Alphatricot family: Difference between revisions

Revision as of 14:40, 16 March 2025

The alphatricot family of temperaments tempers out the alphatricot comma (monzo: [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 hemifamity comma (5120/5103) leads to alphatrimot, porwell comma (6144/6125) leads to alphatrident, and ragisma (4375/4374) leads to alphatrillium.

Alphatricot

Alphatricot is a microtemperament whose generator is the real cube root of 3rd harmonic, 3^1/3, tuned between 63/44 and 13/9. Its ploidacot is alpha-tricot. It is a member of the schismic–Mercator equivalence continuum with n = 3, so unless 53edo is used as a tuning, the schisma is always observed.

The temperament was named by Paul Erlich in 2002 as tricot^[1]^[2], but renamed in 2025 following the specifications of ploidacot.

Subgroup: 2.3.5

Comma list: [39 -29 3⟩

Mapping: [⟨1 0 -13], ⟨0 3 29]]

mapping generators: ~2, ~59049/40960

Wedgie: ⟨⟨ 3 29 39 ]]

Optimal tuning (POTE): ~2 = 1200.000, ~59049/40960 = 634.012

Optimal ET sequence: 53, 229, 282, 335, 388, 441, 1376, 1817, 2258

Badness (Smith): 0.046093

2.3.5.13 subgroup

See also: No-fives subgroup temperaments § Threedic

Subgroup: 2.3.5.13

Comma list: 2197/2187, 41067/40960

Sval mapping: [⟨1 0 -13 0], ⟨0 3 29 7]]

Gencom mapping: [⟨1 0 -13 0 0 0], ⟨0 3 29 0 0 7]]

gencom: [2 13/9; 2197/2187, 41067/40960]

Optimal tuning (POTE): ~2 = 1200.000, ~13/9 = 633.997

Optimal ET sequence: 17c, 36c, 53

RMS error: 0.2342 cents

Scales

Alphatricot17 – proper 2L 15s
Alphatricot19 – improper 17L 2s

Alphatrimot

Alphatrimot, named by Petr Pařízek in 2011^[3], can be described as the 53 & 70 temperament.

Subgroup: 2.3.5.7

Comma list: 2430/2401, 5120/5103

Mapping: [⟨1 0 -13 -3], ⟨0 3 29 11]]

Wedgie: ⟨⟨ 3 29 11 39 9 -56 ]]

Optimal tuning (POTE): ~2 = 1200.0000, ~81/56 = 634.0259

Optimal ET sequence: 17c, 36c, 53, 70, 229dd, 282dd

Badness (Smith): 0.100127

11-limit

Subgroup: 2.3.5.7.11

Comma list: 99/98, 121/120, 5120/5103

Mapping: [⟨1 0 -13 -3 -5], ⟨0 3 29 11 16]]

Optimal tuning (POTE): ~2 = 1200.0000, ~63/44 = 634.0273

Optimal ET sequence: 17c, 36ce, 53, 70, 123de

Badness (Smith): 0.056134

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 99/98, 121/120, 169/168, 352/351

Mapping: [⟨1 0 -13 -3 -5 0], ⟨0 3 29 11 16 7]]

Optimal tuning (POTE): ~2 = 1200.0000, ~13/9 = 634.0115

Optimal ET sequence: 17c, 36ce, 53, 70, 123de

Badness (Smith): 0.032102

Alphatrident

Alphatrident, named by Xenllium in 2021 as trident but renamed following the specifications of ploidacot, can be described as the 53 & 229 temperament.

Subgroup: 2.3.5.7

Comma list: 6144/6125, 14348907/14336000

Mapping: [⟨1 0 -13 25], ⟨0 3 29 -42]]

Wedgie: ⟨⟨ 3 29 -42 39 -75 -179 ]]

Optimal tuning (POTE): ~2 = 1200.0000, ~4096/2835 = 634.0480

Optimal ET sequence: 53, 176, 229, 282, 511

Badness (Smith): 0.101694

11-limit

Subgroup: 2.3.5.7.11

Comma list: 3388/3375, 6144/6125, 8019/8000

Mapping: [⟨1 0 -13 25 -33], ⟨0 3 29 -42 69]]

