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= 9-cents-minimum-limit =
= 9-cents-minimum-limit =
== EDOs with a strong local zeta peak ==
== EDOs with a strong local zeta peak ==
=== 12edo ===
=== 12edo ===
sharpness = 1
sharpness = 1
L = 2 ; s = 1
L = 2 ; s = 1
{| class="wikitable center-all"
{| class="wikitable center-all"
|+
! Degree
!Degree
! Notation
!Notation
! Approximate Ratios
!Approximate Ratios
! Approximate Ratios
!Approximate Ratios
! Notation
!Notation
! Degree
!Degree
|-
|-
|0
| 0
|P1
| P1
|1/1
| 1/1
|2/1
| 2/1
|P8
| P8
|12
| 12
|-
|-
|1
| 1
|m2
| m2
|
|  
|
|  
|M7
| M7
|11
| 11
|-
|-
|2
| 2
|M2
| M2
|10/9, 9/8
| 10/9, 9/8
|16/9, 9/5
| 16/9, 9/5
|m7
| m7
|10
| 10
|-
|-
|3
| 3
|m3
| m3
|6/5
| 6/5
|5/3
| 5/3
|M6
| M6
|9
| 9
|-
|-
|4
| 4
|M3
| M3
|5/4
| 5/4
|8/5
| 8/5
|m6
| m6
|8
| 8
|-
|-
|5
| 5
|P4
| P4
|4/3
| 4/3
|3/2
| 3/2
|P5
| P5
|7
| 7
|-
|-
|6
| 6
|A4
| A4
| colspan="2" |7/5, 10/7
| colspan="2" | 7/5, 10/7
|d5
| d5
|6
| 6
|}
|}


=== 19edo ===
=== 19edo ===
sharpness = 1
sharpness = 1
L = 3 ; s = 2
L = 3 ; s = 2
{| class="wikitable center-all"
{| class="wikitable center-all"
|+
! Degree
!Degree
! Notation
!Notation
! Approximate Ratios
!Approximate Ratios
! Approximate Ratios
!Approximate Ratios
! Notation
!Notation
! Degree
!Degree
|-
|-
|0
| 0
|P1
| P1
|1/1
| 1/1
|2/1
| 2/1
|P8
| P8
|19
| 19
|-
|-
|1
| 1
|A1, d2
| A1, d2
|
|  
|
|  
|A7, d8
| A7, d8
|18
| 18
|-
|-
|2
| 2
|m2
| m2
|14/13
| 14/13
|13/7
| 13/7
|M7
| M7
|17
| 17
|-
|-
|3
| 3
|M2
| M2
|10/9, 9/8
| 10/9, 9/8
|16/9, 9/5
| 16/9, 9/5
|m7
| m7
|16
| 16
|-
|-
|4
| 4
|A2, d3
| A2, d3
|15/13
| 15/13
|26/15
| 26/15
|A6, d7
| A6, d7
|15
| 15
|-
|-
|5
| 5
|m3
| m3
|6/5
| 6/5
|5/3
| 5/3
|M6
| M6
|14
| 14
|-
|-
|6
| 6
|M3
| M3
|5/4
| 5/4
|8/5
| 8/5
|m6
| m6
|13
| 13
|-
|-
|7
| 7
|A3, d4
| A3, d4
|9/7, 13/10
| 9/7, 13/10
|20/13, 14/9
| 20/13, 14/9
|A5, d6
| A5, d6
|12
| 12
|-
|-
|8
| 8
|P4
| P4
|4/3
| 4/3
|3/2
| 3/2
|P5
| P5
|11
| 11
|-
|-
|9
| 9
|A4
| A4
|18/13
| 18/13
|13/9
| 13/9
|d5
| d5
|10
| 10
|}
|}


