[[Badness]] (Sintel): 2.53


=== 11-limit ===
=== 11-limit ===
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.0000, ~63/44 = 634.0214
* WE: ~2 = 1199.9429{{c}}, ~63/44 = 633.9971{{c}}
* POTE: ~2 = 1200.0000, ~63/44 = 634.0273
* CWE: ~2 = 1200.0000{{c}}, ~63/44 = 634.0253{{c}}


{{Optimal ET sequence|legend=0| 17c, 36ce, 53 }}
{{Optimal ET sequence|legend=0| 17c, 36ce, 53 }}


Badness (Smith): 0.056134
Badness (Sintel): 1.86


=== 13-limit ===
=== 13-limit ===
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.0000, ~13/9 = 634.0275
* WE: ~2 = 1200.1213{{c}}, ~13/9 = 634.0757{{c}}
* POTE: ~2 = 1200.0000, ~13/9 = 634.0115
* CWE: ~2 = 1200.0000{{c}}, ~13/9 = 634.0154{{c}}


{{Optimal ET sequence|legend=0| 17c, 36ce, 53 }}
{{Optimal ET sequence|legend=0| 17c, 36ce, 53 }}


Badness (Smith): 0.032102
Badness (Sintel): 1.33


== Tritricot ==
== Tritricot ==
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 250047/250000, 11785390260224/11767897353375
[[Comma list]]: 250047/250000, {{monzo| 35 -23 -3 3 }}


{{Mapping|legend=1| 3 6 19 30 | 0 -3 -29 -52 }}
{{Mapping|legend=1| 3 0 -39 -74 | 0 3 29 52 }}
: mapping generators: ~63/50, ~59049/40960


[[Optimal tuning]] ([[POTE]]): ~63/50 = 400.0000, ~100352/91125 = 165.9837
[[Optimal tuning]]s:
* [[WE]]: ~63/50 = 399.9887{{c}}, ~59049/40960 = 633.7326{{c}} (~100352/91125 = 165.9790{{c}})
: [[error map]]: {{val| -0.034 +0.040 +0.081 -0.073 }}
* [[CWE]]: ~63/50 = 400.0000{{c}}, ~59049/40960 = 634.0155{{c}} (~100352/91125 = 165.9845{{c}})
: error map: {{val| 0.000 +0.092 -0.137 -0.018 }}


{{Optimal ET sequence|legend=1| 159, 282, 441, 2487, 2928, 3369 }}
{{Optimal ET sequence|legend=1| 159, 282, 441, 1605, 2046, 2487, 2928 }}


[[Badness]] (Smith): 0.086081
[[Badness]] (Sintel): 2.18


=== 11-limit ===
=== 11-limit ===
Line 264: Line 268:
Comma list: 4000/3993, 166698/166375, 200704/200475
Comma list: 4000/3993, 166698/166375, 200704/200475


Mapping: {{mapping| 3 6 19 30 22 | 0 -3 -29 -52 -28 }}
Mapping: {{mapping| 3 0 -39 -74 -34 | 0 3 29 52 28 }}


Optimal tuning (POTE): ~63/50 = 400.0000, ~11/10 = 165.9835
Optimal tunings:
* WE: ~63/50 = 399.9686{{c}}, ~3969/2750 = 633.9667{{c}} (~11/10 = 165.9705{{c}})
* CWE: ~63/50 = 400.0000{{c}}, ~3969/2750 = 634.0142{{c}} (~11/10 = 165.9858{{c}})


{{Optimal ET sequence|legend=0| 159, 282, 441 }}
{{Optimal ET sequence|legend=0| 159, 282, 441 }}


Badness (Smith): 0.074002
Badness (Sintel): 2.45


==== 13-limit ====
==== 13-limit ====
Line 277: Line 283:
Comma list: 1575/1573, 2080/2079, 34398/34375, 43904/43875
Comma list: 1575/1573, 2080/2079, 34398/34375, 43904/43875


