Canopus

Canopus

Subgroups	3.5.7
Comma basis	16875/16807
Reduced mapping	⟨1; 5 4]
ET join	b10 & b13
Generators (CWE)	~15/7 = 1318.0 ¢
MOS scales	3L 4s <3/1>, 3L 7s <3/1>, 10L 3s <3/1>
Ploidacot	beta-tetragem
Minimax error	3.5.7 7-throdd-limit: 1.40 ¢; 3.5.7 49-throdd-limit: 2.80 ¢
Target scale size	3.5.7 7-throdd-limit: 7 notes; 3.5.7 49-throdd-limit: 13 notes

Canopus is a non-octave temperament of the 3.5.7 subgroup. It tempers out 16875/16807, the amount by which 27/7 exceeds four 7/5's. Having a generator of ~7/5 (or ~15/7), it possesses non-trivial mos of the families 3L 4s, 3L 7s, and 10L 3s.

As 16875/16807 = (540/539)²⋅(3025/3024), canopus can be extended to the 3.5.7.11/4 subgroup extremely naturally by tempering out these two commas; prime 53 can additionally be incorporated by means of tempering out 1325/1323, equating (7/5)² = 49/25 to 53/27.

For technical data, see No-twos subgroup temperaments #Canopus.

Interval table

In the below, tritave-reduced harmonics and subharmonics 1–7 are indicated in bold.

#	Cents*	Approximate ratios
−3	150.0	49/45
−2	734.0	75/49
−1	1318.0	15/7
0	0.0	1/1
1	584.0	7/5
2	1168.0	49/25
3	1752.0	135/49
4	434.0	9/7
5	1018.0	9/5
6	1602.0	63/25
7	284.0	147/125
8	868.0	81/49
9	1452.0	81/35
10	134.0	27/25

* In 3.5.7-subgroup CWE tuning

Todo: expand add tuning spectrum