71edo: Difference between revisions

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|-
|-
|1
|1
|17.1
|16.9
|superunison
|superunison
|-
|-
|2
|2
|34.3
|33.8
|superunison
|superunison
|-
|-
|3
|3
|51.4
|50.7
|subminor second
|subminor second
|-
|-
|4
|4
|68.6
|67.6
|subminor second
|subminor second
|-
|-
|5
|5
|85.7
|84.5
|minor second
|minor second
|-
|-
|6
|6
|102.9
|101.4
|minor second
|minor second
|-
|-
|7
|7
|120.0
|118.3
|supraminor second
|minor second
|-
|-
|8
|8
|137.1
|135.2
|supraminor second
|supraminor second
|-
|-
|9
|9
|154.3
|152.1
|neutral second
|neutral second
|-
|-
|10
|10
|171.4
|169.0
|submajor second
|submajor second
|-
|-
|11
|11
|188.6
|185.9
|major second
|major second
|-
|-
|12
|12
|205.7
|202.8
|major second
|major second
|-
|-
|13
|13
|222.9
|219.7
|supermajor second
|major second
|-
|-
|14
|14
|240.0
|236.6
|ultramajor second
|supermajor second
|-
|-
|15
|15
|257.1
|253.5
|ultramajor second
|ultramajor second
|-
|-
|16
|16
|274.3
|270.4
|subminor third
|subminor third
|-
|-
|17
|17
|291.4
|287.3
|minor third
|minor third
|-
|-
|18
|18
|308.6
|304.2
|minor third
|minor third
|-
|-
|19
|19
|325.7
|321.1
|supraminor third
|supraminor third
|-
|-
|20
|20
|342.9
|338.0
|neutral third
|supraminor third
|-
|-
|21
|21
|360.0
|354.9
|submajor third
|neutral third
|-
|-
|22
|22
|377.1
|371.8
|submajor third
|submajor third
|-
|-
|23
|23
|394.3
|388.7
|major third
|major third
|-
|-
|24
|24
|411.4
|405.6
|major third
|major third
|-
|-
|25
|25
|428.6
|422.5
|supermajor third
|supermajor third
|-
|-
|26
|26
|445.7
|439.4
|ultramajor third
|supermajor third
|-
|-
|27
|27
|462.9
|456.3
|subfourth
|ultramajor third
|-
|-
|28
|28
|480.0
|473.2
|perfect fourth
|subfourth
|-
|-
|29
|29
|497.1
|490.1
|perfect fourth
|perfect fourth
|-
|-
|30
|30
|514.3
|507.0
|perfect fourth
|perfect fourth
|-
|-
|31
|31
|531.4
|523.9
|superfourth
|superfourth
|-
|-
|32
|32
|548.6
|540.8
|superfourth
|superfourth
|-
|-
|33
|33
|565.7
|557.7
|low tritone
|superfourth
|-
|-
|34
|34
|582.9
|574.6
|low tritone
|low tritone
|-
|-
|35
|35
|600.0
|591.5
|high tritone
|low tritone
|-
|-
|36
|36
|617.1
|608.5
|high tritone
|high tritone
|-
|-
|37
|37
|634.3
|625.4
|high tritone
|high tritone
|-
|-
|38
|38
|651.4
|642.3
|subfifth
|subfifth
|-
|-
|39
|39
|668.6
|659.2
|subfifth
|subfifth
|-
|-
|40
|40
|685.7
|676.1
|perfect fifth
|subfifth
|-
|-
|41
|41
|702.9
|693.0
|perfect fifth
|perfect fifth
|-
|-
|42
|42
|720.0
|709.9
|superfifth
|perfect fifth
|-
|-
|43
|43
|737.1
|726.8
|superfifth
|superfifth
|-
|-
|44
|44
|754.3
|743.7
|ultrafifth
|ultrafifth
|-
|-
|45
|45
|771.4
|760.6
|subminor sixth
|subminor sixth
|-
|-
|46
|46
|788.6
|777.5
|minor sixth
|subminor sixth
|-
|-
|47
|47
|805.7
|794.4
|minor sixth
|minor sixth
|-
|-
|48
|48
|822.9
|811.3
|supraminor sixth
|minor sixth
|-
|-
|49
|49
|840.0
|828.2
|neutral sixth
|supraminor sixth
|-
|-
|50
|50
|857.1
|845.1
|neutral sixth
|neutral sixth
|-
|-
|51
|51
|874.3
|862.0
|submajor sixth
|submajor sixth
|-
|-
|52
|52
|891.4
|878.9
|major sixth
|submajor sixth
|-
|-
|53
|53
|908.6
|895.8
|major sixth
|major sixth
|-
|-
|54
|54
|925.7
|912.7
|supermajor sixth
|major sixth
|-
|-
|55
|55
|942.9
|929.6
|ultramajor sixth
|supermajor sixth
|-
|-
|56
|56
|960.0
|946.5
|subminor seventh
|ultramajor sixth
|-
|-
|57
|57
|977.1
|963.4
|subminor seventh
|subminor seventh
|-
|-
|58
|58
|994.3
|980.3
|minor seventh
|minor seventh
|-
|-
|59
|59
|1011.4
|997.2
|minor seventh
|minor seventh
|-
|-
|60
|60
|1028.6
|1014.1
|supraminor seventh
|minor seventh
|-
|-
|61
|61
|1045.7
|1031.0
|neutral seventh
|supraminor seventh
|-
|-
|62
|62
|1062.9
|1047.9
|submajor seventh
|neutral seventh
|-
|-
|63
|63
|1080.0
|1064.8
|major seventh
|submajor seventh
|-
|-
|64
|64
|1097.1
|1081.7
|major seventh
|major seventh
|-
|-
|65
|65
|1114.3
|1098.6
|major seventh
|major seventh
|-
|-
|66
|66
|1131.4
|1115.5
|supermajor seventh
|major seventh
|-
|-
|67
|67
|1148.6
|1132.4
|ultramajor seventh
|supermajor seventh
|-
|-
|68
|68
|1165.7
|1149.3
|suboctave
|ultramajor seventh
|-
|-
|69
|69
|1182.9
|1166.2
|suboctave
|suboctave
|-
|-
|70
|70
|1183.1
|suboctave
|-
|71
|1200.0
|1200.0
|perfect octave
|perfect octave
|}
|}
[[Category:Prime EDO]]
[[Category:Prime EDO]]

