73edo: Difference between revisions

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== Intervals ==
== Intervals ==
{|class="wikitable"
{{Interval table}}
|-
!#
!Cents
!Diatonic interval category
|-
|0
|0.0
|perfect unison
|-
|1
|16.4
|superunison
|-
|2
|32.9
|superunison
|-
|3
|49.3
|subminor second
|-
|4
|65.8
|subminor second
|-
|5
|82.2
|minor second
|-
|6
|98.6
|minor second
|-
|7
|115.1
|minor second
|-
|8
|131.5
|supraminor second
|-
|9
|147.9
|neutral second
|-
|10
|164.4
|submajor second
|-
|11
|180.8
|major second
|-
|12
|197.3
|major second
|-
|13
|213.7
|major second
|-
|14
|230.1
|supermajor second
|-
|15
|246.6
|ultramajor second
|-
|16
|263.0
|subminor third
|-
|17
|279.5
|subminor third
|-
|18
|295.9
|minor third
|-
|19
|312.3
|minor third
|-
|20
|328.8
|supraminor third
|-
|21
|345.2
|neutral third
|-
|22
|361.6
|submajor third
|-
|23
|378.1
|submajor third
|-
|24
|394.5
|major third
|-
|25
|411.0
|major third
|-
|26
|427.4
|supermajor third
|-
|27
|443.8
|ultramajor third
|-
|28
|460.3
|subfourth
|-
|29
|476.7
|subfourth
|-
|30
|493.2
|perfect fourth
|-
|31
|509.6
|perfect fourth
|-
|32
|526.0
|superfourth
|-
|33
|542.5
|superfourth
|-
|34
|558.9
|superfourth
|-
|35
|575.3
|low tritone
|-
|36
|591.8
|low tritone
|-
|37
|608.2
|high tritone
|-
|38
|624.7
|high tritone
|-
|39
|641.1
|subfifth
|-
|40
|657.5
|subfifth
|-
|41
|674.0
|subfifth
|-
|42
|690.4
|perfect fifth
|-
|43
|706.8
|perfect fifth
|-
|44
|723.3
|superfifth
|-
|45
|739.7
|superfifth
|-
|46
|756.2
|ultrafifth
|-
|47
|772.6
|subminor sixth
|-
|48
|789.0
|minor sixth
|-
|49
|805.5
|minor sixth
|-
|50
|821.9
|supraminor sixth
|-
|51
|838.4
|supraminor sixth
|-
|52
|854.8
|neutral sixth
|-
|53
|871.2
|submajor sixth
|-
|54
|887.7
|major sixth
|-
|55
|904.1
|major sixth
|-
|56
|920.5
|supermajor sixth
|-
|57
|937.0
|supermajor sixth
|-
|58
|953.4
|ultramajor sixth
|-
|59
|969.9
|subminor seventh
|-
|60
|986.3
|minor seventh
|-
|61
|1002.7
|minor seventh
|-
|62
|1019.2
|minor seventh
|-
|63
|1035.6
|supraminor seventh
|-
|64
|1052.1
|neutral seventh
|-
|65
|1068.5
|submajor seventh
|-
|66
|1084.9
|major seventh
|-
|67
|1101.4
|major seventh
|-
|68
|1117.8
|major seventh
|-
|69
|1134.2
|supermajor seventh
|-
|70
|1150.7
|ultramajor seventh
|-
|71
|1167.1
|suboctave
|-
|72
|1183.6
|suboctave
|-
|73
|1200.0
|perfect octave
|}
 
[[Category:Equal divisions of the octave|##]] <!-- 2-digit number -->
[[Category:Equal divisions of the octave|##]] <!-- 2-digit number -->
[[Category:Prime EDO]]
[[Category:Prime EDO]]
[[Category:Marrakesh]]
[[Category:Marrakesh]]

Revision as of 03:10, 5 July 2023

← 72edo 73edo 74edo →
Prime factorization 73 (prime)
Step size 16.4384 ¢ 
Fifth 43\73 (706.849 ¢)
Semitones (A1:m2) 9:4 (147.9 ¢ : 65.75 ¢)
Consistency limit 7
Distinct consistency limit 7

73 EDO divides the octave into 73 equal parts of 16.438 cents each. It tempers out 78732/78125 and 262144/253125 in the 5-limit, 126/125 and 245/243 in the 7-limit, 176/175, 441/440 and 4000/3993 in the 11-limit, and 91/90, 169/168, 196/195, 325/324, 351/350 and 352/351 in the 13-limit. It provides the optimal patent val for marrakesh temperament. 73 EDO has a sharp tendency, with the approximations of 3, 5, 7, 11 all sharp, see following table.

