# Semicanousmic clan

(Redirected from Deuteromere)

The semicanousmic clan of rank-3 temperaments tempers out the semicanousma, 14641/14580 = [-2 -6 -1 0 4.

Temperaments discussed elsewhere are:

Considered below are syndeute and hemireiwa, in addition to deuteromere, the no-7 subgroup temperament.

For the rank-4 semicanousmic temperament, see Rank-4 temperament #Semicanousmic (14641/14580).

## Deuteromere

Lattice
Lattice rearranged into neutral thirds

Subgroup: 2.3.5.11

Comma list: 14641/14580

Sval mapping[1 0 2 1], 0 1 2 2], 0 0 -4 -1]]

sval mapping generators: ~2, ~3, ~18/11

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.3342, ~18/11 = 854.5548

Optimal ET sequence7, 17c, 24, 31, 56, 73, 80, 87, 118, 205, 323, 528e

### 2.3.5.11.17 subgroup

Subgroup: 2.3.5.11.17

Comma list: 1089/1088, 14641/14580

Sval mapping: [1 0 2 1 -4], 0 1 2 2 6], 0 0 -4 -1 -2]]

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.3427, ~18/11 = 854.5587

### 2.3.5.11.17.19 subgroup

Subgroup: 2.3.5.11.17.19

Comma list: 1089/1088, 1216/1215, 1445/1444

Sval mapping: [1 0 2 1 -4 -4], 0 1 2 2 6 7], 0 0 -4 -1 -2 -4]]

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.2987, ~18/11 = 854.5520

## Syndeute

Subgroup: 2.3.5.7.11

Comma list: 14641/14580, 19712/19683

Mapping[1 0 2 -9 1], 0 1 2 7 2], 0 0 -4 1 -1]]

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.0812, ~18/11 = 854.4115

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 1573/1568, 2080/2079, 14641/14580

Mapping: [1 0 2 -9 1 -15], 0 1 2 7 2 10], 0 0 -4 1 -1 4]]

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.1682, ~18/11 = 854.5074

### 17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 442/441, 561/560, 715/714, 14641/14580

Mapping: [1 0 2 -9 1 -15 -4], 0 1 2 7 2 10 6], 0 0 -4 1 -1 4 -2]]

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.1910, ~18/11 = 854.4751

### 19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 442/441, 561/560, 715/714, 1216/1215, 1445/1444

Mapping: [1 0 2 -9 1 -15 -4 -4], 0 1 2 7 2 10 6 7], 0 0 -4 1 -1 4 -2 -4]]

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.1925, ~18/11 = 854.4721

## Hemireiwa

Hemireiwa is in a certain sense dual to semicanou. It splits the perfect twelfth into two, whereas semicanou splits the octave.

Subgroup: 2.3.5.7.11

Comma list: 14641/14580, 160083/160000

Mapping[1 0 2 7 1], 0 2 0 -6 3], 0 0 4 7 1]]

mapping generators: ~2, ~400/231, ~200/189

Optimal tuning (CTE): ~2 = 1\1, ~400/231 = 951.1975, ~200/189 = 96.5851

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 676/675, 1001/1000, 14641/14580

Mapping: [1 0 2 7 1 1], 0 2 0 -6 3 3], 0 0 4 7 1 4]]

Optimal tuning (CTE): ~2 = 1\1, ~26/15 = 951.2316, ~55/52 = 96.6155

### 17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 676/675, 715/714, 1001/1000, 14641/14580

Mapping: [1 0 2 7 1 1 -4], 0 2 0 -6 3 3 10], 0 0 4 7 1 4 2]]

Optimal tuning (CTE): ~2 = 1\1, ~26/15 = 951.2022, ~55/52 = 96.6006