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. 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 diasem translated by (49/48)''m''(567/512)''n'' for integer ''m'' and ''n''. 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.

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; it is possible to tile the entire infinite lattice with copies of left-hand diasem translated by (49/48)''m''(567/512)''n'' for integer ''m'' and ''n''. 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.

== Modes ==

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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. 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 diasem translated by (49/48)<sup>''m''</sup>(567/512)<sup>''n''</sup> for integer ''m'' and ''n''. 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.
+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; 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''. 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.
 == Modes ==