User:Jerdle/Beryl

Beryl

Beryl is a loose group of high-rank temperaments (primarily rank-4) that temper out the berylisma.

Emerald

Emerald tempers out the kalisma and the berylisma, creating a rank-4 temperament in the 2.3.5.7.11.37 subgroup. This resembles berylismic, but the use of the kalisma allows the high primes to be calculated in terms of the low ones and the quarters of the octave. 11/8 is 36/35 flat of 2\4, and 37/32 is 36/35 flat of 1\4.

Aquamarine

Because of the association of 13 with the Archipelago and the Biosphere, the 2.3.5.7.11.13.37 extension of emerald is called aquamarine. However, this is rather difficult to achieve, the best approximations I have found providing a 20th-octave temperament with far greater badness than either berylic or emerald.