74edo: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
18,215 edits
m Added to category "historical"
CompactStar (talk | contribs)
5,020 edits
No edit summary
Line 6: Line 6:


== Intervals ==
== Intervals ==
{|class="wikitable"
{{Interval table}}
|-
!#
!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 03:10, 5 July 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

Steps Cents Approximate ratios Ups and downs notation
0 0 1/1 D
1 16.2 ^D, vE♭♭
2 32.4 ^^D, E♭♭
3 48.6 34/33, 37/36, 38/37 vvD♯, ^E♭♭
4 64.9 26/25 vD♯, ^^E♭♭
5 81.1 21/20, 22/21 D♯, vvE♭
6 97.3 18/17 ^D♯, vE♭
7 113.5 16/15 ^^D♯, E♭
8 129.7 14/13 vvD𝄪, ^E♭
9 145.9 25/23, 37/34 vD𝄪, ^^E♭
10 162.2 11/10 D𝄪, vvE
11 178.4 31/28 ^D𝄪, vE
12 194.6 19/17, 28/25, 37/33 E
13 210.8 26/23, 35/31 ^E, vF♭
14 227 33/29 ^^E, F♭
15 243.2 23/20, 38/33 vvE♯, ^F♭
16 259.5 vE♯, ^^F♭
17 275.7 34/29 E♯, vvF
18 291.9 13/11 ^E♯, vF
19 308.1 F
20 324.3 29/24 ^F, vG♭♭
21 340.5 28/23 ^^F, G♭♭
22 356.8 16/13 vvF♯, ^G♭♭
23 373 26/21, 31/25, 36/29 vF♯, ^^G♭♭
24 389.2 5/4 F♯, vvG♭
25 405.4 24/19 ^F♯, vG♭
26 421.6 37/29 ^^F♯, G♭
27 437.8 vvF𝄪, ^G♭
28 454.1 13/10 vF𝄪, ^^G♭
29 470.3 21/16, 38/29 F𝄪, vvG
30 486.5 ^F𝄪, vG
31 502.7 G
32 518.9 31/23 ^G, vA♭♭
33 535.1 15/11 ^^G, A♭♭
34 551.4 11/8 vvG♯, ^A♭♭
35 567.6 vG♯, ^^A♭♭
36 583.8 7/5 G♯, vvA♭
37 600 17/12, 24/17 ^G♯, vA♭
38 616.2 10/7 ^^G♯, A♭
39 632.4 vvG𝄪, ^A♭
40 648.6 16/11 vG𝄪, ^^A♭
41 664.9 22/15 G𝄪, vvA
42 681.1 ^G𝄪, vA
43 697.3 A
44 713.5 ^A, vB♭♭
45 729.7 29/19, 32/21, 35/23 ^^A, B♭♭
46 745.9 20/13, 37/24 vvA♯, ^B♭♭
47 762.2 31/20 vA♯, ^^B♭♭
48 778.4 A♯, vvB♭
49 794.6 19/12 ^A♯, vB♭
50 810.8 8/5 ^^A♯, B♭
51 827 21/13, 29/18 vvA𝄪, ^B♭
52 843.2 13/8 vA𝄪, ^^B♭
53 859.5 23/14 A𝄪, vvB
54 875.7 ^A𝄪, vB
55 891.9 B
56 908.1 22/13 ^B, vC♭
57 924.3 29/17 ^^B, C♭
58 940.5 vvB♯, ^C♭
59 956.8 33/19 vB♯, ^^C♭
60 973 B♯, vvC
61 989.2 23/13 ^B♯, vC
62 1005.4 25/14, 34/19 C
63 1021.6 ^C, vD♭♭
64 1037.8 20/11 ^^C, D♭♭
65 1054.1 vvC♯, ^D♭♭
66 1070.3 13/7 vC♯, ^^D♭♭
67 1086.5 15/8 C♯, vvD♭
68 1102.7 17/9 ^C♯, vD♭
69 1118.9 21/11 ^^C♯, D♭
70 1135.1 25/13 vvC𝄪, ^D♭
71 1151.4 33/17, 37/19 vC𝄪, ^^D♭
72 1167.6 C𝄪, vvD
73 1183.8 ^C𝄪, vD
74 1200 2/1 D

Music

Retrieved from "https://en.xen.wiki/index.php?title=74edo&oldid=118418"