mode, transposition in semi-tones for each scale degree;
0 chromatic, 0 1 2 3 4 5 6 7 8 9 10 11;
1 ionian, 0 0 2 2 4 5 5 7 7 9 9 11;
2 dorian, 0 0 2 3 3 5 5 7 7 9 10 10;
3 phrygian, 0 1 1 3 3 5 5 7 8 8 10 10;
4 lydian, 0 0 2 2 4 4 6 7 7 9 9 11;
5 mixolydian, 0 0 2 2 4 5 5 7 7 9 10 10;
6 aeolian, 0 0 2 3 3 5 5 7 8 8 10 10;
7 locrian, 0 1 1 3 3 5 6 6 8 8 10 10;
8 wholetone, 0 0 2 2 4 4 6 6 8 8 10 10;
9 min7, 0 0 0 3 3 3 7 7 7 10 10 10;
10 dim7, 0 0 0 3 3 3 6 6 6 9 9 9;
11 octatonic2-1, 0 0 2 3 3 5 6 6 8 9 9 11;
12 octatonic1-2, 0 1 1 3 4 4 6 7 7 9 10 10;
13 major-pentatonic, 0 0 2 2 4 4 7 7 7 9 9 9;
14 minor-pentatonic, 0 0 0 3 3 5 5 5 7 7 10 10;
15 invert, 11 10 9 8 7 6 5 4 3 2 1 0;