Diasem: Difference between revisions

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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 right-hand diasem translated by (49/48)''m''(567/512)''n'' 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 three of the other [[dome]]s of diasem, and translates of the parallelogram that do not have lattice points on the boundary lead to other domes of this Fokker block. However, only one other choice, 28/27, yields a diasem scale, and it yields the left-handed diasem mode MLLSLMLSL.

The notes of diasem form the {49/48, 567/512} Fokker block, which is a fundamental domain of the 2.3.7 pitch class lattice; it is possible to tile the entire infinite lattice with copies of right-hand diasem translated by (49/48)''m''(567/512)''n'' 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 three of the other [[dome]]s of diasem, and translates of the parallelogram that do not have lattice points on the boundary lead to other domes of this Fokker block. However, only one other choice, 28/27, yields a diasem scale, and it yields the left-handed diasem mode MLLSLMLSL.

As a Fokker block, 2.3.7 JI diasem is also a product word scale, a product of the tempered 2.3.7 mosses semaphore[9] (LsLsLsLsL) and septimal mavila[9] (LLLsLLLsL).

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 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 right-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 three of the other [[dome]]s of diasem, and translates of the parallelogram that do not have lattice points on the boundary lead to other domes of this Fokker block. However, only one other choice, 28/27, yields a diasem scale, and it yields the left-handed diasem mode MLLSLMLSL.
+The notes of diasem form the {49/48, 567/512} Fokker block, which is a fundamental domain of the 2.3.7 pitch class lattice; it is possible to tile the entire infinite lattice with copies of right-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 three of the other [[dome]]s of diasem, and translates of the parallelogram that do not have lattice points on the boundary lead to other domes of this Fokker block. However, only one other choice, 28/27, yields a diasem scale, and it yields the left-handed diasem mode MLLSLMLSL.
 As a Fokker block, 2.3.7 JI diasem is also a product word scale, a product of the tempered 2.3.7 mosses semaphore[9] (LsLsLsLsL) and septimal mavila[9] (LLLsLLLsL).