# Diaschismic rank three family

(Redirected from Varda)

The diaschismic rank-3 family of temperaments tempers out the diaschisma, 2048/2025. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.

## Rank-3 diaschismic

Subgroup: 2.3.5.7

Mapping[2 0 11 0], 0 1 -2 0], 0 0 0 1]]

mapping generators: ~45/32, ~3, ~7

Optimal tuning (POTE): ~3/2 = 704.8982, ~7/4 = 972.1330

## Julius aka varda

Subgroup: 2.3.5.7.11

Comma list: 176/175, 896/891

Mapping[2 0 11 0 14], 0 1 -2 0 -4], 0 0 0 1 1]]

Mapping to lattice: [0 1 -2 2 -2], 0 0 0 -1 -1]]

Lattice basis:

3/2, 9/7
Angle (3/2, 9/7) = 82.289 degrees
[[1 0 0 0 0, [11/8 1/2 -1/4 0 0, [11/4 -1 1/2 0 0, [-1/8 3/2 -5/4 0 1, [11/8 -1/2 -1/4 0 1]
eigenmonzo (unchanged-interval) basis: 2.9/5.11/3

Julius[22] hobbit transversal:

28/27, 16/15, 11/10, 9/8, 32/27, 6/5, 5/4, 9/7, 4/3, 15/11, 45/32, 22/15, 3/2, 14/9, 8/5, 5/3, 27/16, 16/9, 20/11, 15/8, 27/14, 2

Julius[24] hobbit transversal

28/27, 16/15, 11/10, 9/8, 7/6, 6/5, 40/33, 5/4, 9/7, 4/3, 15/11, 45/32, 16/11, 3/2, 14/9, 8/5, 33/20, 27/16, 7/4, 16/9, 20/11, 15/8, 27/14, 2

### Varda

Subgroup: 2.3.5.7.11.13

Comma list: 176/175, 351/350, 364/363

Mapping: [2 0 11 0 14 24], 0 1 -2 0 -4 -7], 0 0 0 1 1 1]]

##### 17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 136/135, 176/175, 256/255, 351/350

Mapping: [2 0 11 0 14 24 5], 0 1 -2 0 -4 -7 1], 0 0 0 1 1 1 0]]

### Julius

Subgroup: 2.3.5.7.11.13

Comma list: 176/175, 325/324, 896/891

Mapping: [2 0 11 0 14 -18], 0 1 -2 0 -4 8], 0 0 0 1 1 0]]

##### 17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 136/135, 176/175, 256/255, 325/324

Mapping: [2 0 11 0 14 -18 5], 0 1 -2 0 -4 8 1], 0 0 0 1 1 0 0]]

##### 19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 136/135, 176/175, 190/189, 256/255, 286/285

Mapping: [2 0 11 0 14 -18 5 -13], 0 1 -2 0 -4 8 1 5], 0 0 0 1 1 0 0 1]]

## Augustus

Subgroup: 2.3.5.7.11

Comma list: 385/384, 1232/1215

Mapping[2 0 11 0 3], 0 1 -2 0 3], 0 0 0 1 -1]]

[[1 0 0 0 0, [11/8 1/2 -1/4 0 0, [11/4 -1 1/2 0 0, [45/16 3/4 -3/8 1/2 -1/2, [45/16 3/4 -3/8 -1/2 1/2]
eigenmonzo (unchanged-interval) basis: 2.9/5.11/7

## Tiberius

Subgroup: 2.3.5.7.11

Comma list: 441/440, 2048/2025

Mapping[2 0 11 0 -17], 0 1 -2 0 4], 0 0 0 1 2]]

[[1 0 0 0 0, [11/8 1/2 -1/4 0 0, [11/4 -1 1/2 0 0, [0 0 0 1 0, [-3 2 -1 2 0]
eigenmonzo (unchanged-interval) basis: 2.9/5.7