=== 22edo ===
=== 22edo ===
sharpness = 3
sharpness = 3
L = 4 ; s = 1
L = 4 ; s = 1
{| class="wikitable center-all"
{| class="wikitable center-all"
|+
! Degree
!Degree
! Notation
!Notation
! Approximate Ratios
!Approximate Ratios
! Approximate Ratios
!Approximate Ratios
! Notation
!Notation
! Degree
!Degree
|-
|-
|0
| 0
|P1
| P1
|1/1
| 1/1
|2/1
| 2/1
|P8
| P8
|22
| 22
|-
|-
|1
| 1
|m2
| m2
|
|  
|
|  
|M7
| M7
|21
| 21
|-
|-
|2
| 2
|↑m2
| ↑m2
|16/15
| 16/15
|15/8
| 15/8
|↓M7
| ↓M7
|20
| 20
|-
|-
|3
| 3
|↓M2
| ↓M2
|11/10
| 11/10
|20/11
| 20/11
|↑m7
| ↑m7
|19
| 19
|-
|-
|4
| 4
|M2
| M2
|9/8, 8/7
| 9/8, 8/7
|7/4, 16/9
| 7/4, 16/9
|m7
| m7
|18
| 18
|-
|-
|5
| 5
|m3
| m3
|7/6
| 7/6
|12/7
| 12/7
|M6
| M6
|17
| 17
|-
|-
|6
| 6
|↑m3
| ↑m3
|6/5
| 6/5
|5/3
| 5/3
|↓M6
| ↓M6
|16
| 16
|-
|-
|7
| 7
|↓M3
| ↓M3
|5/4
| 5/4
|8/5
| 8/5
|↑m6
| ↑m6
|15
| 15
|-
|-
|8
| 8
|M3
| M3
|9/7
| 9/7
|14/9
| 14/9
|m6
| m6
|14
| 14
|-
|-
|9
| 9
|P4
| P4
|4/3
| 4/3
|3/2
| 3/2
|P5
| P5
|13
| 13
|-
|-
|10
| 10
|↑P4
| ↑P4
|11/8
| 11/8
|16/11
| 16/11
|↓P5
| ↓P5
|12
| 12
|-
|-
|11
| 11
|↓A4
| ↓A4
| colspan="2" |7/5, 10/7
| colspan="2" | 7/5, 10/7
|↑d5
| ↑d5
|11
| 11
|}
|}


=== 24edo ===
=== 24edo ===
sharpness = 2
sharpness = 2
L = 4 ; s = 2
L = 4 ; s = 2
{| class="wikitable center-all"
{| class="wikitable center-all"
|+
24d
24d
!Degree
! Degree
!Notation
! Notation
!Approximate Ratios
! Approximate Ratios
!Approximate Ratios
! Approximate Ratios
!Notation
! Notation
!Degree
! Degree
|-
|-
|0
| 0
|P1
| P1
|1/1
| 1/1
|2/1
| 2/1
|P8
| P8
|24
| 24
|-
|-
|1
| 1
|↑P1, ↓m2
| ↑P1, ↓m2
|
|  
|
|  
|↑M7, ↓P8
| ↑M7, ↓P8
|23
| 23
|-
|-
|2
| 2
|m2
| m2
|
|  
|
|  
|M7
| M7
|22
| 22
|-
|-
|3
| 3
|~2
| ~2
|12/11
| 12/11
|11/6
| 11/6
|~7
| ~7
|21
| 21
|-
|-
|4
| 4
|M2
| M2
|10/9, 9/8
| 10/9, 9/8
|16/9, 9/5
| 16/9, 9/5
|m7
| m7
|20
| 20
|-
|-
|5
| 5
|↑M2, ↓m3
| ↑M2, ↓m3
|15/13
| 15/13
|26/15
| 26/15
|↑M6, ↓m7
| ↑M6, ↓m7
|19
| 19
|-
|-
|6
| 6
|m3
| m3
|6/5
| 6/5
|5/3
| 5/3
|M6
| M6
|18
| 18
|-
|-
|7
| 7
|~3
| ~3
|11/9
| 11/9
|18/11
| 18/11
|~6
| ~6
|17
| 17
|-
|-
|8
| 8
|M3
| M3
|5/4
| 5/4
|8/5
| 8/5
|m6
| m6
|16
| 16
|-
|-
|9
| 9
|↑M3, ↓P4
| ↑M3, ↓P4
|13/10
| 13/10
|20/13
| 20/13
|↑P5, ↓m6
| ↑P5, ↓m6
|15
| 15
|-
|-
|10
| 10
|P4
| P4
|4/3
| 4/3
|3/2
| 3/2
|P5
| P5
|14
| 14
|-
|-
|11
| 11
|~4
| ~4
|11/8
| 11/8
|16/11
| 16/11
|~5
| ~5
|13
| 13
|-
|-
|12
| 12
|A4
| A4
| colspan="2" |7/5, 10/7
| colspan="2" | 7/5, 10/7
|d5
| d5
|12
| 12
|}
|}


