User:Xenwolf/Fifthspan

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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 (2x 2edo)
5edo 3\5 0 +1 -1 -2 -1 -2 0 +2 +1
6edo N/A (2x 3edo)
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 (2x 5edo)
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 (2x 7edo)
15edo N/A (3x 5edo)
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 (4x 5edo)
21edo N/A (3x 7edo)
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 (2x 12edo)
25edo N/A (5x 5edo)
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 (4x 7edo)
29edo 17\29 0 +1 -8 -14 +11 +8 +7 -3 +6
30edo N/A (6x 5edo)
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 (2x 17edo)
35edo N/A (5x 7edo)
36edo N/A (3x 12edo)
37edo 22\37 0 +1 +14 -2 -11 +18 -15 -8 +16
38edo N/A (2x 19edo)
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 (2x 22edo)
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 (4x 12edo)
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 (3x 17edo)
52edo N/A (2x 26edo)
53edo 31\53 0 +1 -8 -14 +23 +20 +7 -3 +18
54edo N/A (2x 27edo)
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 (3x 19edo)
58edo N/A (2x 29edo)
59edo 35\59 0 +1 -18 -2 +21 -14 +17 -8 +11
60edo N/A (5x 12edo)
61edo 36\61 0 +1 -13 +20 -6 +30 +12 -25 +28
62edo N/A (2x 31edo)
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 (3x 22edo)
67edo 39\67 0 +1 +4 +22 +30 -28 -5 -3 -18
68edo N/A (4x 17edo)
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 (6x 12edo)
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 (4x 19edo)
77edo 45\77 0 +1 -8 -26 +35 +32 +7 -3 +18
78edo N/A (2x 39edo)
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 (2x 41edo)
83edo 49\83 0 +1 -13 +20 -6 -31 +12 +36 -33
84edo N/A (7x 12edo)
85edo N/A (5x 17edo)
86edo N/A (2x 43edo)
87edo N/A (3x 29edo)
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 (2x 46edo)
93edo N/A (3x 31edo)
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 (8x 12edo)
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

EDO information

Script error: No such module "primes_in_edo". Script error: No such module "primes_in_edo". Script error: No such module "primes_in_edo". Script error: No such module "primes_in_edo". Script error: No such module "primes_in_edo". Script error: No such module "primes_in_edo". Script error: No such module "primes_in_edo". Script error: No such module "primes_in_edo". Script error: No such module "primes_in_edo". Script error: No such module "primes_in_edo". Script error: No such module "primes_in_edo". Script error: No such module "primes_in_edo". Script error: No such module "primes_in_edo". Script error: No such module "primes_in_edo". Script error: No such module "primes_in_edo". Script error: No such module "primes_in_edo". Script error: No such module "primes_in_edo". Script error: No such module "primes_in_edo". Script error: No such module "primes_in_edo". Script error: No such module "primes_in_edo". Script error: No such module "primes_in_edo".

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
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