# Cataharry temperaments

This is a collection of rank-2 temperaments tempering out the cataharry comma, [-4 9 -2 -2 = 19683/19600. These include swetneus, considered below, as well as others discussed elsewhere:

## Swetneus

The swetneus temperament takes its name from the fact that an approximate swetismic neutral second, ~49/45, is the generator.

Subgroup: 2.3.5.7

Comma list: 19683/19600, 50421/50000

Mapping[1 4 8 8], 0 -20 -47 -43]]

Wedgie⟨⟨20 47 43 28 12 -32]]

Optimal tuning (POTE): ~2 = 1\1, ~49/45 = 144.956

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 441/440, 3388/3375, 19683/19600

Mapping: [1 4 8 8 13], 0 -20 -47 -43 -79]]

Optimal tuning (POTE): ~2 = 1\1, ~49/45 = 144.941

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 351/350, 441/440, 676/675, 847/845

Mapping: [1 4 8 8 13 13], 0 -20 -47 -43 -79 -77]]

Optimal tuning (POTE): ~2 = 1\1, ~49/45 = 144.939

## Majvamoid

The majvamoid temperament (149 & 183) is an extension of the majvam temperament which tempers out the cataharry comma and the quasiorwellisma (29360128/29296875, sazoquinbigu) in the 7-limit.

Subgroup: 2.3.5.7

Comma list: 19683/19600, 29360128/29296875

Mapping[1 10 5 38], 0 -22 -7 -92]]

Wedgie⟨⟨22 7 92 -40 84 94]]

Optimal tuning (POTE): ~2 = 1\1, ~125/96 = 459.031

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 5632/5625, 19683/19600

Mapping: [1 10 5 38 31], 0 -22 -7 -92 -72]]

Optimal tuning (POTE): ~2 = 1\1, ~125/96 = 459.027

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 351/350, 676/675, 1573/1568, 4225/4224

Mapping: [1 10 5 38 31 19], 0 -22 -7 -92 -72 -40]]

Optimal tuning (POTE): ~2 = 1\1, ~125/96 = 459.028