Compound scale: Difference between revisions

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Compound scale is a scale that is produced from two or more copies of the same scale overlaid on top of one another. The name derives from stellar compounds, which are several polygons laid on top of one another in a symmetric fashion (like the Star of David, which is a compound of two triangles).

'''Compound scale''' is a [[scale]] that is produced from two or more copies of the same scale overlaid on top of one another. The name derives from stellar compounds, which are several polygons laid on top of one another in a symmetric fashion (like the Star of David, which is a compound of two triangles).

== Theory ==

Eliora proposes the following way to notate compound scales: {A, Scale[B], C1, C2, ...}, where A is the number of scales intertwined, B is the number of notes, and Cn are the offsets between the ~~tonics~~ of the two scales. For example, Blackwood[10] in 15edo can be notated as {2, 5edo, 1}.

[[Eliora]] proposes the following way to notate compound scales: {A, Scale[B], C1, C2, ...}, where A is the number of scales intertwined, B is the number of notes, and Cn are the offsets between the root notes of the two scales. For example, [[Blackwood]][10] in [[15edo]] can be notated as {2, 5edo, 1}.

The naming shall be the following:

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Offset must be coprime to the number A, otherwise notes would just overlap.

In instances where root notes of the scales make a regular polygon, the "offset" description is omitted. For example, a compound of two [[novemkleismic]] scales from [[333edo]] in [[666edo]], set up two tritones apart, is just a compound of two novemkleismics. Likewise, a compound of five diatonics in [[60edo]] with each tonic being a step of [[5edo]] is just a compound of 5 diatonics.

=== Examples ===

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[[Category:Scale]]

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-Compound scale is a scale that is produced from two or more copies of the same scale overlaid on top of one another. The name derives from stellar compounds, which are several polygons laid on top of one another in a symmetric fashion (like the Star of David, which is a compound of two triangles).
+'''Compound scale''' is a [[scale]] that is produced from two or more copies of the same scale overlaid on top of one another. The name derives from stellar compounds, which are several polygons laid on top of one another in a symmetric fashion (like the Star of David, which is a compound of two triangles).
 == Theory ==
-Eliora proposes the following way to notate compound scales: {A, Scale[B], C1, C2, ...}, where A is the number of scales intertwined, B is the number of notes, and Cn are the offsets between the tonics of the two scales. For example, Blackwood[10] in 15edo can be notated as {2, 5edo, 1}.
+[[Eliora]] proposes the following way to notate compound scales: {A, Scale[B], C1, C2, ...}, where A is the number of scales intertwined, B is the number of notes, and Cn are the offsets between the root notes of the two scales. For example, [[Blackwood]][10] in [[15edo]] can be notated as {2, 5edo, 1}.
 The naming shall be the following:
@@ Line 11: / Line 11: @@
 Offset must be coprime to the number A, otherwise notes would just overlap.
+In instances where root notes of the scales make a regular polygon, the "offset" description is omitted. For example, a compound of two [[novemkleismic]] scales from [[333edo]] in [[666edo]], set up two tritones apart, is just a compound of two novemkleismics. Likewise, a compound of five diatonics in [[60edo]] with each tonic being a step of [[5edo]] is just a compound of 5 diatonics.
 === Examples ===
@@ Line 16: / Line 18: @@
 1 4 5 8 9 10 11 14 25 18 22 23.
+[[Category:Scale]]