User:Contribution/Basic analysis of selected EDOs: Difference between revisions

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Created page with "= EDOs with a strong local zeta peak = == 12edo == == 19edo == == 22edo == == 24edo == == 27edo == == 31edo == == 34edo == == 36edo == == 41edo == == 46edo == == 50..."
 
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= EDOs with a strong local zeta peak =
= 9-cents-minimum-limit =
== EDOs with a strong local zeta peak ==
=== 12edo ===
sharpness = 1
L = 2 ; s = 1
{| class="wikitable center-all"
! 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
| colspan="2" | 7/5, 10/7
| d5
| 6
|}


== 12edo ==
=== 19edo ===
sharpness = 1
L = 3 ; s = 2
{| class="wikitable center-all"
! 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
|}


== 19edo ==
=== 22edo ===
sharpness = 3
L = 4 ; s = 1
{| class="wikitable center-all"
! 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
| colspan="2" | 7/5, 10/7
| ↑d5
| 11
|}


== 22edo ==
=== 24edo ===
sharpness = 2
L = 4 ; s = 2
{| class="wikitable center-all"
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
| colspan="2" | 7/5, 10/7
| d5
| 12
|}


== 24edo ==
=== 27edo ===
sharpness = 4
L = 5 ; s = 1
{| class="wikitable center-all"
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
|}


== 27edo ==
=== 31edo ===
sharpness = 2
L = 5 ; s = 3
{| class="wikitable center-all"
! 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
|}


== 31edo ==
=== 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
{| class="wikitable center-all"
! 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
| ϕ<sup>3</sup>/4
| 8/ϕ<sup>3</sup>
| 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
| ϕ<sup>2</sup>/2
| 4/ϕ<sup>2</sup>
| ↑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
| colspan="2" | 24/17, 17/12
| d5
| 18
|}


== 34edo ==
=== 37edo ===
 
=== 49edo ===
== 36edo ==
=== 93edo ===
 
= 4 exceptions outside the 9-cents-minimum-limit =
== 41edo ==
== 7-limit ==
 
=== 171edo ===
== 46edo ==
== 15-limit ==
 
=== 270edo ===
== 50edo ==
== Harmonic series ==
 
=== 311edo ===
== 53edo ==
== 31-limit ==
 
=== 16808edo ===
== 58edo ==
 
== 60edo ==
 
== 65edo ==
 
== 68edo ==
 
== 72edo ==
 
== 77edo ==
 
== 80edo ==
 
== 84edo ==
 
== 87edo ==
 
== 94edo ==
 
== 99edo ==
 
== 103edo ==
 
== 111edo ==
 
== 118edo ==
 
== 130edo ==
 
== 140edo ==
 
== 152edo ==
 
== 171edo ==
 
= EDOs from 9 to 17 =
 
== 9edo ==
 
== 10edo ==
 
== 11edo ==
 
== 13edo ==
 
== 14edo ==
 
== 15edo ==
 
== 16edo ==
 
== 17edo ==
 
= Other noteworthy EDOs below 36 =
 
== 23edo ==
 
== 26edo ==
 
== 29edo ==

Latest revision as of 15:10, 13 August 2024

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

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