User:Contribution/Basic analysis of selected EDOs

From Xenharmonic Wiki
Jump to navigation Jump to search

9-cents-minimum-limit

EDOs with a strong local zeta peak

12edo

sharpness = 1

L = 2 ; s = 1

Degree Notation Approximate Ratios Approximate Ratios Notation Degree
0 P1 1/1 2/1 P8 12
1 m2 M7 11
2 M2 10/9, 9/8 16/9, 9/5 m7 10
3 m3 6/5 5/3 M6 9
4 M3 5/4 8/5 m6 8
5 P4 4/3 3/2 P5 7
6 A4 7/5, 10/7 d5 6

19edo

sharpness = 1

L = 3 ; s = 2

Degree Notation Approximate Ratios Approximate Ratios Notation Degree
0 P1 1/1 2/1 P8 19
1 A1, d2 A7, d8 18
2 m2 14/13 13/7 M7 17
3 M2 10/9, 9/8 16/9, 9/5 m7 16
4 A2, d3 15/13 26/15 A6, d7 15
5 m3 6/5 5/3 M6 14
6 M3 5/4 8/5 m6 13
7 A3, d4 9/7, 13/10 20/13, 14/9 A5, d6 12
8 P4 4/3 3/2 P5 11
9 A4 18/13 13/9 d5 10

22edo

sharpness = 3

L = 4 ; s = 1

Degree Notation Approximate Ratios Approximate Ratios Notation Degree
0 P1 1/1 2/1 P8 22
1 m2 M7 21
2 ↑m2 16/15 15/8 ↓M7 20
3 ↓M2 11/10 20/11 ↑m7 19
4 M2 9/8, 8/7 7/4, 16/9 m7 18
5 m3 7/6 12/7 M6 17
6 ↑m3 6/5 5/3 ↓M6 16
7 ↓M3 5/4 8/5 ↑m6 15
8 M3 9/7 14/9 m6 14
9 P4 4/3 3/2 P5 13
10 ↑P4 11/8 16/11 ↓P5 12
11 ↓A4 7/5, 10/7 ↑d5 11

24edo

sharpness = 2

L = 4 ; s = 2

24d
Degree Notation Approximate Ratios Approximate Ratios Notation Degree
0 P1 1/1 2/1 P8 24
1 ↑P1, ↓m2 ↑M7, ↓P8 23
2 m2 M7 22
3 ~2 12/11 11/6 ~7 21
4 M2 10/9, 9/8 16/9, 9/5 m7 20
5 ↑M2, ↓m3 15/13 26/15 ↑M6, ↓m7 19
6 m3 6/5 5/3 M6 18
7 ~3 11/9 18/11 ~6 17
8 M3 5/4 8/5 m6 16
9 ↑M3, ↓P4 13/10 20/13 ↑P5, ↓m6 15
10 P4 4/3 3/2 P5 14
11 ~4 11/8 16/11 ~5 13
12 A4 7/5, 10/7 d5 12

27edo

sharpness = 4

L = 5 ; s = 1

27e
Degree Notation Approximate Ratios Approximate Ratios Notation Degree
0 P1 1/1 2/1 P8 27
1 m2 M7 26
2 ↑m2 ↓M7 25
3 ~2 14/13, 13/12 24/13, 13/7 ~7 24
4 ↓M2 10/9 9/5 ↑m7 23
5 M2 9/8, 8/7 7/4, 16/9 m7 22
6 m3 7/6 12/7 M6 21
7 ↑m3 6/5 5/3 ↓M6 20
8 ~3 16/13 13/8 ~6 19
9 ↓M3 5/4 8/5 ↑m6 18
10 M3 9/7, 13/10 20/13, 14/9 m6 17
11 P4 4/3 3/2 P5 16
12 ↑P4 15/11 22/15 ↓P5 15
13 ~4 7/5 10/7 ~5 14

31edo

sharpness = 2

L = 5 ; s = 3

Degree Notation Approximate Ratios Approximate Ratios Notation Degree
0 P1 1/1 2/1 P8 31
1 ↑P1 ↓P8 30
2 ↓m2 ↑M7 29
3 m2 16/15, 15/14 28/15, 15/8 M7 28
4 ~2 12/11, 11/10 20/11, 11/6 ~7 27
5 M2 10/9, 9/8 16/9, 9/5 m7 26
6 ↑M2 8/7 7/4 ↓m7 25
7 ↓m3 7/6 12/7 ↑M6 24
8 m3 6/5 5/3 M6 23
9 ~3 11/9 18/11 ~6 22
10 M3 5/4 8/5 m6 21
11 ↑M3 14/11, 9/7 14/9, 11/7 ↓m6 20
12 ↓P4 17/13 26/17 ↑P5 19
13 P4 4/3 3/2 P5 18
14 ~4 15/11, 11/8 16/11, 22/15 ~5 17
15 A4 7/5 10/7 d5 16

34edo

41edo

46edo

50edo

53edo

58edo

60edo

65edo

68edo

72edo

77edo

80edo

84edo

87edo

94edo

99edo

111edo

118edo

130edo

EDOs from 9 to 17

9edo

10edo

11edo

13edo

14edo

15edo

16edo

17edo

Other noteworthy EDOs

23edo

26edo

29edo

36edo

sharpness = 3

L = 6 ; s = 3

Degree Notation Approximate Ratios Approximate Ratios Notation Degree
0 P1 1/1 2/1 P8 36
1 ↑P1 ↓P8 35
2 ↓m2 ↑M7 34
3 m2 ϕ3/4 8/ϕ3 M7 33
4 ↑m2 14/13, 13/12 24/13, 13/7 ↓M7 32
5 ↓M2 11/10 20/11 ↑m7 31
6 M2 9/8 16/9 m7 30
7 ↑M2 8/7 7/4 ↓m7 29
8 ↓m3 7/6 12/7 ↑M6 28
9 m3 6/5 5/3 M6 27
10 ↑m3 17/14 28/17 ↓M6 26
11 ↓M3 2/ϕ ϕ ↑m6 25
12 M3 5/4 8/5 m6 24
13 ↑M3 9/7 14/9 ↓m6 23
14 ↓P4 ϕ2/2 4/ϕ2 ↑P5 22
15 P4 4/3 3/2 P5 21
16 ↑P4 15/11 22/15 ↓P5 20
17 ↓A4 18/13 13/9 ↑d5 19
18 A4 24/17, 17/12 d5 18


37edo

49edo

93edo

4 exceptions outside the 9-cents-minimum-limit

7-limit

171edo

15-limit

270edo

Harmonic series

311edo

31-limit

16808edo

Retrieved from "https://en.xen.wiki/index.php?title=User:Contribution/Basic_analysis_of_selected_EDOs&oldid=115739"