User:Inthar/List of ternary parallelogram scales: Difference between revisions

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Parallelogram-shaped (parallelogram substring with full first and last rows) ~~[[MOS substitution|MOS-substitution]]~~ scales for scale sizes from 6 to 36

Parallelogram-shaped (parallelogram substring with full first and last rows) scales for scale sizes from 6 to 36. Only axbycz for which a > b > c > 0 are shown.

~~Only aLbmcs for which [a, b, c] is a partition of the scale size are shown~~

Ternary parallelogram scales are always MOS substitution. (Proof forthcoming)

~~== 6 note scales ==~~

== 6 notes ==

* scale: LLmLLs, row_count: 2, full_row_len: 3, lattice basis: gx: [3, 1, 1], gy: [2, 0, 1]

* xyxyxz row_count: 2 full_row_len: 3, lattice basis: gx: [1, 0, 0], gy: [4, 1, 3]

~~== 8 note scales ==~~

* xxyxxz row_count: 2 full_row_len: 3, lattice basis: gx: [3, 1, 3], gy: [4, 2, 3]

* scale: LmLsmLms, row_count: 2, full_row_len: 4, lattice basis: gx: [2, 2, 1], gy: [2, 1, 1]

== 8 notes ==

* scale: LmLmLmLs, row_count: 2, full_row_len: 4, lattice basis: gx: [3, 2, 1], gy: [1, 0, 0]

* xyxzyxyz row_count: 2 full_row_len: 4, lattice basis: gx: [4, 0, 2], gy: [4, 1, 2]

* scale: LLLmLLLs, row_count: 2, full_row_len: 4, lattice basis: gx: [5, 1, 1], gy: [3, 0, 1]

* xyxyxyxz row_count: 2 full_row_len: 4, lattice basis: gx: [1, 0, 0], gy: [4, 1, 3]

~~== 9 note scales ==~~

* xxxyxxxz row_count: 2 full_row_len: 4, lattice basis: gx: [2, 1, 3], gy: [4, 2, 3]

* scale: LLmsLmLsm, row_count: 3, full_row_len: 3, lattice basis: gx: [2, 1, 1], gy: [1, 1, 1]

== 9 notes ==

* scale: LLmLLmLLs, row_count: 3, full_row_len: 3, lattice basis: gx: [5, 2, 1], gy: [4

* xxyzxyxzy row_count: 3 full_row_len: 3, lattice basis: gx: [1, 1, 1], gy: [2, 1, 1]

* xxyxxyxxz row_count: 3 full_row_len: 3, lattice basis: gx: [3, 1, 3], gy: [4, 2, 3]

== 10 notes ==

* xyxzyxzxyz row_count: 2 full_row_len: 5, lattice basis: gx:

@@ Line 1: / Line 1: @@
-Parallelogram-shaped (parallelogram substring with full first and last rows) [[MOS substitution|MOS-substitution]] scales for scale sizes from 6 to 36
+Parallelogram-shaped (parallelogram substring with full first and last rows) scales for scale sizes from 6 to 36. Only axbycz for which a > b > c > 0 are shown.
-Only aLbmcs for which [a, b, c] is a partition of the scale size are shown
+Ternary parallelogram scales are always MOS substitution. (Proof forthcoming)
-== 6 note scales ==
+== 6 notes ==
-* scale: LLmLLs, row_count: 2, full_row_len: 3, lattice basis: gx: [3, 1, 1], gy: [2, 0, 1]
+* xyxyxz row_count: 2 full_row_len: 3, lattice basis: gx: [1, 0, 0], gy: [4, 1, 3]
-== 8 note scales ==
+* xxyxxz row_count: 2 full_row_len: 3, lattice basis: gx: [3, 1, 3], gy: [4, 2, 3]
-* scale: LmLsmLms, row_count: 2, full_row_len: 4, lattice basis: gx: [2, 2, 1], gy: [2, 1, 1]
+== 8 notes ==
-* scale: LmLmLmLs, row_count: 2, full_row_len: 4, lattice basis: gx: [3, 2, 1], gy: [1, 0, 0]
+* xyxzyxyz row_count: 2 full_row_len: 4, lattice basis: gx: [4, 0, 2], gy: [4, 1, 2]
-* scale: LLLmLLLs, row_count: 2, full_row_len: 4, lattice basis: gx: [5, 1, 1], gy: [3, 0, 1]
+* xyxyxyxz row_count: 2 full_row_len: 4, lattice basis: gx: [1, 0, 0], gy: [4, 1, 3]
-== 9 note scales ==
+* xxxyxxxz row_count: 2 full_row_len: 4, lattice basis: gx: [2, 1, 3], gy: [4, 2, 3]
-* scale: LLmsLmLsm, row_count: 3, full_row_len: 3, lattice basis: gx: [2, 1, 1], gy: [1, 1, 1]
+== 9 notes ==
-* scale: LLmLLmLLs, row_count: 3, full_row_len: 3, lattice basis: gx: [5, 2, 1], gy: [4
+* xxyzxyxzy row_count: 3 full_row_len: 3, lattice basis: gx: [1, 1, 1], gy: [2, 1, 1]
+* xxyxxyxxz row_count: 3 full_row_len: 3, lattice basis: gx: [3, 1, 3], gy: [4, 2, 3]
+== 10 notes ==
+* xyxzyxzxyz row_count: 2 full_row_len: 5, lattice basis: gx: