71edo: Difference between revisions

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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&amp;71 and 34&amp;37 temperaments.<!-- 2-digit number -->
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&amp;71 and 34&amp;37 temperaments.<!-- 2-digit number -->


== Intervals ==
{|class="wikitable"
|-
!#
!Cents
!Diatonic interval category
|-
|0
|0.0
|perfect unison
|-
|1
|17.1
|superunison
|-
|2
|34.3
|superunison
|-
|3
|51.4
|subminor second
|-
|4
|68.6
|subminor second
|-
|5
|85.7
|minor second
|-
|6
|102.9
|minor second
|-
|7
|120.0
|supraminor second
|-
|8
|137.1
|supraminor second
|-
|9
|154.3
|neutral second
|-
|10
|171.4
|submajor second
|-
|11
|188.6
|major second
|-
|12
|205.7
|major second
|-
|13
|222.9
|supermajor second
|-
|14
|240.0
|ultramajor second
|-
|15
|257.1
|ultramajor second
|-
|16
|274.3
|subminor third
|-
|17
|291.4
|minor third
|-
|18
|308.6
|minor third
|-
|19
|325.7
|supraminor third
|-
|20
|342.9
|neutral third
|-
|21
|360.0
|submajor third
|-
|22
|377.1
|submajor third
|-
|23
|394.3
|major third
|-
|24
|411.4
|major third
|-
|25
|428.6
|supermajor third
|-
|26
|445.7
|ultramajor third
|-
|27
|462.9
|subfourth
|-
|28
|480.0
|perfect fourth
|-
|29
|497.1
|perfect fourth
|-
|30
|514.3
|perfect fourth
|-
|31
|531.4
|superfourth
|-
|32
|548.6
|superfourth
|-
|33
|565.7
|low tritone
|-
|34
|582.9
|low tritone
|-
|35
|600.0
|high tritone
|-
|36
|617.1
|high tritone
|-
|37
|634.3
|high tritone
|-
|38
|651.4
|subfifth
|-
|39
|668.6
|subfifth
|-
|40
|685.7
|perfect fifth
|-
|41
|702.9
|perfect fifth
|-
|42
|720.0
|superfifth
|-
|43
|737.1
|superfifth
|-
|44
|754.3
|ultrafifth
|-
|45
|771.4
|subminor sixth
|-
|46
|788.6
|minor sixth
|-
|47
|805.7
|minor sixth
|-
|48
|822.9
|supraminor sixth
|-
|49
|840.0
|neutral sixth
|-
|50
|857.1
|neutral sixth
|-
|51
|874.3
|submajor sixth
|-
|52
|891.4
|major sixth
|-
|53
|908.6
|major sixth
|-
|54
|925.7
|supermajor sixth
|-
|55
|942.9
|ultramajor sixth
|-
|56
|960.0
|subminor seventh
|-
|57
|977.1
|subminor seventh
|-
|58
|994.3
|minor seventh
|-
|59
|1011.4
|minor seventh
|-
|60
|1028.6
|supraminor seventh
|-
|61
|1045.7
|neutral seventh
|-
|62
|1062.9
|submajor seventh
|-
|63
|1080.0
|major seventh
|-
|64
|1097.1
|major seventh
|-
|65
|1114.3
|major seventh
|-
|66
|1131.4
|supermajor seventh
|-
|67
|1148.6
|ultramajor seventh
|-
|68
|1165.7
|suboctave
|-
|69
|1182.9
|suboctave
|-
|70
|1200.0
|perfect octave
|}
[[Category:Prime EDO]]
[[Category:Prime EDO]]

Revision as of 21:53, 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 17.1 superunison
2 34.3 superunison
3 51.4 subminor second
4 68.6 subminor second
5 85.7 minor second
6 102.9 minor second
7 120.0 supraminor second
8 137.1 supraminor second
9 154.3 neutral second
10 171.4 submajor second
11 188.6 major second
12 205.7 major second
13 222.9 supermajor second
14 240.0 ultramajor second
15 257.1 ultramajor second
16 274.3 subminor third
17 291.4 minor third
18 308.6 minor third
19 325.7 supraminor third
20 342.9 neutral third
21 360.0 submajor third
22 377.1 submajor third
23 394.3 major third
24 411.4 major third
25 428.6 supermajor third
26 445.7 ultramajor third
27 462.9 subfourth
28 480.0 perfect fourth
29 497.1 perfect fourth
30 514.3 perfect fourth
31 531.4 superfourth
32 548.6 superfourth
33 565.7 low tritone
34 582.9 low tritone
35 600.0 high tritone
36 617.1 high tritone
37 634.3 high tritone
38 651.4 subfifth
39 668.6 subfifth
40 685.7 perfect fifth
41 702.9 perfect fifth
42 720.0 superfifth
43 737.1 superfifth
44 754.3 ultrafifth
45 771.4 subminor sixth
46 788.6 minor sixth
47 805.7 minor sixth
48 822.9 supraminor sixth
49 840.0 neutral sixth
50 857.1 neutral sixth
51 874.3 submajor sixth
52 891.4 major sixth
53 908.6 major sixth
54 925.7 supermajor sixth
55 942.9 ultramajor sixth
56 960.0 subminor seventh
57 977.1 subminor seventh
58 994.3 minor seventh
59 1011.4 minor seventh
60 1028.6 supraminor seventh
61 1045.7 neutral seventh
62 1062.9 submajor seventh
63 1080.0 major seventh
64 1097.1 major seventh
65 1114.3 major seventh
66 1131.4 supermajor seventh
67 1148.6 ultramajor seventh
68 1165.7 suboctave
69 1182.9 suboctave
70 1200.0 perfect octave
Retrieved from "https://en.xen.wiki/index.php?title=71edo&oldid=105176"