Optimal tuning (POTE): ~2 = 1200.0000, ~231/160 = 634.0669

Optimal ET sequence: 53, 176, 229

Badness (Smith): 0.074272

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 351/350, 2080/2079, 2197/2187, 3146/3125

Mapping: [⟨1 0 -13 25 -33 0], ⟨0 3 29 -42 69 7]]

Optimal tuning (POTE): ~2 = 1200.0000, ~13/9 = 634.0652

Optimal ET sequence: 53, 176, 229

Badness (Smith): 0.046593

Alphatrillium

Alphatrillium, also named by Xenllium in 2021 as trillium but renamed following the specifications of ploidacot, can be described as the 53 & 441 temperament.

Subgroup: 2.3.5.7

Comma list: 4375/4374, 1099511627776/1098337086315

Mapping: [⟨1 0 -13 53], ⟨0 3 29 -95]]

Wedgie: ⟨⟨ 3 29 -95 39 -159 -302 ]]

Optimal tuning (POTE): ~2 = 1200.0000, ~23625/16384 = 634.0118

Optimal ET sequence: 53, 441, 494, 935, 1376, 3193, 4569

Badness (Smith): 0.030852

11-limit

Subgroup: 2.3.5.7.11

Comma list: 4375/4374, 131072/130977, 759375/758912

Mapping: [⟨1 0 -13 53 -89], ⟨0 3 29 -95 175]]

Optimal tuning (POTE): ~2 = 1200.0000, ~3888/2695 = 634.0094

Optimal ET sequence: 53, 441, 494, 935, 1429

Badness (Smith): 0.046758

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 2080/2079, 4096/4095, 4375/4374, 78125/78078

Mapping: [⟨1 0 -13 53 -89 -28], ⟨0 3 29 -95 175 60]]

Optimal tuning (POTE): ~2 = 1200.0000, ~75/52 = 634.0095

Optimal ET sequence: 53, 441, 494, 935, 1429

Badness (Smith): 0.019393

Pseudotrillium

Subgroup: 2.3.5.7.11

Comma list: 4375/4374, 5632/5625, 4108797/4096000

Mapping: [⟨1 0 -13 53 -61], ⟨0 3 29 -95 122]]

Optimal tuning (POTE): ~2 = 1200.0000, ~231/160 = 634.0190

Optimal ET sequence: 53, 335, 388

Badness (Smith): 0.111931

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 847/845, 1001/1000, 4096/4095, 4375/4374

Mapping: [⟨1 0 -13 53 -61 -28], ⟨0 3 29 -95 122 60]]

Optimal tuning (POTE): ~2 = 1200.0000, ~75/52 = 634.0181

Optimal ET sequence: 53, 335, 388

Badness (Smith): 0.054837

Tritricot

Subgroup: 2.3.5.7

Comma list: 250047/250000, 11785390260224/11767897353375

Mapping: [⟨3 6 19 30], ⟨0 -3 -29 -52]]

Wedgie: ⟨⟨ 9 87 156 117 222 118 ]]

Optimal tuning (POTE): ~63/50 = 400.0000, ~100352/91125 = 165.9837

Optimal ET sequence: 159, 282, 441, 2487, 2928, 3369

Badness (Smith): 0.086081

11-limit

Subgroup: 2.3.5.7.11

Comma list: 4000/3993, 166698/166375, 200704/200475

Mapping: [⟨3 6 19 30 22], ⟨0 -3 -29 -52 -28]]

Optimal tuning (POTE): ~63/50 = 400.0000, ~11/10 = 165.9835

Optimal ET sequence: 159, 282, 441

Badness (Smith): 0.074002

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 1575/1573, 2080/2079, 34398/34375, 43904/43875

Mapping: [⟨3 6 19 30 22 36], ⟨0 -3 -29 -52 -28 -60]]

Optimal tuning (POTE): ~63/50 = 400.0000, ~11/10 = 165.9842

Optimal ET sequence: 159, 282, 441

Badness (Smith): 0.035641

17-limit

Subgroup: 2.3.5.7.11.13.17

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]]

Optimal tuning (POTE): ~34/27 = 400.0000, ~11/10 = 165.9805

Optimal ET sequence: 159, 282, 441

Badness (Smith): 0.025972

Noletaland

Noletaland is described as 282 & 1323, and it combines the smallest consistent edo in the 29-odd-limit with the smallest uniquely consistent. It reaches 4/3 in nine generators (noleta-…) and tempers out the landscape comma (…-land). Noletaland reaches 13/11 in 2 generators, and 29/19 in 5. Then there is 44/25 in 4, and 152/115 in also 4.

