User:Jerdle/Beryl: Difference between revisions

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=Beryl=

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

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 ~~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~~.

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]].

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