Script error: No such module "primes_in_edo".

73 EDO fits in mavila scale, by the 9;5 relation in the superdiatonic scheme.

73 EDO is the 21st prime EDO.

Intervals

Steps Cents Approximate ratios Ups and downs notation
0 0 1/1 D
1 16.4 ^D, v3E♭
2 32.9 ^^D, vvE♭
3 49.3 36/35, 38/37 ^3D, vE♭
4 65.8 ^4D, E♭
5 82.2 21/20, 22/21 v4D♯, ^E♭
6 98.6 35/33 v3D♯, ^^E♭
7 115.1 31/29 vvD♯, ^3E♭
8 131.5 14/13, 27/25 vD♯, ^4E♭
9 147.9 12/11, 37/34 D♯, v4E
10 164.4 11/10 ^D♯, v3E
11 180.8 10/9 ^^D♯, vvE
12 197.3 ^3D♯, vE
13 213.7 26/23 E
14 230.1 8/7 ^E, v3F
15 246.6 ^^E, vvF
16 263 ^3E, vF
17 279.5 F
18 295.9 19/16 ^F, v3G♭
19 312.3 6/5 ^^F, vvG♭
20 328.8 23/19, 29/24, 35/29 ^3F, vG♭
21 345.2 11/9 ^4F, G♭
22 361.6 16/13 v4F♯, ^G♭
23 378.1 v3F♯, ^^G♭
24 394.5 vvF♯, ^3G♭
25 411 vF♯, ^4G♭
26 427.4 F♯, v4G
27 443.8 31/24 ^F♯, v3G
28 460.3 ^^F♯, vvG
29 476.7 29/22 ^3F♯, vG
30 493.2 G
31 509.6 ^G, v3A♭
32 526 19/14, 23/17 ^^G, vvA♭
33 542.5 26/19 ^3G, vA♭
34 558.9 29/21 ^4G, A♭
35 575.3 v4G♯, ^A♭
36 591.8 31/22 v3G♯, ^^A♭
37 608.2 37/26 vvG♯, ^3A♭
38 624.7 vG♯, ^4A♭
39 641.1 29/20 G♯, v4A
40 657.5 19/13 ^G♯, v3A
41 674 28/19, 31/21, 34/23 ^^G♯, vvA
42 690.4 ^3G♯, vA
43 706.8 A
44 723.3 ^A, v3B♭
45 739.7 ^^A, vvB♭
46 756.2 31/20 ^3A, vB♭
47 772.6 ^4A, B♭
48 789 v4A♯, ^B♭
49 805.5 35/22 v3A♯, ^^B♭
50 821.9 37/23 vvA♯, ^3B♭
51 838.4 13/8 vA♯, ^4B♭
52 854.8 18/11 A♯, v4B
53 871.2 38/23 ^A♯, v3B
54 887.7 5/3 ^^A♯, vvB
55 904.1 32/19 ^3A♯, vB
56 920.5 B
57 937 ^B, v3C
58 953.4 ^^B, vvC
59 969.9 7/4 ^3B, vC
60 986.3 23/13 C
61 1002.7 ^C, v3D♭
62 1019.2 9/5 ^^C, vvD♭
63 1035.6 20/11 ^3C, vD♭
64 1052.1 11/6 ^4C, D♭
65 1068.5 13/7 v4C♯, ^D♭
66 1084.9 v3C♯, ^^D♭
67 1101.4 vvC♯, ^3D♭
68 1117.8 21/11 vC♯, ^4D♭
69 1134.2 C♯, v4D
70 1150.7 35/18, 37/19 ^C♯, v3D
71 1167.1 ^^C♯, vvD
72 1183.6 ^3C♯, vD
73 1200 2/1 D
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