User:Xenwolf/Fifthspan

Fifthspan examples

	Prime →	2	3	5	7	11	13	17	19	23
EDO ↓	Unique fifth (mapping) ↓	↓ (octave-reduced corresponding primary intervals) ↓
		(1/1)	(3/2)	(5/4)	(7/4)	(11/8)	(13/8)	(17/16)	(19/16)	(23/16)
1edo	N/A
2edo	1\2	0	+1	+1	0	+1	+1	0	0	+1
3edo	2\3	0	+1	-1	+1	-1	+1	0	-1	+1
4edo	N/A
5edo	3\5	0	+1	-1	-2	-1	-2	0	+2	+1
6edo	N/A
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
10edo	N/A
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	-6	-2	+4	+6	+5	+2	-4
14edo	N/A
15edo	N/A
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
20edo	N/A
21edo	N/A
22edo	13\22	0	+1	+9	-2	-6	-9	-10	-3	+6
23edo	13\23	0	+1	-3	+5	-8	+3	+9	+4	+8
24edo	N/A
25edo	N/A
26edo	15\26	0	+1	+4	-9	+6	-4	-12	-10	-6
27edo	16\27	0	+1	+9	-2	-6	+13	-10	-8	+11
28edo	N/A
29edo	17\29	0	+1	-8	-14	+11	+8	+7	-3	+6
30edo	N/A
31edo	18\31	0	+1	+4	+10	-13	+15	-5	-3	-6
32edo	19\32	0	+1	+14	-2	-11	-14	-15	-8	+11
33edo	19\33	0	+1	+11	-9	+6	-4	-12	-10	-13
34edo	N/A
35edo	N/A
36edo	N/A
37edo	22\37	0	+1	+14	-2	-11	+18	-15	-8	+16
38edo	N/A
39edo	23\39	0	+1	-13	-19	-6	-9	+12	+14	-11
40edo	23\40	0	+1	+11	-16	+6	-4	-19	-10	-13
41edo	24\41	0	+1	-8	-14	-18	+20	+7	-3	+6
42edo	25\42	0	+1	+14	-2	-11	-19	-20	-8	+16
43edo	25\43	0	+1	+4	+10	+18	-16	-5	-3	-18
44edo	N/A
45edo	26\45	0	+1	+4	-9	+6	+22	+14	+16	-6
46edo	27\46	0	+1	+21	+15	+11	+8	-22	-3	+6
47edo	27\47	0	+1	+11	-16	+13	-4	-19	-10	-13
48edo	N/A
49edo	29\49	0	+1	+9	-2	+16	+13	-10	+19	-16
50edo	29\50	0	+1	+4	+10	-13	+15	-24	-22	-6
51edo	N/A
52edo	N/A
53edo	31\53	0	+1	-8	-14	+23	+20	+7	-3	+18
54edo	N/A
55edo	32\55	0	+1	+4	+22	-25	+27	-5	-3	-18
56edo	33\56	0	+1	+26	-19	-6	-9	-27	+14	-11
57edo	N/A
58edo	N/A
59edo	35\59	0	+1	-18	-2	+21	-14	+17	-8	+11
60edo	N/A
61edo	36\61	0	+1	-13	+20	-6	+30	+12	-25	+28
62edo	N/A
63edo	37\63	0	+1	-25	+15	+11	+8	+24	-20	+6
64edo	37\64	0	+1	-15	-28	+25	-23	+14	+16	-6
65edo	38\65	0	+1	-8	-26	-30	+32	+7	-3	+18
66edo	N/A
67edo	39\67	0	+1	+4	+22	+30	-28	-5	-3	-18
68edo	N/A
69edo	40\69	0	+1	+4	+29	-13	+15	-24	-22	-6
70edo	41\70	0	+1	+33	+27	-18	-21	-34	-3	-23
71edo	42\71	0	+1	+9	-24	+16	+35	-10	-30	+33
72edo	N/A
73edo	43\73	0	+1	-30	-19	-6	-9	+29	+14	-11
74edo	43\74	0	+1	+4	+10	+18	-16	-36	-34	+25
75edo	44\75	0	+1	+21	-31	+11	+37	-22	+26	+6
76edo	N/A
77edo	45\77	0	+1	-8	-26	+35	+32	+7	-3	+18
78edo	N/A
79edo	46\79	0	+1	+16	+22	-37	-28	-5	-3	-18
80edo	47\80	0	+1	+38	+15	+11	+8	-39	-20	+6
81edo	47\81	0	+1	+4	+10	-13	+15	+26	+28	-6
82edo	N/A
83edo	49\83	0	+1	-13	+20	-6	-31	+12	+36	-33
84edo	N/A
85edo	N/A
86edo	N/A
87edo	N/A
88edo	51\88	0	+1	+4	+29	-32	+34	-24	-22	-6
89edo	52\89	0	+1	-8	-26	-42	+32	+7	-3	+30
90edo	53\90	0	+1	+43	-19	-23	-9	-44	+14	-11
91edo	53\91	0	+1	+16	+34	+42	-40	-5	-3	-30
92edo	N/A
93edo	N/A
94edo	55\94	0	+1	-8	-14	+23	+20	-46	-3	-35
95edo	56\95	0	+1	+26	+37	-6	+47	-27	+14	+45
96edo	N/A
97edo	57\97	0	+1	-42	+32	+11	+8	-39	-20	+6
98edo	57\98	0	+1	+4	-33	-25	+27	-5	-46	+37
99edo	58\99	0	+1	-37	-43	-18	-21	+36	-32	-23

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	patent val	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