Subgroup: 2.3.5.7.11

Comma list: 250047/250000, 56723625/56689952, 78675968/78594219

Mapping: [⟨3 6 19 30 35], ⟨0 -9 -87 -156 -178]]

mappin generators: ~63/50, ~1936/1875

Optimal tuning (CTE): ~63/50 = 400.0000, ~1936/1875 = 55.3290

Optimal ET sequence: 282, 759de, 1041, 1323, 4251e

Badness (Smith): 0.158

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 10648/10647, 43904/43875, 85750/85683, 250047/250000

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 ET sequence: 282, 759def, 1041, 1323

Badness (Smith): 0.0725

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 2058/2057, 4914/4913, 8624/8619, 12376/12375, 250047/250000

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 ET sequence: 282, 759def, 1041, 1323

Badness (Smith): 0.0380

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 2058/2057, 2926/2925, 3136/3135, 4200/4199, 4914/4913, 250047/250000

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 ET sequence: 282, 759def, 1041, 1323

Badness (Smith): 0.0269

23-limit

Subgroup: 2.3.5.7.11.13.17.19.23

Comma list: 2058/2057, 2926/2925, 3136/3135, 3381/3380, 3520/3519, 4914/4913, 18515/18513

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 ET sequence: 282, 759def, 1041, 1323

Badness (Smith): 0.0194

29-limit

Subgroup: 2.3.5.7.11.13.17.19.23.29

Comma list: 2058/2057, 2755/2754, 2926/2925, 3136/3135, 3381/3380, 3451/3450, 3520/3519, 4914/4913

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 ET sequence: 282, 759def, 1041, 1323

Badness (Smith): 0.0168

Notes

[1] Yahoo! Tuning Group | Paul's new names

[2] Yahoo! Tuning Group | Ultimate 5-limit comma list

[3] Yahoo! Tuning Group | Suggested names for the unclasified temperaments

[1]

[2]

[3]

