730edo

The 730 equal temperament divides the octave into 730 equal parts of 1.644 cents each. It is a very strong five-limit system, but is also distinctly consistent up to the 15-limit. It tempers out the minortone comma, |-16 35 -17>, the kwasy comma, |-53 10 16>, the whoosh comma, |37 25 -33> and the pirate comma, |-90 -15 49>. In the 7-limit it tempers out 4375/4374 and | -21 0 3 5 >, so that it supports mitonic temperament. In the 11-limit, 3025/3024 and | 4 -3 -6 4 1 > , so that it supports deca temperament. In the 13-limit, 1001/1000 and 4225/4224, supporting 13-limit deca.

W. S. B. Woolhouse proposed 730edo as a logarithmic measure of interval size, sometimes called the Woolhouse unit. While 730 is divisible by 2, 5, 10, 73, 146 and 365, it is not divisible by 12, which can be regarded as either a good thing or a bad one.

A summary of W. S. B. Woolhouse's Essay on musical intervals Permalink