Diasem: Difference between revisions

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(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]]

[[File:Diasem as fokker block.png|600px|thumbnail|2..3.7 JI 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 2.3.7 JI diasem scale 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. Note that both 49/48 and 567/512 are tempered out by (the 2.3.7 [[patent val]] of) [[9edo]]. 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.

@@ Line 196: / Line 196: @@
 (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]]
+[[File:Diasem as fokker block.png|600px|thumbnail|2..3.7 JI 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 2.3.7 JI diasem scale 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. Note that both 49/48 and 567/512 are tempered out by (the 2.3.7 [[patent val]] of) [[9edo]]. 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.