Alphatricot family: Difference between revisions

Revision as of 14:40, 16 March 2025

Contents

Alphatricot

2.3.5.13 subgroup

Alphatrimot

11-limit

13-limit

Alphatrident

11-limit

13-limit

Alphatrillium

11-limit

13-limit

Pseudotrillium

13-limit

Tritricot

11-limit

13-limit

17-limit

Noletaland

13-limit

17-limit

19-limit

23-limit

29-limit

Notes

Navigation menu

@@ Line 18: / Line 18: @@
 {{Multival|legend=1| 3 29 39 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~59049/40960 = 634.012
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~59049/40960 = 634.012
 {{Optimal ET sequence|legend=1| 53, 229, 282, 335, 388, 441, 1376, 1817, 2258 }}
-[[Badness]]: 0.046093
+[[Badness]] (Smith): 0.046093
 === 2.3.5.13 subgroup ===
@@ Line 29: / Line 29: @@
 Subgroup: 2.3.5.13
-[[Comma list]]: 2197/2187, 41067/40960
+Comma list: 2197/2187, 41067/40960
-[[Gencom]]: [2 13/9; 2197/2187, 41067/40960]
+[[Sval]] [[mapping]]: {{mapping| 1 0 -13 0 | 0 3 29 7 }}
-[[Gencom|Gencom mapping]]: [{{val|1 0 -13 0 0 0}}, {{val|0 3 29 0 0 7}}]
+[[Gencom]] [[mapping]]: {{mapping| 1 0 -13 0 0 0 | 0 3 29 0 0 7 }}
-[[Mapping|Sval mapping]]: [{{val|1 0 -13 0}}, {{val|0 3 29 7}}]
+: gencom: [2 13/9; 2197/2187, 41067/40960]
-[[Tp tuning|POL2 generator]]: ~13/9 = 633.997
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~13/9 = 633.997
-{{Optimal ET sequence|legend=1| 17c, 36c, 53 }}
+{{Optimal ET sequence|legend=0| 17c, 36c, 53 }}
 [[Tp tuning #T2 tuning|RMS error]]: 0.2342 cents
@@ Line 58: / Line 58: @@
 {{Multival|legend=1| 3 29 11 39 9 -56 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~81/56 = 634.0259
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000, ~81/56 = 634.0259
 {{Optimal ET sequence|legend=1| 17c, 36c, 53, 70, 229dd, 282dd }}
-[[Badness]]: 0.100127
+[[Badness]] (Smith): 0.100127
 === 11-limit ===
@@ Line 71: / Line 71: @@
 Mapping: {{mapping| 1 0 -13 -3 -5 | 0 3 29 11 16 }}
-Optimal tuning (POTE): ~2 = 1\1, ~63/44 = 634.0273
+Optimal tuning (POTE): ~2 = 1200.0000, ~63/44 = 634.0273
-{{Optimal ET sequence|legend=1| 17c, 36ce, 53, 70, 123de }}
+{{Optimal ET sequence|legend=0| 17c, 36ce, 53, 70, 123de }}
-Badness: 0.056134
+Badness (Smith): 0.056134
 === 13-limit ===
@@ Line 84: / Line 84: @@
 Mapping: {{mapping| 1 0 -13 -3 -5 0 | 0 3 29 11 16 7 }}
-Optimal tuning (POTE): ~2 = 1\1, ~13/9 = 634.0115
+Optimal tuning (POTE): ~2 = 1200.0000, ~13/9 = 634.0115
-{{Optimal ET sequence|legend=1| 17c, 36ce, 53, 70, 123de }}
+{{Optimal ET sequence|legend=0| 17c, 36ce, 53, 70, 123de }}
-Badness: 0.032102
+Badness (Smith): 0.032102
 == Alphatrident ==
@@ Line 101: / Line 101: @@
 {{Multival|legend=1| 3 29 -42 39 -75 -179 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~4096/2835 = 634.0480
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000, ~4096/2835 = 634.0480
 {{Optimal ET sequence|legend=1| 53, 176, 229, 282, 511 }}
-[[Badness]]: 0.101694
+[[Badness]] (Smith): 0.101694
 === 11-limit ===
@@ Line 114: / Line 114: @@
 Mapping: {{mapping| 1 0 -13 25 -33 | 0 3 29 -42 69 }}
-Optimal tuning (POTE): ~2 = 1\1, ~231/160 = 634.0669
+Optimal tuning (POTE): ~2 = 1200.0000, ~231/160 = 634.0669
-{{Optimal ET sequence|legend=1| 53, 176, 229 }}
+{{Optimal ET sequence|legend=0| 53, 176, 229 }}
