74edo: Difference between revisions

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74 tunes 11 only 1/30 of a cent sharp, and 13 2.7 cents sharp, making it a distinctly interesting choice for higher-limit meantone.
74 tunes 11 only 1/30 of a cent sharp, and 13 2.7 cents sharp, making it a distinctly interesting choice for higher-limit meantone.
== Intervals ==
{|class="wikitable"
|-
!#
!Cents
!Diatonic interval category
|-
|0
|0.0
|perfect unison
|-
|1
|16.2
|superunison
|-
|2
|32.4
|superunison
|-
|3
|48.6
|subminor second
|-
|4
|64.9
|subminor second
|-
|5
|81.1
|minor second
|-
|6
|97.3
|minor second
|-
|7
|113.5
|minor second
|-
|8
|129.7
|supraminor second
|-
|9
|145.9
|neutral second
|-
|10
|162.2
|submajor second
|-
|11
|178.4
|submajor second
|-
|12
|194.6
|major second
|-
|13
|210.8
|major second
|-
|14
|227.0
|supermajor second
|-
|15
|243.2
|ultramajor second
|-
|16
|259.5
|ultramajor second
|-
|17
|275.7
|subminor third
|-
|18
|291.9
|minor third
|-
|19
|308.1
|minor third
|-
|20
|324.3
|supraminor third
|-
|21
|340.5
|neutral third
|-
|22
|356.8
|neutral third
|-
|23
|373.0
|submajor third
|-
|24
|389.2
|major third
|-
|25
|405.4
|major third
|-
|26
|421.6
|supermajor third
|-
|27
|437.8
|supermajor third
|-
|28
|454.1
|ultramajor third
|-
|29
|470.3
|subfourth
|-
|30
|486.5
|perfect fourth
|-
|31
|502.7
|perfect fourth
|-
|32
|518.9
|perfect fourth
|-
|33
|535.1
|superfourth
|-
|34
|551.4
|superfourth
|-
|35
|567.6
|low tritone
|-
|36
|583.8
|low tritone
|-
|37
|600.0
|high tritone
|-
|38
|616.2
|high tritone
|-
|39
|632.4
|high tritone
|-
|40
|648.6
|subfifth
|-
|41
|664.9
|subfifth
|-
|42
|681.1
|perfect fifth
|-
|43
|697.3
|perfect fifth
|-
|44
|713.5
|perfect fifth
|-
|45
|729.7
|superfifth
|-
|46
|745.9
|ultrafifth
|-
|47
|762.2
|subminor sixth
|-
|48
|778.4
|subminor sixth
|-
|49
|794.6
|minor sixth
|-
|50
|810.8
|minor sixth
|-
|51
|827.0
|supraminor sixth
|-
|52
|843.2
|neutral sixth
|-
|53
|859.5
|neutral sixth
|-
|54
|875.7
|submajor sixth
|-
|55
|891.9
|major sixth
|-
|56
|908.1
|major sixth
|-
|57
|924.3
|supermajor sixth
|-
|58
|940.5
|ultramajor sixth
|-
|59
|956.8
|ultramajor sixth
|-
|60
|973.0
|subminor seventh
|-
|61
|989.2
|minor seventh
|-
|62
|1005.4
|minor seventh
|-
|63
|1021.6
|supraminor seventh
|-
|64
|1037.8
|supraminor seventh
|-
|65
|1054.1
|neutral seventh
|-
|66
|1070.3
|submajor seventh
|-
|67
|1086.5
|major seventh
|-
|68
|1102.7
|major seventh
|-
|69
|1118.9
|major seventh
|-
|70
|1135.1
|supermajor seventh
|-
|71
|1151.4
|ultramajor seventh
|-
|72
|1167.6
|suboctave
|-
|73
|1183.8
|suboctave
|-
|74
|1200.0
|perfect octave
|}


== Music ==
== Music ==

Revision as of 21:56, 9 March 2023

← 73edo 74edo 75edo →
Prime factorization 2 × 37
Step size 16.2162 ¢ 
Fifth 43\74 (697.297 ¢)
Semitones (A1:m2) 5:7 (81.08 ¢ : 113.5 ¢)
Consistency limit 5
Distinct consistency limit 5

74edo divides the octave into 74 equal parts of size 16.216 cents each. It is most notable as a meantone tuning, tempering out 81/80 in the 5-limit; 81/80 and 126/125 (and hence 225/224) in the 7-limit; 99/98, 176/175 and 441/440 in the 11-limit; and 144/143 and 847/845 in the 13-limit. Discarding 847/845 from that gives 13-limit meantone, aka 13-limit huygens, for which 74edo gives the optimal patent val; and discarding 144/143 gives a 13-limit 62&74 temperament with half-octave period and two parallel tracks of meantone. Script error: No such module "primes_in_edo".

74 tunes 11 only 1/30 of a cent sharp, and 13 2.7 cents sharp, making it a distinctly interesting choice for higher-limit meantone.

Intervals

# Cents Diatonic interval category
0 0.0 perfect unison
1 16.2 superunison
2 32.4 superunison
3 48.6 subminor second
4 64.9 subminor second
5 81.1 minor second
6 97.3 minor second
7 113.5 minor second
8 129.7 supraminor second
9 145.9 neutral second
10 162.2 submajor second
11 178.4 submajor second
12 194.6 major second
13 210.8 major second
14 227.0 supermajor second
15 243.2 ultramajor second
16 259.5 ultramajor second
17 275.7 subminor third
18 291.9 minor third
19 308.1 minor third
20 324.3 supraminor third
21 340.5 neutral third
22 356.8 neutral third
23 373.0 submajor third
24 389.2 major third
25 405.4 major third
26 421.6 supermajor third
27 437.8 supermajor third
28 454.1 ultramajor third
29 470.3 subfourth
30 486.5 perfect fourth
31 502.7 perfect fourth
32 518.9 perfect fourth
33 535.1 superfourth
34 551.4 superfourth
35 567.6 low tritone
36 583.8 low tritone
37 600.0 high tritone
38 616.2 high tritone
39 632.4 high tritone
40 648.6 subfifth
41 664.9 subfifth
42 681.1 perfect fifth
43 697.3 perfect fifth
44 713.5 perfect fifth
45 729.7 superfifth
46 745.9 ultrafifth
47 762.2 subminor sixth
48 778.4 subminor sixth
49 794.6 minor sixth
50 810.8 minor sixth
51 827.0 supraminor sixth
52 843.2 neutral sixth
53 859.5 neutral sixth
54 875.7 submajor sixth
55 891.9 major sixth
56 908.1 major sixth
57 924.3 supermajor sixth
58 940.5 ultramajor sixth
59 956.8 ultramajor sixth
60 973.0 subminor seventh
61 989.2 minor seventh
62 1005.4 minor seventh
63 1021.6 supraminor seventh
64 1037.8 supraminor seventh
65 1054.1 neutral seventh
66 1070.3 submajor seventh
67 1086.5 major seventh
68 1102.7 major seventh
69 1118.9 major seventh
70 1135.1 supermajor seventh
71 1151.4 ultramajor seventh
72 1167.6 suboctave
73 1183.8 suboctave
74 1200.0 perfect octave

Music

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