User:Jerdle/Beryl

Beryl

Beryl is a loose group of temperaments 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.

Goshenite

Goshenite takes emerald and adds some simpler commas, namely the rastma and 4107/4096. However, this is simply an extension of hours to the 2.3.5.7.11.37 subgroup.

Aquamarine

Because of the association of 13 with the Archipelago and the Biosphere, the 2.3.5.7.11.13.37 extension of goshenite is called aquamarine. It equates 15/13 with 37/32, tempering out the 481/480 comma.

Again, this is hours.