-Badness: 0.074272
+Badness (Smith): 0.074272
 === 13-limit ===
@@ Line 127: / Line 127: @@
 Mapping: {{mapping| 1 0 -13 25 -33 0 | 0 3 29 -42 69 7 }}
-Optimal tuning (POTE): ~2 = 1\1, ~13/9 = 634.0652
+Optimal tuning (POTE): ~2 = 1200.0000, ~13/9 = 634.0652
-{{Optimal ET sequence|legend=1| 53, 176, 229 }}
+{{Optimal ET sequence|legend=0| 53, 176, 229 }}
-Badness: 0.046593
+Badness (Smith): 0.046593
 == Alphatrillium ==
@@ Line 144: / Line 144: @@
 {{Multival|legend=1| 3 29 -95 39 -159 -302 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~23625/16384 = 634.0118
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000, ~23625/16384 = 634.0118
 {{Optimal ET sequence|legend=1| 53, 441, 494, 935, 1376, 3193, 4569 }}
-[[Badness]]: 0.030852
+[[Badness]] (Smith): 0.030852
 === 11-limit ===
@@ Line 157: / Line 157: @@
 Mapping: {{mapping| 1 0 -13 53 -89 | 0 3 29 -95 175 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3888/2695 = 634.0094
+Optimal tuning (POTE): ~2 = 1200.0000, ~3888/2695 = 634.0094
-{{Optimal ET sequence|legend=1| 53, 441, 494, 935, 1429 }}
+{{Optimal ET sequence|legend=0| 53, 441, 494, 935, 1429 }}
-Badness: 0.046758
+Badness (Smith): 0.046758
 ==== 13-limit ====
@@ Line 170: / Line 170: @@
 Mapping: {{mapping| 1 0 -13 53 -89 -28 | 0 3 29 -95 175 60 }}
-Optimal tuning (POTE): ~2 = 1\1, ~75/52 = 634.0095
+Optimal tuning (POTE): ~2 = 1200.0000, ~75/52 = 634.0095
-{{Optimal ET sequence|legend=1| 53, 441, 494, 935, 1429 }}
+{{Optimal ET sequence|legend=0| 53, 441, 494, 935, 1429 }}
-Badness: 0.019393
+Badness (Smith): 0.019393
 === Pseudotrillium ===
@@ Line 183: / Line 183: @@
 Mapping: {{mapping| 1 0 -13 53 -61 | 0 3 29 -95 122 }}
-Optimal tuning (POTE): ~2 = 1\1, ~231/160 = 634.0190
+Optimal tuning (POTE): ~2 = 1200.0000, ~231/160 = 634.0190
-{{Optimal ET sequence|legend=1| 53, 335, 388 }}
+{{Optimal ET sequence|legend=0| 53, 335, 388 }}
-Badness: 0.111931
+Badness (Smith): 0.111931
 ==== 13-limit ====
@@ Line 196: / Line 196: @@
 Mapping: {{mapping| 1 0 -13 53 -61 -28 | 0 3 29 -95 122 60 }}
-Optimal tuning (POTE): ~2 = 1\1, ~75/52 = 634.0181
+Optimal tuning (POTE): ~2 = 1200.0000, ~75/52 = 634.0181
-{{Optimal ET sequence|legend=1| 53, 335, 388 }}
+{{Optimal ET sequence|legend=0| 53, 335, 388 }}
-Badness: 0.054837
+Badness (Smith): 0.054837
 == Tritricot ==
@@ Line 211: / Line 211: @@
 {{Multival|legend=1| 9 87 156 117 222 118 }}
-[[Optimal tuning]] ([[POTE]]): ~63/50 = 1\3, ~100352/91125 = 165.9837
+[[Optimal tuning]] ([[POTE]]): ~63/50 = 400.0000, ~100352/91125 = 165.9837
 {{Optimal ET sequence|legend=1| 159, 282, 441, 2487, 2928, 3369 }}
-[[Badness]]: 0.086081
+[[Badness]] (Smith): 0.086081
 === 11-limit ===
@@ Line 224: / Line 224: @@
 Mapping: {{mapping| 3 6 19 30 22 | 0 -3 -29 -52 -28 }}
-Optimal tuning (POTE): ~63/50 = 1\3, ~11/10 = 165.9835
+Optimal tuning (POTE): ~63/50 = 400.0000, ~11/10 = 165.9835
-{{Optimal ET sequence|legend=1| 159, 282, 441 }}
+{{Optimal ET sequence|legend=0| 159, 282, 441 }}
-Badness: 0.074002
+Badness (Smith): 0.074002
 ==== 13-limit ====
@@ Line 237: / Line 237: @@
 Mapping: {{mapping| 3 6 19 30 22 36 | 0 -3 -29 -52 -28 -60 }}
-Optimal tuning (POTE): ~63/50 = 1\3, ~11/10 = 165.9842
+Optimal tuning (POTE): ~63/50 = 400.0000, ~11/10 = 165.9842