Mapping: {{mapping| 3 6 19 30 22 36 | 0 -3 -29 -52 -28 -60 }}
Mapping: {{mapping| 3 0 -39 -74 -34 -84 | 0 3 29 52 28 60 }}


Optimal tuning (POTE): ~63/50 = 400.0000, ~11/10 = 165.9842
Optimal tunings:
* WE: ~63/50 = 399.9692{{c}}, ~75/52 = 633.9669{{c}} (~11/10 = 165.9714{{c}})
* CWE: ~63/50 = 400.0000{{c}}, ~75/52 = 634.0137{{c}} (~11/10 = 165.9863{{c}})


{{Optimal ET sequence|legend=0| 159, 282, 441 }}
{{Optimal ET sequence|legend=0| 159, 282, 441 }}


Badness (Smith): 0.035641
Badness (Sintel): 1.47


==== 17-limit ====
==== 17-limit ====
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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: {{mapping| 3 6 19 30 22 36 16 | 0 -3 -29 -52 -28 -60 -9 }}
Mapping: {{mapping| 3 0 -39 -74 -34 -84 -2 | 0 3 29 52 28 60 9 }}


Optimal tuning (POTE): ~34/27 = 400.0000, ~11/10 = 165.9805
Optimal tunings:
* WE: ~34/27 = 399.9491{{c}}, ~75/52 = 633.9389{{c}} (~11/10 = 165.9594{{c}})
* CWE: ~34/27 = 400.0000{{c}}, ~75/52 = 634.0166{{c}} (~11/10 = 165.9834{{c}})


{{Optimal ET sequence|legend=0| 159, 282, 441 }}
{{Optimal ET sequence|legend=0| 159, 282, 441, 723efg, 1164eefgg }}


Badness (Smith): 0.025972
Badness (Sintel): 1.32


=== Noletaland ===
=== Noletaland ===
Line 306: Line 316:


Mapping: {{mapping| 3 6 19 30 35 | 0 -9 -87 -156 -178 }}
Mapping: {{mapping| 3 6 19 30 35 | 0 -9 -87 -156 -178 }}
: mappin generators: ~63/50, ~1936/1875
: mappin generators: ~63/50, ~1936/1875


Optimal tuning (CTE): ~63/50 = 400.0000, ~1936/1875 = 55.3290
Optimal tunings:
* WE: ~63/50 = 399.9895{{c}}, ~1936/1875 = 55.3269{{c}}
* CWE: ~63/50 = 400.0000{{c}}, ~1936/1875 = 55.3286{{c}}


{{Optimal ET sequence|legend=0| 282, 759de, 1041, 1323, 4251e }}
{{Optimal ET sequence|legend=0| 282, 759de, 1041, 1323, 4251e }}


Badness (Smith): 0.158
Badness (Sintel): 5.23


==== 13-limit ====
==== 13-limit ====
Line 322: Line 333:
Mapping: {{mapping| 3 6 19 30 35 36 | 0 -9 -87 -156 -178 -180 }}
Mapping: {{mapping| 3 6 19 30 35 36 | 0 -9 -87 -156 -178 -180 }}


Optimal tuning (CTE): ~63/50 = 400.0000, ~1936/1875 = 55.3294
Optimal tunings:
* WE: ~63/50 = 399.9896{{c}}, ~1936/1875 = 55.3273{{c}}
* CWE: ~63/50 = 400.0000{{c}}, ~1936/1875 = 55.3289{{c}}


{{Optimal ET sequence|legend=0| 282, 759def, 1041, 1323 }}
{{Optimal ET sequence|legend=0| 282, 759def, 1041, 1323 }}


