# Octagar family

(Redirected from Octagar)

The octagar family of temperaments are rank-3 temperaments tempering out the octagar comma, 4000/3969. While most 7-limit planar temperaments exhibit a tendency towards tuning flat, many people seem to prefer a slight sharp tendency instead. Octagar provides this; for instance the 7-odd-limit minimax tuning has fifths and 7's 2.245 cents sharp, with just major thirds.

Linear temperaments that temper out the octagar comma can be found in octagar temperaments.

## Octagar

This temperament is also known as octagari.

Subgroup: 2.3.5.7

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

mapping generators: ~2, ~3, ~63/40

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

Lattice basis:

63/50 length = 0.8966, 21/20 length = 1.0605
Angle (63/50, 21/20) = 97.743 degrees
[[1 0 0 0, [5/6 1/3 1/2 -1/3, [0 0 1 0, [5/6 -2/3 1/2 2/3]
eigenmonzo (unchanged-interval) basis: 2.5.7/3
[[1 0 0 0, [5/8 1/2 3/8 -1/4, [0 0 1 0, [5/4 -1 3/4 1/2]
eigenmonzo (unchanged-interval) basis: 2.5.9/7

Projection pairs: 5 - 3969/800, 7 - 27783/4000 to 2.3.7/5

Hobbit bases

2.3.7/5 subgroup

• 12: 50/49, 256000/250047
• 15: 256000/250047, 1029/1000
• 23: 12800000/12252303, 107163/102400

## Nakika

Subgroup: 2.3.5.7.11

Comma list: 100/99, 245/242

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

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

Lattice basis:

11/7 length = 0.798, 22/21 length = 0.906
Angle (11/7, 22/21) = 97.747 degrees