-{{Optimal ET sequence|legend=1| 159, 282, 441 }}
+{{Optimal ET sequence|legend=0| 159, 282, 441 }}
-Badness: 0.035641
+Badness (Smith): 0.035641
 ==== 17-limit ====
@@ Line 250: / Line 250: @@
 Mapping: {{mapping| 3 6 19 30 22 36 16 | 0 -3 -29 -52 -28 -60 -9 }}
-Optimal tuning (POTE): ~34/27 = 1\3, ~11/10 = 165.9805
+Optimal tuning (POTE): ~34/27 = 400.0000, ~11/10 = 165.9805
-{{Optimal ET sequence|legend=1| 159, 282, 441 }}
+{{Optimal ET sequence|legend=0| 159, 282, 441 }}
-Badness: 0.025972
+Badness (Smith): 0.025972
 === Noletaland ===
@@ Line 267: / Line 267: @@
 : mappin generators: ~63/50, ~1936/1875
-Optimal tuning (CTE): ~63/50 = 1\3, ~1936/1875 = 55.3290
+Optimal tuning (CTE): ~63/50 = 400.0000, ~1936/1875 = 55.3290
-{{Optimal ET sequence|legend=1| 282, 759de, 1041, 1323, 4251e }}
+{{Optimal ET sequence|legend=0| 282, 759de, 1041, 1323, 4251e }}
-Badness: 0.158
+Badness (Smith): 0.158
 ==== 13-limit ====
@@ Line 280: / Line 280: @@
 Mapping: {{mapping| 3 6 19 30 35 36 | 0 -9 -87 -156 -178 -180 }}
-Optimal tuning (CTE): ~63/50 = 1\3, ~1936/1875 = 55.3294
+Optimal tuning (CTE): ~63/50 = 400.0000, ~1936/1875 = 55.3294
-{{Optimal ET sequence|legend=1| 282, 759def, 1041, 1323 }}
+{{Optimal ET sequence|legend=0| 282, 759def, 1041, 1323 }}
-Badness: 0.0725
+Badness (Smith): 0.0725
 ==== 17-limit ====
@@ Line 293: / Line 293: @@
 Mapping: {{mapping| 3 6 19 30 35 36 29 | 0 -9 -87 -156 -178 -180 -121 }}
-Optimal tuning (CTE): ~63/50 = 1\3, ~351/340 = 55.3295
+Optimal tuning (CTE): ~63/50 = 400.0000, ~351/340 = 55.3295
-{{Optimal ET sequence|legend=1| 282, 759def, 1041, 1323 }}
+{{Optimal ET sequence|legend=0| 282, 759def, 1041, 1323 }}
-Badness: 0.0380
+Badness (Smith): 0.0380
 ==== 19-limit ====
@@ Line 306: / Line 306: @@
 Mapping: {{mapping| 3 6 19 30 35 36 29 18 | 0 -9 -87 -156 -178 -180 -121 -38 }}
-Optimal tuning (CTE): ~63/50 = 1\3, ~351/340 = 55.3295
+Optimal tuning (CTE): ~63/50 = 400.0000, ~351/340 = 55.3295
-{{Optimal ET sequence|legend=1| 282, 759def, 1041, 1323 }}
+{{Optimal ET sequence|legend=0| 282, 759def, 1041, 1323 }}
-Badness: 0.0269
+Badness (Smith): 0.0269
 ==== 23-limit ====
@@ Line 319: / Line 319: @@
 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 = 1\3, ~351/340 = 55.3296
+Optimal tuning (CTE): ~63/50 = 400.0000, ~351/340 = 55.3296
-{{Optimal ET sequence|legend=1| 282, 759def, 1041, 1323 }}
+{{Optimal ET sequence|legend=0| 282, 759def, 1041, 1323 }}
-Badness: 0.0194
+Badness (Smith): 0.0194
 ==== 29-limit ====
@@ Line 332: / Line 332: @@
 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 = 1\3, ~351/340 = 55.3296
+Optimal tuning (CTE): ~63/50 = 400.0000, ~351/340 = 55.3296
-{{Optimal ET sequence|legend=1| 282, 759def, 1041, 1323 }}
+{{Optimal ET sequence|legend=0| 282, 759def, 1041, 1323 }}
-Badness: 0.0168
+Badness (Smith): 0.0168
 == Notes ==

Alphatricot family: Difference between revisions

Revision as of 14:40, 16 March 2025

Alphatricot

2.3.5.13 subgroup

Alphatrimot

11-limit

13-limit

Alphatrident

11-limit

13-limit

Alphatrillium

11-limit

13-limit

Pseudotrillium

13-limit

Tritricot

11-limit

13-limit

17-limit

Noletaland

13-limit

17-limit

19-limit

23-limit

29-limit

Notes

Navigation menu

Search