=== 27edo ===
=== 27edo ===
sharpness = 4
sharpness = 4
L = 5 ; s = 1
L = 5 ; s = 1
{| class="wikitable center-all"
{| class="wikitable center-all"
|+
27e
27e
!Degree
! Degree
!Notation
! Notation
!Approximate Ratios
! Approximate Ratios
!Approximate Ratios
! Approximate Ratios
!Notation
! Notation
!Degree
! Degree
|-
|-
|0
| 0
|P1
| P1
|1/1
| 1/1
|2/1
| 2/1
|P8
| P8
|27
| 27
|-
|-
|1
| 1
|m2
| m2
|
|  
|
|  
|M7
| M7
|26
| 26
|-
|-
|2
| 2
|↑m2
| ↑m2
|
|  
|
|  
|↓M7
| ↓M7
|25
| 25
|-
|-
|3
| 3
|~2
| ~2
|14/13, 13/12
| 14/13, 13/12
|24/13, 13/7
| 24/13, 13/7
|~7
| ~7
|24
| 24
|-
|-
|4
| 4
|↓M2
| ↓M2
|10/9
| 10/9
|9/5
| 9/5
|↑m7
| ↑m7
|23
| 23
|-
|-
|5
| 5
|M2
| M2
|9/8, 8/7
| 9/8, 8/7
|7/4, 16/9
| 7/4, 16/9
|m7
| m7
|22
| 22
|-
|-
|6
| 6
|m3
| m3
|7/6
| 7/6
|12/7
| 12/7
|M6
| M6
|21
| 21
|-
|-
|7
| 7
|↑m3
| ↑m3
|6/5
| 6/5
|5/3
| 5/3
|↓M6
| ↓M6
|20
| 20
|-
|-
|8
| 8
|~3
| ~3
|16/13
| 16/13
|13/8
| 13/8
|~6
| ~6
|19
| 19
|-
|-
|9
| 9
|↓M3
| ↓M3
|5/4
| 5/4
|8/5
| 8/5
|↑m6
| ↑m6
|18
| 18
|-
|-
|10
| 10
|M3
| M3
|9/7, 13/10
| 9/7, 13/10
|20/13, 14/9
| 20/13, 14/9
|m6
| m6
|17
| 17
|-
|-
|11
| 11
|P4
| P4
|4/3
| 4/3
|3/2
| 3/2
|P5
| P5
|16
| 16
|-
|-
|12
| 12
|↑P4
| ↑P4
|15/11
| 15/11
|22/15
| 22/15
|↓P5
| ↓P5
|15
| 15
|-
|-
|13
| 13
|~4
| ~4
|7/5
| 7/5
|10/7
| 10/7
|~5
| ~5
|14
| 14
|}
|}


