User:Xenwolf/Fifthspan

Fifthspan examples

	Prime →	2	3	5	7	11	13	17	19	23
EDO ↓	Mapping ↓	(1/1)	(3/2)	(5/4)	(7/4)	(11/8)	(13/8)	(17/16)	(19/16)	(23/16)
5edo	3\5	0	+1	-1	-2	-1	-2	0	+2	+1
7edo	4\7	0	+1	-3	-2	-1	+3	+2	-3	+1
8edo	5\8	0	+1	-1	-2	+4	-2	-3	+2	+4
9edo	5\9	0	+1	-3	-4	-1	+3	+2	+4	+1
11edo	6\11	0	+1	-3	-4	-1	+5	+2	-5	+1
12edo	7\12	0	+1	+4	-2	+6	-4	-5	-3	+6
13edo	8\13	0	+1	+7	-2	+4	+6	+5	+2	-4
16edo	9\16	0	+1	-3	+5	-1	+3	-7	+4	+8
17edo	10\17	0	+1	-8	-2	-6	+8	-5	-3	+6
18edo	11\18	0	+1	-6	+3	+4	-7	-8	+2	+9
19edo	11\19	0	+1	+4	-9	+6	-4	-5	-3	-6
22edo	13\22	0	+1	+9	-2	-6	-9	-10	-3	+6
23edo	13\23	0	+1	-3	+5	-8	+3	+9	+4	+8
26edo	15\26	0	+1	+4	-9	+6	-4	-12	-10	-6
27edo	16\27	0	+1	+9	-2	-6	+13	-10	-8	+11
29edo	17\29	0	+1	-8	-14	+11	+8	+7	-3	+6
31edo	18\31	0	+1	+4	+10	-13	+15	-5	-3	-6
32edo	todo
33edo	todo
37edo	todo
39edo	23\39	0	+1	-13	-19	-6	-9	+12	+14	-11
40edo	todo
41edo	24\41	0	+1	-8	-14	-18	+20	+7	-3	+6
42edo	todo
43edo	todo
45edo	todo
46edo	27\46	0	+1	+21	+15	+11	+8	-22	-3	+6
47edo	todo
49edo	todo
50edo	todo
53edo	31\53	0	+1	-8	-14	+23	+20	+7	-3	+18

Separate mod steps

Shown on the example of 17edo.

All fifthspans are given as positive values. (This can be transformed into mixed mode by subtracting 17 from all values > 17/2 == 8.5)

		prime 2	prime 3	prime 5	prime 7	prime 11	prime 13	prime 17	prime 19	prime 23
Error	absolute (¢)	0.0	+3.9	-33.4	+19.4	+13.4	+6.5	-34.3	-15.2	+7.0
	relative (%)	0	+6	-47	+27	+19	+9	-49	-21	+10
Mapping	steps	17	27	39	48	59	63	69	72	77
	mod 17	0	10	5	14	8	12	1	4	9
fifthspan (steps)		0	1	9	15	11	8	12	14	6
fifthspan explained		-	10= 1 *10 %17	5= 9 *10 %17	14= 15 *10 %17	8= 11 *10 %17	12= 8 *10 %17	1= 12 *10 %17	4= 14 *10 %17	9= 6 *10 %17
			1= 10 *12 %17	9= 5 *12 %17	15= 14 *12 %17	11= 8 *12 %17	8= 12 *12 %17	12= 1 *12 %17	14= 4 *12 %17	6= 9 *12 %17

Fifthspans of 17edo steps

step	span
0	0
1	12
2	7
3	2
4	14
5	9
6	4
7	16
8	11
9	6
10	1
11	13
12	8
13	3
14	15
15	10
16	5