User:Contribution/Basic analysis of selected EDOs

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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

Other noteworthy EDOs

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