Compound scale

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 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:

Compound of A B-tone scale names with offset(s) C1, C2, ...

So Blackwood[10] would be called Compound of 2 5edos with offset 1 or Compound of 2 equipentatonics with offset 1.

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

24edo: Compound of two diatonics with offset 1.

0 1 4 5 8 9 10 11 14 25 18 22 23.