# Trienstonic clan

(Redirected from Uncle)
Jump to navigation Jump to search

The trienstonic clan of rank-2 temperaments tempers out 28/27, the septimal third-tone or trienstonic comma.

Adding 16/15 to 28/27 leads to father, adding 256/245 gives uncle, adding 50/49 gives octokaidecal and adding 35/32 gives wallaby. Other members of the clan discussed elsewhere are:

## Trienstonian

Subgroup: 2.3.7

Comma list: 28/27

Sval mapping[1 0 -2], 0 1 3]]

mapping generators: ~2, ~3

Gencom mapping[1 0 0 -2], 0 1 0 3]]

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 721.5586

## Father

Main article: Father
See also: Father family #Father

Subgroup: 2.3.5.7

Comma list: 16/15, 28/27

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

Wedgie⟨⟨1 -1 3 -4 2 10]]

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 742.002

eigenmonzo (unchanged-interval) basis: 2.7/5
eigenmonzo (unchanged-interval) basis: 2.9/7

Badness: 0.021312

## Uncle

Subgroup: 2.3.5.7

Comma list: 28/27, 256/245

Mapping[1 0 12 -2], 0 1 -6 3]]

Wedgie⟨⟨1 -6 3 -12 2 24]]

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 731.177

Badness: 0.072653

## Wallaby

See also: Pelogic family

Subgroup: 2.3.5.7

Comma list: 28/27, 35/32

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

Wedgie⟨⟨1 -3 3 -7 2 15]]

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 691.351

Badness: 0.058468

## Octokaidecal

### 5-limit (supersharp)

Subgroup: 2.3.5

Comma list: 800/729

Mapping[2 0 -5], 0 1 3]]

Optimal tuning (POTE): ~27/20 = 1\2, ~3/2 = 729.097

Badness: 0.122848

### 7-limit

Subgroup: 2.3.5.7

Comma list: 28/27, 50/49

Mapping[2 0 -5 -4], 0 1 3 3]]

Wedgie⟨⟨2 6 6 5 4 -2]]

Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 728.874

Badness: 0.036747

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 28/27, 50/49, 55/54

Mapping: [2 0 -5 -4 7], 0 1 3 3 0]]

Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 732.330

Badness: 0.030235

## Kangaroo

For the 5-limit version of this temperament, see High badness temperaments #Kangaroo.

Subgroup: 2.3.5.7

Comma list: 28/27, 1029/1000

Mapping[1 0 -3 -2], 0 3 10 9]]

Wedgie⟨⟨3 10 9 9 6 -7]]

Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 560.328

Badness: 0.077857

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 28/27, 77/75, 245/242

Mapping: [1 0 -3 -2 -4], 0 3 10 9 14]]

Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 560.155

Badness: 0.043195

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 28/27, 40/39, 66/65, 147/143

Mapping: [1 0 -3 -2 -4 0], 0 3 10 9 14 7]]

Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 559.770

Badness: 0.032653

## Quindecic

Subgroup: 2.3.5.7.11.13

Comma list: 28/27, 49/48, 55/54, 77/75

Mapping: [15 24 35 42 52 0], 0 0 0 0 0 1]]

Optimal tuning (POTE): ~22/21 = 1\15, ~13/8 = 852.924

Badness: 0.028944