Diasem: Difference between revisions
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* < 4\7 if L < m + s | * < 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.) | (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.) | ||
== As a Fokker block == | |||
[[File:Diasem as fokker block.png|600px|thumbnail|Diasem as a Fokker block]] | |||
Diasem can be viewed as a [[Fokker block]] living in the 2.3.7 octave-equivalent pitch class lattice. The x-axis goes along the 3 direction and the y-axis goes along the 7 direction. | |||
The diagram shows the LMLSLMLSL mode. All the notes of the mode are marked as solid purple dots. The notes of diasem form a Fokker block, which is a fundamental domain of the pitch class lattice. Notes of the lattice outside the mode are black hollow dots. The red dashed lines are separated by the chroma 49/48, and the blue dotted lines are separated by the chroma 567/512. Including any one of the other three points on the boundary (28/27, 147/128, or 64/63) instead of 9/8 also yields Fokker blocks (more specifically, modes of the three other domes of diasem). However, only one other choice, 28/27, yields a diasem scale, and it yields the left-handed diasem mode MLLSLMLSL. | |||
== Modes == | == Modes == | ||