User:Inthar/5L3m2s

Onyxwood is a 3-step generator-offset scale with pattern LmLsLmLsLm (step size composition 5L 3m 2s). It is a hybrid of oneirotonic (5L 3s) and "blackwood" (5L 5s), hence the name. It consists of two copies of oneirotonic[5] (3L 2s with a generator between 720¢ and 750¢) with offset L.

Onyxwood is associated with the following mosses:

• Identifying L with m yields 8L 2s.
• Identifying m with s yields 5L 5s, commonly interpreted as blackwood[10].
• Letting s vanish yields 5L 3s or oneirotonic.

3:2:1 onyxwood is found in 23edo, and 4:2:1 onyxwood is found in 28edo.

Properties

• LmLs must be an oneirotonic generator (between 450¢ and 480¢).

Tunings

Onyxwood admits some JI tunings, albeit with somewhat high complexity.

The simplest example is in the 2.3.7 subgroup, with step sizes L = 54/49, m = 256/243 and s = 16807/16384, and the resulting scale yields LmLs = 21/16. Notice that 21/16 = ~471¢ generates a 3L 2s scale.

Another example is in the 2.3.5.11.13 subgroup, with step sizes L = 12/11, m = 550/507 and s = 24167/24000. The resulting scale yields LmLs = 13/10.