User:Inthar/5L3m2s: Difference between revisions

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'''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 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:

* Identifying L with M yields [[8L 2s]].

* Identifying L with m yields [[8L 2s]].

* Identifying M with S yields [[5L 5s]], commonly interpreted as [[blackwood]][10].

* Identifying m with s yields [[5L 5s]], commonly interpreted as [[blackwood]][10].

* Letting S vanish yields [[5L 3s]] or oneirotonic.

* 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¢).

* LmLs must be an [[oneirotonic]] generator (between 450¢ and 480¢).

== Tunings ==

Onyxwood admits some JI tunings, albeit with very 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 is generated by the intervals [[21/16]] and [[54/49]] (i.e. every interval in the scale is a stack consisting of these two intervals). 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 is generated by the intervals [[12/11]] and [[20/13]].

[[Category:GO scales]]

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-'''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 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:
-* Identifying L with M yields [[8L 2s]].
+* Identifying L with m yields [[8L 2s]].
-* Identifying M with S yields [[5L 5s]], commonly interpreted as [[blackwood]][10].
+* Identifying m with s yields [[5L 5s]], commonly interpreted as [[blackwood]][10].
-* Letting S vanish yields [[5L 3s]] or oneirotonic.
+* Letting s vanish yields [[5L 3s]] or oneirotonic.
 :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¢).
+* LmLs must be an [[oneirotonic]] generator (between 450¢ and 480¢).
 == Tunings ==
+Onyxwood admits some JI tunings, albeit with very 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 is generated by the intervals [[21/16]] and [[54/49]] (i.e. every interval in the scale is a stack consisting of these two intervals). 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 is generated by the intervals [[12/11]] and [[20/13]].
 [[Category:GO scales]]