Revision as of 21:54, 9 March 2023

← 70edo 71edo 72edo →
Prime factorization 71 (prime)
Step size 16.9014 ¢ 
Fifth 42\71 (709.859 ¢)
Semitones (A1:m2) 10:3 (169 ¢ : 50.7 ¢)
Dual sharp fifth 42\71 (709.859 ¢)
Dual flat fifth 41\71 (692.958 ¢)
Dual major 2nd 12\71 (202.817 ¢)
Consistency limit 5
Distinct consistency limit 5

The 71 equal temperament or 71-EDO divides the octave into 71 equal parts of 16.901 cents each.

71edo is the 20th prime EDO.

Theory

Approximation of odd harmonics in 71edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +7.90 +2.42 -5.45 -1.09 +6.43 +4.54 -6.58 -3.55 +6.71 +2.46 -2.92
Relative (%) +46.8 +14.3 -32.2 -6.5 +38.0 +26.9 -38.9 -21.0 +39.7 +14.5 -17.3
Steps
(reduced) 		113
(42) 		165
(23) 		199
(57) 		225
(12) 		246
(33) 		263
(50) 		277
(64) 		290
(6) 		302
(18) 		312
(28) 		321
(37)

It tempers out 20480/19683 and 393216/390625 in the 5-limit, 875/864, 4000/3969 and 1029/1024 in the 7-limit, 245/242 and 100/99 in the 11-limit, and 91/90 in the 13-limit. In the 13-limit it supplies the optimal patent val for the 29&71 and 34&37 temperaments.

Intervals

# Cents Diatonic interval category
0 0.0 perfect unison
1 16.9 superunison
2 33.8 superunison
3 50.7 subminor second
4 67.6 subminor second
5 84.5 minor second
6 101.4 minor second
7 118.3 minor second
8 135.2 supraminor second
9 152.1 neutral second
10 169.0 submajor second
11 185.9 major second
12 202.8 major second
13 219.7 major second
14 236.6 supermajor second
15 253.5 ultramajor second
16 270.4 subminor third
17 287.3 minor third
18 304.2 minor third
19 321.1 supraminor third
20 338.0 supraminor third
21 354.9 neutral third
22 371.8 submajor third
23 388.7 major third
24 405.6 major third
25 422.5 supermajor third
26 439.4 supermajor third
27 456.3 ultramajor third
28 473.2 subfourth
29 490.1 perfect fourth
30 507.0 perfect fourth
31 523.9 superfourth
32 540.8 superfourth
33 557.7 superfourth
34 574.6 low tritone
35 591.5 low tritone
36 608.5 high tritone
37 625.4 high tritone
38 642.3 subfifth
39 659.2 subfifth
40 676.1 subfifth
41 693.0 perfect fifth
42 709.9 perfect fifth
43 726.8 superfifth
44 743.7 ultrafifth
45 760.6 subminor sixth
46 777.5 subminor sixth
47 794.4 minor sixth
48 811.3 minor sixth
49 828.2 supraminor sixth
50 845.1 neutral sixth
51 862.0 submajor sixth
52 878.9 submajor sixth
53 895.8 major sixth
54 912.7 major sixth
55 929.6 supermajor sixth
56 946.5 ultramajor sixth
57 963.4 subminor seventh
58 980.3 minor seventh
59 997.2 minor seventh
60 1014.1 minor seventh
61 1031.0 supraminor seventh
62 1047.9 neutral seventh
63 1064.8 submajor seventh
64 1081.7 major seventh
65 1098.6 major seventh
66 1115.5 major seventh
67 1132.4 supermajor seventh
68 1149.3 ultramajor seventh
69 1166.2 suboctave
70 1183.1 suboctave
71 1200.0 perfect octave
Retrieved from "https://en.xen.wiki/index.php?title=71edo&oldid=105177"