User:Inthar/5L3m2s: Difference between revisions
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'''Onyxwood''' is a 3-step [[generator-offset]] scale with pattern | '''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 [[mos]]ses: | Onyxwood is associated with the following [[mos]]ses: | ||
* Identifying L with | * Identifying L with m yields [[8L 2s]]. | ||
* Identifying | * Identifying m with s yields [[5L 5s]], commonly interpreted as [[blackwood]][10]. | ||
* Letting | * 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]]. | 3:2:1 onyxwood is found in [[23edo]], and 4:2:1 onyxwood is found in [[28edo]]. | ||
== Properties == | == Properties == | ||
* | * LmLs must be an [[oneirotonic]] generator (between 450¢ and 480¢). | ||
== Tunings == | == 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]]. | |||
[[Category:GO scales]] | [[Category:GO scales]] | ||
Latest revision as of 18:13, 29 April 2024
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.