Badness (Smith): 0.0725
Badness (Sintel): 2.99


==== 17-limit ====
==== 17-limit ====
Line 335: Line 348:
Mapping: {{mapping| 3 6 19 30 35 36 29 | 0 -9 -87 -156 -178 -180 -121 }}
Mapping: {{mapping| 3 6 19 30 35 36 29 | 0 -9 -87 -156 -178 -180 -121 }}


Optimal tuning (CTE): ~63/50 = 400.0000, ~351/340 = 55.3295
Optimal tunings:
* WE: ~63/50 = 399.9876{{c}}, ~351/340 = 55.3270{{c}}
* CWE: ~63/50 = 400.0000{{c}}, ~351/340 = 55.3290{{c}}


{{Optimal ET sequence|legend=0| 282, 759def, 1041, 1323 }}
{{Optimal ET sequence|legend=0| 282, 759def, 1041, 1323 }}


Badness (Smith): 0.0380
Badness (Sintel): 1.93


==== 19-limit ====
==== 19-limit ====
Line 348: Line 363:
Mapping: {{mapping| 3 6 19 30 35 36 29 18 | 0 -9 -87 -156 -178 -180 -121 -38 }}
Mapping: {{mapping| 3 6 19 30 35 36 29 18 | 0 -9 -87 -156 -178 -180 -121 -38 }}


Optimal tuning (CTE): ~63/50 = 400.0000, ~351/340 = 55.3295
Optimal tunings:
* WE: ~63/50 = 399.9914{{c}}, ~351/340 = 55.3277{{c}}
* CWE: ~63/50 = 400.0000{{c}}, ~351/340 = 55.3291{{c}}


{{Optimal ET sequence|legend=0| 282, 759def, 1041, 1323 }}
{{Optimal ET sequence|legend=0| 282, 759def, 1041, 1323 }}


Badness (Smith): 0.0269
Badness (Sintel): 1.64


==== 23-limit ====
==== 23-limit ====
Line 361: Line 378:
Mapping: {{mapping| 3 6 19 30 35 36 29 18 31 | 0 -9 -87 -156 -178 -180 -121 -38 -126 }}
Mapping: {{mapping| 3 6 19 30 35 36 29 18 31 | 0 -9 -87 -156 -178 -180 -121 -38 -126 }}


Optimal tuning (CTE): ~63/50 = 400.0000, ~351/340 = 55.3296
Optimal tunings:
* WE: ~63/50 = 399.9899{{c}}, ~351/340 = 55.3276{{c}}
* CWE: ~63/50 = 400.0000{{c}}, ~351/340 = 55.3291{{c}}


{{Optimal ET sequence|legend=0| 282, 759def, 1041, 1323 }}
{{Optimal ET sequence|legend=0| 282, 759def, 1041, 1323 }}


Badness (Smith): 0.0194
Badness (Sintel): 1.39


==== 29-limit ====
==== 29-limit ====
Line 374: Line 393:
Mapping: {{mapping| 3 6 19 30 35 36 29 18 31 19 | 0 -9 -87 -156 -178 -180 -121 -38 -126 -32 }}
Mapping: {{mapping| 3 6 19 30 35 36 29 18 31 19 | 0 -9 -87 -156 -178 -180 -121 -38 -126 -32 }}


Optimal tuning (CTE): ~63/50 = 400.0000, ~351/340 = 55.3296
Optimal tunings:
* WE: ~63/50 = 399.9940{{c}}, ~351/340 = 55.3283{{c}}
* CWE: ~63/50 = 400.0000{{c}}, ~351/340 = 55.3293{{c}}


{{Optimal ET sequence|legend=0| 282, 759def, 1041, 1323 }}
{{Optimal ET sequence|legend=0| 282, 759def, 1041, 1323 }}


Badness (Smith): 0.0168
Badness (Sintel): 1.40


== Notes ==
== Notes ==
Line 384: Line 405:
[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Alphatricot family| ]] <!-- main article -->
[[Category:Alphatricot family| ]] <!-- main article -->
[[Category:Alphatricot| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Alphatricot_family"