Fourths Hub

Holdsworth Scale Generator

Based on Allan Holdsworth's Approach to Scales

Note: This has a number of bugs and is a work in progress

Total number of possible scales 495

N = Number of scales to generate

M = Maximum number of consecutive half steps

X = Number of notes per scale

Root N M X
R b2 2 3 4
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
1
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
2
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
3
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
4
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
5
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
6
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
R b2 2 3 #4
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
1
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
2
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
3
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
4
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
5
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
6
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
R b2 2 3 5
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
1
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
2
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
3
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
4
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
5
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
6
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
R b2 2 3 b6
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
1
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
2
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
3
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
4
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
5
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
6
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
R b2 2 3 6
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
1
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
2
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
3
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
4
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
5
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
6
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
R b2 2 3 b7
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
1
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
2
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
3
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
4
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
5
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
6
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
R b2 2 3 7
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
1
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
2
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
3
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
4
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
5
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
6
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
R b2 2 4 #4
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
1
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
2
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
3
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
4
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
5
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
6
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
R b2 2 4 5
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
1
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
2
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
3
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
4
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
5
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
6
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
R b2 2 4 b6
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
1
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
2
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
3
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
4
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
5
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
6
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
D ♯
E
F
F ♯
G
G ♯
A
A ♯
B
C
C ♯
D
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22