Diasem: Difference between revisions

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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. 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]].

The diagram shows the LMLSLMLSL mode. Each dot represents a pitch class of a note in the 2.3.7 lattice. All the notes of the mode are marked as solid purple dots. 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]].

The notes of diasem form a Fokker block, which is a fundamental domain of the pitch class lattice; it is possible to tile the entire infinite lattice with copies of left-hand diasem translated by (49/48)<sup>''m''</sup>(567/512)<sup>''n''</sup> for integer ''m'' and ''n''. 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 [[dome]]s of diasem). However, only one other choice, 28/27, yields a diasem scale, and it yields the left-handed diasem mode MLLSLMLSL.

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 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. 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]].
+The diagram shows the LMLSLMLSL mode. Each dot represents a pitch class of a note in the 2.3.7 lattice. All the notes of the mode are marked as solid purple dots. 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]].
 The notes of diasem form a Fokker block, which is a fundamental domain of the pitch class lattice; it is possible to tile the entire infinite lattice with copies of left-hand diasem translated by (49/48)<sup>''m''</sup>(567/512)<sup>''n''</sup> for integer ''m'' and ''n''. 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 [[dome]]s of diasem). However, only one other choice, 28/27, yields a diasem scale, and it yields the left-handed diasem mode MLLSLMLSL.