Hemiwuerschmidt

While I'm pondering what tuning system to try next, I've got an
opportunity to present the sort of stuff I like to work out in
advance. Here is hemiwuerschmidt, giving the tetrad generator of
[2,1,0] and the tetrads within various DE scales (19, 25, 31, 37
notes) in terms of that generator. Then something which is especially
nice when it is symmetric, but useful even when it isn't, as here--the
number of common notes of two tetrads, separated by n generators. To
get the same thing for a minor tetrad (which will represented by an
odd number, if 0 is a major tetrad) we read the table in the minus
direction for plus generator steps. For example, I want to know the
number of notes in common for tetrad 5 and tetrad 9, where 5 is odd
and hence is a minor tetrad; 9-5=4, so I look up -4, and see it has
one common note with 0; hence 5 will have a common note with 9, +4
steps up.

Generator: 28/25

TM basis: <2401/2400, 3136/3125>

Tetrad generator: [2, 1, 0]

Tetrads in DE scales

s19: [0, 2, 4, 9, 11, 13]

s25: [0, 2, 4, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 21, 23, 25]

s31: [0, 2, 4, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22,
23, 24, 25, 26, 27, 28, 29, 31, 33, 35, 37]

s37: [0, 2, 4, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22,
23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39,
40, 41,
43, 45, 47, 49]

Common notes of tetrads

-32: 1
-31: 0
-30: 0
-29: 0
-28: 1
-27: 0
-26: 0
-25: 0
-24: 0
-23: 1
-22: 1
-21: 0
-20: 0
-19: 2
-18: 0
-17: 0
-16: 0
-15: 1
-14: 0
-13: 2
-12: 0
-11: 0
-10: 1
-9: 2
-8: 0
-7: 0
-6: 1
-5: 0
-4: 1
-3: 1
-2: 0
-1: 0
0: 4
1: 0
2: 0
3: 0
4: 1
5: 0
6: 1
7: 0
8: 0
9: 2
10: 1
11: 0
12: 0
13: 2
14: 0
15: 0
16: 0
17: 0
18: 0
19: 2
20: 0
21: 0
22: 1
23: 0
24: 0
25: 0
26: 0
27: 0
28: 1
29: 0
30: 0
31: 0
32: 1