Diasem: Difference between revisions

* < 4\7 if L < m + s

(This can be seen as follows: Let s' = m + s. Then the fifth generates the mos 5L 2s', which is either diatonic, 7edo or antidiatonic depending on the above conditions.)

Diasem has 18 modes, 9 modes of LH diasem and 9 modes of RH diasem. We have provided names based on the modes of the [[5L 4s]], [[5L 2s]] and [[7L 2s]] temperings of each mode.

=== Cyclic order ===

Notice that we have two generator chains of equal length. To give this scale a generator-offset structure we can treat the large 7-step as the offset of the 10-note scale. We treat L+S as one scale step and consider the scale an interleaving of two pentatonic scales, using the notes of C-D-F-G-Bb for the even numbered notes and Cv-Ebv-Fv-Abv-Bbv for the odd ones. This gives the following ordering: C Cv D Ebv F Fv G Abv Bb Bbv C, or in step sizes, -s L+s M L+s -s L+s M L+s -s L+s. This is formally a [[blackdye]] (sL'ML's'L'ML's'L') pattern, albeit with a negative step size s' = -s! This scale has been called '''negative blackdye''' or '''negative-s blackdye'''.

== Alterations ==