=== 31edo ===
=== 31edo ===
sharpness = 2
sharpness = 2
L = 5 ; s = 3
L = 5 ; s = 3
{| class="wikitable center-all"
{| class="wikitable center-all"
|+
! Degree
!Degree
! Notation
!Notation
! Approximate Ratios
!Approximate Ratios
! Approximate Ratios
!Approximate Ratios
! Notation
!Notation
! Degree
!Degree
|-
|-
|0
| 0
|P1
| P1
|1/1
| 1/1
|2/1
| 2/1
|P8
| P8
|31
| 31
|-
|-
|1
| 1
|↑P1
| ↑P1
|
|  
|
|  
|↓P8
| ↓P8
|30
| 30
|-
|-
|2
| 2
|↓m2
| ↓m2
|
|  
|
|  
|↑M7
| ↑M7
|29
| 29
|-
|-
|3
| 3
|m2
| m2
|16/15, 15/14
| 16/15, 15/14
|28/15, 15/8
| 28/15, 15/8
|M7
| M7
|28
| 28
|-
|-
|4
| 4
|~2
| ~2
|12/11, 11/10
| 12/11, 11/10
|20/11, 11/6
| 20/11, 11/6
|~7
| ~7
|27
| 27
|-
|-
|5
| 5
|M2
| M2
|10/9, 9/8
| 10/9, 9/8
|16/9, 9/5
| 16/9, 9/5
|m7
| m7
|26
| 26
|-
|-
|6
| 6
|↑M2
| ↑M2
|8/7
| 8/7
|7/4
| 7/4
|↓m7
| ↓m7
|25
| 25
|-
|-
|7
| 7
|↓m3
| ↓m3
|7/6
| 7/6
|12/7
| 12/7
|↑M6
| ↑M6
|24
| 24
|-
|-
|8
| 8
|m3
| m3
|6/5
| 6/5
|5/3
| 5/3
|M6
| M6
|23
| 23
|-
|-
|9
| 9
|~3
| ~3
|11/9
| 11/9
|18/11
| 18/11
|~6
| ~6
|22
| 22
|-
|-
|10
| 10
|M3
| M3
|5/4
| 5/4
|8/5
| 8/5
|m6
| m6
|21
| 21
|-
|-
|11
| 11
|↑M3
| ↑M3
|14/11, 9/7
| 14/11, 9/7
|14/9, 11/7
| 14/9, 11/7
|↓m6
| ↓m6
|20
| 20
|-
|-
|12
| 12
|↓P4
| ↓P4
|17/13
| 17/13
|26/17
| 26/17
|↑P5
| ↑P5
|19
| 19
|-
|-
|13
| 13
|P4
| P4
|4/3
| 4/3
|3/2
| 3/2
|P5
| P5
|18
| 18
|-
|-
|14
| 14
|~4
| ~4
|15/11, 11/8
| 15/11, 11/8
|16/11, 22/15
| 16/11, 22/15
|~5
| ~5
|17
| 17
|-
|-
|15
| 15
|A4
| A4
|7/5
| 7/5
|10/7
| 10/7
|d5
| d5
|16
| 16
|}
|}


=== 34edo ===
=== 34edo ===
=== 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
|}
=== 41edo ===
=== 41edo ===
=== 46edo ===
=== 46edo ===
=== 50edo ===
=== 50edo ===
=== 53edo ===
=== 53edo ===
=== 58edo ===
=== 58edo ===
=== 60edo ===
=== 60edo ===
=== 65edo ===
=== 65edo ===
=== 68edo ===
=== 68edo ===
=== 72edo ===
=== 72edo ===
=== 77edo ===
=== 77edo ===
=== 80edo ===
=== 80edo ===
=== 84edo ===
=== 84edo ===
=== 87edo ===
=== 87edo ===
=== 94edo ===
=== 94edo ===
=== 99edo ===
=== 99edo ===
=== 103edo ===
=== 111edo ===
=== 111edo ===
=== 118edo ===
=== 118edo ===
=== 130edo ===
=== 130edo ===
== EDOs from 9 to 17 ==
== EDOs from 9 to 17 ==
=== 9edo ===
=== 9edo ===
=== 10edo ===
=== 10edo ===
=== 11edo ===
=== 11edo ===
=== 13edo ===
=== 13edo ===
=== 14edo ===
=== 14edo ===
=== 15edo ===
=== 15edo ===
=== 16edo ===
=== 16edo ===
=== 17edo ===
=== 17edo ===
== Other noteworthy EDOs ==
== Other noteworthy EDOs ==
=== 23edo ===
=== 23edo ===
=== 26edo ===
=== 26edo ===
=== 29edo ===
=== 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
|}


=== 37edo ===
=== 37edo ===
=== 49edo ===
=== 49edo ===
=== 93edo ===
=== 93edo ===
= 4 exceptions outside the 9-cents-minimum-limit =
= 4 exceptions outside the 9-cents-minimum-limit =
== 7-limit ==
== 7-limit ==
=== 171edo ===
=== 171edo ===
== 15-limit ==
== 15-limit ==
=== 270edo ===
=== 270edo ===
== Harmonic series ==
== Harmonic series ==
=== 311edo ===
=== 311edo ===
== 31-limit ==
== 31-limit ==
=== 16808edo ===
=== 16808edo ===
Retrieved from "https://en.xen.wiki/w/User:Contribution/Basic_analysis_of_selected_EDOs"