# Valinorsmic clan

(Redirected from Valinorsmic temperaments)

The valinorsmic clan of rank-3 temperaments tempers out the valinorsma, 176/175, which equates 48/35 with 15/11 (rather than 11/8, which is what the keenanisma 385/384 does).

Discussed elsewhere are:

Considered below are manwe, mandos and ulmo besides the no-3 subgroup temperament, but we can begin with the rank-4 temperament.

## Valinorsmic

Subgroup: 2.3.5.7.11

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

Mapping generators: ~2, ~3, ~5, ~7

POTE generators: ~3/2 = 703.0449, ~5/4 = 389.7641, ~7/4 = 972.1113

## No-3 valinorsmic

Subgroup: 2.5.7.11

Comma list: 176/175

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

Sval mapping generators: ~2, ~5, ~7

POTE generators: ~5/4 = 389.7641, ~7/4 = 972.1113

## Manwe

Subgroup: 2.3.5.7.11

Comma list: 176/175, 1331/1323

Mapping: [1 0 0 12 8], 0 1 0 3 3], 0 0 1 -6 -4]]

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 176/175, 1331/1323, 351/350

Mapping: [1 0 0 12 8], 0 1 0 3 3], 0 0 1 -6 -4]]

Vals: 31, 46, 77, 80, 111

## Mandos

Subgroup: 2.3.5.7.11

Comma list: 176/175, 243/242

Mapping: [1 1 0 6 2], 0 2 0 5 5], 0 0 1 -2 0]]

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 144/143, 176/175, 243/242

Mapping: [1 1 0 6 2 4], 0 2 0 5 5 -1], 0 0 1 -2 0 0]]

Vals: 7, 24, 31, 58

## Ulmo

Subgroup: 2.3.5.7.11

Comma list: 176/175, 2200/2187

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