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{|class="wikitable"
{|class="wikitable"
!Interval
!Degrees
!Cents
!Cents
|-
|-
|0| 0.000
|0
|0.000
|-
|-
|1| 17.910  
|1
|17.910  
|-
|-
|2| 35.821  
|2
|35.821  
|-
|-
|3| 53.731  
|3
|53.731  
|-
|-
|4| 71.642  
|4
|71.642  
|-
|-
|5| 89.552  
|5
|89.552  
|-
|-
|6| 107.463  
|6
|107.463  
|-
|-
|7| 125.373  
|7
|125.373  
|-
|-
|8| 143.284  
|8
|143.284  
|-
|-
|9| 161.194  
|9
|161.194  
|-
|-
|10| 179.104  
|10
|179.104  
|-
|-
|11| 197.015  
|11
|197.015  
|-
|-
|12| 214.925  
|12
|214.925  
|-
|-
|13| 232.836  
|13
|232.836  
|-
|-
|14| 250.746  
|14
|250.746  
|-
|-
|15| 268.657  
|15
|268.657  
|-
|-
|16| 286.567  
|16
|286.567  
|-
|-
|17| 304.478  
|17
|304.478  
|-
|-
|18| 322.388  
|18
|322.388  
|-
|-
|19| 340.299  
|19
|340.299  
|-
|-
|20| 358.209  
|20
|358.209  
|-
|-
|21| 376.119  
|21
|376.119  
|-
|-
|22| 394.030  
|22
|394.030  
|-
|-
|23| 411.940  
|23
|411.940  
|-
|-
|24| 429.851  
|24
|429.851  
|-
|-
|25| 447.761  
|25
|447.761  
|-
|-
|26| 465.672  
|26
|465.672  
|-
|-
|27| 483.582  
|27
|483.582  
|-
|-
|28| 501.493  
|28
|501.493  
|-
|-
|29| 519.403  
|29
|519.403  
|-
|-
|30| 537.313  
|30
|537.313  
|-
|-
|31| 555.224  
|31
|555.224  
|-
|-
|32| 573.134  
|32
|573.134  
|-
|-
|33| 591.045  
|33
|591.045  
|-
|-
|34| 608.955  
|34
|608.955  
|-
|-
|35| 626.866  
|35
|626.866  
|-
|-
|36| 644.776  
|36
|644.776  
|-
|-
|37| 662.687  
|37
|662.687  
|-
|-
|38| 680.597  
|38
|680.597  
|-
|-
|39| 698.507  
|39
|698.507  
|-
|-
|40| 716.418  
|40
|716.418  
|-
|-
|41| 734.328  
|41
|734.328  
|-
|-
|42| 752.239  
|42
|752.239  
|-
|-
|43| 770.149  
|43
|770.149  
|-
|-
|44| 788.060  
|44
|788.060  
|-
|-
|45| 805.970  
|45
|805.970  
|-
|-
|46| 823.881  
|46
|823.881  
|-
|-
|47| 841.791  
|47
|841.791  
|-
|-
|48| 859.701  
|48
|859.701  
|-
|-
|49| 877.612  
|49
|877.612  
|-
|-
|50| 895.522  
|50
|895.522  
|-
|-
|51| 913.433  
|51
|913.433  
|-
|-
|52| 931.343  
|52
|931.343  
|-
|-
|53| 949.254  
|53
|949.254  
|-
|-
|54| 967.164  
|54
|967.164  
|-
|-
|55| 985.075  
|55
|985.075  
|-
|-
|56| 1002.985  
|56
|1002.985  
|-
|-
|57| 1020.896  
|57
|1020.896  
|-
|-
|58| 1038.806  
|58
|1038.806  
|-
|-
|59| 1056.716  
|59
|1056.716  
|-
|-
|60| 1074.627  
|60
|1074.627  
|-
|-
|61| 1092.537  
|61
|1092.537  
|-
|-
|62| 1110.448  
|62
|1110.448  
|-
|-
|63| 1128.358  
|63
|1128.358  
|-
|-
|64| 1146.269  
|64
|1146.269  
|-
|-
|65| 1164.179  
|65
|1164.179  
|-
|-
|66| 1182.090  
|66
|1182.090  
|-
|-
|67| 1200.000
|67
|1200.000
|}
|}


Revision as of 02:31, 19 May 2023

← 66edo 67edo 68edo →
Prime factorization 67 (prime)
Step size 17.9104 ¢ 
Fifth 39\67 (698.507 ¢)
Semitones (A1:m2) 5:6 (89.55 ¢ : 107.5 ¢)
Consistency limit 3
Distinct consistency limit 3

Template:EDO intro

Theory

67edo tempers out 81/80, supporting meantone temperament, with a tuning which is approximately 1/6 comma (the tuning favored by Mozart and contemporaries), or 0.16 comma, meantone. In the 7-limit the patent val tempers out 1029/1024 and 1728/1715, so that it supports mothra temperament. In the 11-limit it tempers out 176/175 and 540/539, supporting mosura, an alternative 11-limit mothra. In the 13-limit it tempers out 144/143 and 196/195, supporting 13-limit mosura. It tempers out the orgonisma, and on the 2.7.11 subgroup it supports orgone temperament.

A promising tuning which has, as many relatively large equal temperaments do, a variety of tonal resources: it is the first edo to have both meantone (26 could be called meantone, but it's more of a flattone) and an orgone temperament. It has relatively good approximations of the 3rd, 7th, 11th, 13th, 15th, 17th harmonics, although the 5th, 9th, and 19th as well as certain higher ones are workable as well. 33+34 can be used to construct this temperament explaining some of its properties. It does well on the 2.3.7.11.13.17.23.31.37.41 subgroup.

67edo is the 19th prime EDO.

Prime harmonics

Script error: No such module "primes_in_edo".

Music

Beginning of a piece in 67 tone, Peter Kosmorsky [dead link]

Intervals

Tables

Degrees Cents
0 0.000
1 17.910
2 35.821
3 53.731
4 71.642
5 89.552
6 107.463
7 125.373
8 143.284
9 161.194
10 179.104
11 197.015
12 214.925
13 232.836
14 250.746
15 268.657
16 286.567
17 304.478
18 322.388
19 340.299
20 358.209
21 376.119
22 394.030
23 411.940
24 429.851
25 447.761
26 465.672
27 483.582
28 501.493
29 519.403
30 537.313
31 555.224
32 573.134
33 591.045
34 608.955
35 626.866
36 644.776
37 662.687
38 680.597
39 698.507
40 716.418
41 734.328
42 752.239
43 770.149
44 788.060
45 805.970
46 823.881
47 841.791
48 859.701
49 877.612
50 895.522
51 913.433
52 931.343
53 949.254
54 967.164
55 985.075
56 1002.985
57 1020.896
58 1038.806
59 1056.716
60 1074.627
61 1092.537
62 1110.448
63 1128.358
64 1146.269
65 1164.179
66 1182.090
67 1200.000
Retrieved from "https://en.xen.wiki/index.php?title=67edo&oldid=113638"