# Tricot family

(Redirected from Trillium)

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: septimal tricot (53 & 70, also called as "trimot"), trident (53 & 229) and trillium (53 & 441). Tempering out hemifamity comma (5120/5103) leads to septimal tricot, porwell comma (6144/6125) leads to trident, and ragisma (4375/4374) leads to trillium.

## Tricot

Subgroup: 2.3.5

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

Mapping[1 0 -13], 0 3 29]]

mapping generators: ~2, ~59049/40960

Wedgie⟨⟨3 29 39]]

Optimal tuning (POTE): ~2 = 1\1, ~59049/40960 = 634.012

## Septimal tricot aka trimot

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 = 1\1, ~81/56 = 634.0259

### 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 = 1\1, ~63/44 = 634.0273

### 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 = 1\1, ~13/9 = 634.0115

## Trident

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 = 1\1, ~4096/2835 = 634.0480

### 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 = 1\1, ~231/160 = 634.0669

### 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 = 1\1, ~13/9 = 634.0652

## Trillium

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 = 1\1, ~23625/16384 = 634.0118

### 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 = 1\1, ~3888/2695 = 634.0094

#### 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 = 1\1, ~75/52 = 634.0095

### 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 = 1\1, ~231/160 = 634.0190

#### 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 = 1\1, ~75/52 = 634.0181

## 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 = 1\3, ~100352/91125 = 165.9837

### 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 = 1\3, ~11/10 = 165.9835

#### 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 = 1\3, ~11/10 = 165.9842

#### 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 = 1\3, ~11/10 = 165.9805

### 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 = 1\3, ~1936/1875 = 55.3290

#### 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 = 1\3, ~1936/1875 = 55.3294

#### 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 = 1\3, ~351/340 = 55.3295

#### 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 = 1\3, ~351/340 = 55.3295

#### 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 = 1\3, ~351/340 = 55.3296