Canopus

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This page on a regular temperament, temperament collection, or aspect of regular temperament theory is being revised for clarity as part of WikiProject TempClean.

Canopus is the rank two 3.5.7 subgroup temperament tempering out 16875/16807, the amount by which 27/7 exceeds four 7/5s. Having a generator of ~7:5, it possesses non-trivial MOS of the families 1L 2s, 3L 1s, 3L 4s, 3L 7s, and (in most cases) 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 information see No-twos subgroup temperaments #Canopus.

Interval table

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

Canopus
# Cents* Approximate Ratios
3.5.7.11/4.53 subgroup
−3 149.9 12/11, 49/45
−2 733.9 55/36, 75/49, 81/53, 84/55
−1 1318.0 15/7
0 0.0 1/1
1 584.0 7/5
2 1168.0 49/25, 53/27, 55/28, 108/55
3 1752.0 11/4, 135/49
4 434.1 9/7
5 1018.1 9/5
6 1602.1 53/21, 63/25
7 284.1 33/28, 53/45
8 868.1 33/20, 81/49
9 1452.1 81/35
10 134.2 27/25, 53/49

* In 3.5.7-targeted DKW tuning

Todo: expand

add tuning spectrum