The first hexagonal pattern demonstrates how the 12 note major/minor system can be represented
in the form of a hexagonal lattice. You'll see this same pattern on the main scale page
Below that, you'll see a larger hexagonal pattern based on a 16 note scale, proving that (rather unfortunately) this neat honeycomb system is not unique to 12-eT. In this 16 note scale, the 'perfect fifth' is the 9th note (instead of the 7th), and the minor and major thirds are the 4th and 5th notes respectively (instead of the usual 3rd and 4th notes in 12-eT).
12-eT honeycomb lattice
C = 0
C# = 1
D = 2
D# = 3
E = 4
F = 5
F# = 6
G = 7
G# = 8
A = 9
A# = 10
B = 11
6 1 8 3 10 5 0
2 9 4 11 6 1 8 3
10 5 0 7 2 9 4 11 6
6 1 8 3 10 5 0 7 2 9
2 9 4 11 6 1 8 3 10 5 0
10 5 0 7 2 9 4 11 6 1 8 3
6 1 8 3 10 5 0 7 2 9 4 11 6
9 4 11 6 1 8 3 10 5 0 7 2
0 7 2 9 4 11 6 1 8 3 10
3 10 5 0 7 2 9 4 11 6
6 1 8 3 10 5 0 7 2
9 4 11 6 1 8 3 10
0 7 2 9 4 11 6
16 note honeycomb lattice:
11 4 13 6 15 8 1 10 3 12
6 15 8 1 10 3 12 5 14 7 0
1 10 3 12 5 14 7 0 9 2 11 4
12 5 14 7 0 9 2 11 4 13 6 15 8
7 0 9 2 11 4 13 6 15 8 1 10 3 12
2 11 4 13 6 15 8 1 10 3 12 5 14 7 0
13 6 15 8 1 10 3 12 5 14 7 0 9 2 11 4
8 1 10 3 12 5 14 7 0 9 2 11 4 13 6 15 8
12 5 14 7 0 9 2 11 4 13 6 15 8 1 10 3
0 9 2 11 4 13 6 15 8 1 10 3 12 5 14
4 13 6 15 8 1 10 3 12 5 14 7 0 9
8 1 10 3 12 5 14 7 0 9 2 11 4
12 5 14 7 0 9 2 11 4 13 6 15
0 9 2 11 4 13 6 15 8 1 10
4 13 6 15 8 1 10 3 12 5
8 1 10 3 12 5 14 7 0