39edf: Difference between revisions

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{{Infobox ET}}
'''39EDF''' is the [[EDF|equal division of the just perfect fifth]] into 39 parts of 17.9988 [[cent|cents]] each, corresponding to 66.6709 [[edo]]. It is nearly identical to every third step of [[200edo]].
'''39EDF''' is the [[EDF|equal division of the just perfect fifth]] into 39 parts of 17.9988 [[cent|cents]] each, corresponding to 66.6709 [[edo]]. It is nearly identical to every third step of [[200edo]].
== Harmonics ==
{{Harmonics in equal|39|3|2}}
{{Harmonics in equal|39|3|2|start=12|collapsed=1}}


==Intervals==
==Intervals==
{| class="wikitable"
{| class="wikitable mw-collapsible"
|+ Intervals of 39edf
|-
|-
! | degree
! | degree
Line 9: Line 15:
! | comments
! | comments
|-
|-
| | 0
| colspan="2"| 0
| | 0.0000
| | '''exact [[1/1]]'''
| | '''exact [[1/1]]'''
| |  
| |  
Line 41: Line 46:
| | 6
| | 6
| | 107.9931
| | 107.9931
| |  
| |16/15
| |  
| |  
|-
|-
Line 61: Line 66:
| | 10
| | 10
| | 179.9885
| | 179.9885
| |  
| |10/9
| |  
| |  
|-
|-
Line 75: Line 80:
|-
|-
| | 13
| | 13
| | 233.9850
| | 233.985
| |  
| |8/7
| |  
| |  
|-
|-
Line 86: Line 91:
| | 15
| | 15
| | 269.9827
| | 269.9827
| |  
| |7/6
| |  
| |  
|-
|-
Line 101: Line 106:
| | 18
| | 18
| | 323.9792
| | 323.9792
| |  
| |6/5
| | pseudo-[[6/5]]
| |
|-
|-
| | 19
| | 19
Line 117: Line 122:
| | 377.9758
| | 377.9758
| |  
| |  
| | pseudo-[[5/4]]
| | lower pseudo-[[5/4]]
|-
|-
| | 22
| | 22
| | 395.9746
| | 395.9746
| |  
| |  
| |  
| |upper pseudo-[[5/4]]
|-
|-
| | 23
| | 23
Line 131: Line 136:
| | 24
| | 24
| | 431.9723
| | 431.9723
| |  
| |9/7
| |  
| |  
|-
|-
Line 140: Line 145:
|-
|-
| | 26
| | 26
| | 467.9700
| | 467.97
| |  
| |  
| |  
| |  
Line 151: Line 156:
| | 28
| | 28
| | 503.9677
| | 503.9677
| |  
| |4/3
| | pseudo-[[4/3]]
| |
|-
|-
| | 29
| | 29
| | 521.9665
| | 521.9665
| |  
| |27/20
| |  
| |  
|-
|-
Line 181: Line 186:
| | 34
| | 34
| | 611.9608
| | 611.9608
| |  
| |64/45
| |  
| |  
|-
|-
Line 192: Line 197:
| | 647.9585
| | 647.9585
| | [[16/11]]
| | [[16/11]]
| |  
| |pseudo-36/25
|-
|-
| | 37
| | 37
Line 201: Line 206:
| | 38
| | 38
| | 683.9562
| | 683.9562
| | 95/64, 49/33
| | 95/64, 49/33, 297/200, 40/27
| |  
| |  
|-
|-
| | 39
| | 39
| | 701.9550
| | 701.955
| | '''exact [[3/2]]'''
| | '''exact [[3/2]]'''
| | just perfect fifth
| | just perfect fifth
|-
|40
|720.9388
|50/33, 297/196, 144/95
|
|-
|41
|737.9527
|75/49, 49/32
|
|-
|42
|755.9515
|99/64
|
|-
|43
|773.9504
|25/16, 36/23
|
|-
|44
|791.9492
|
|
|-
|45
|809.9481
|8/5
|
|-
|46
|827.9469
|
|
|-
|47
|845.9458
|75/46
|
|-
|48
|863.9446
|
|
|-
|49
|881.9435
|5/3
|
|-
|50
|899.9423
|
|
|-
|51
|917.9412
|17/10
|
|-
|52
|935.94
|12/7
|
|-
|53
|954.9388
|
|
|-
|54
|971.9377
|7/4
|
|-
|55
|989.9365
|39/22
|
|-
|56
|1007.9354
|34/19
|
|-
|57
|1025.9342
|9/5
|
|-
|58
|1043.9331
|117/64
|
|-
|59
|1061.9319
|24/13
|
|-
|60
|1079.9308
|
|lower pseudo-15/8
|-
|61
|1097.9296
|
|upper pseudo-15/8
|-
|62
|1115.9285
|99/52
|
|-
|63
|1134.9273
|27/14
|
|-
|64
|1151.9261
|
|
|-
|65
|1169.925
|49/25
|
|-
|66
|1187.9238
|135/68
|
|-
|67
|1205.9227
|2/1
|
|-
|68
|1223.9215
|81/40
|
|-
|69
|1241.9204
|
|
|-
|70
|1259.9192
|
|
|-
|71
|1277.9181
|
|
|-
|72
|1295.9169
|
|
|-
|73
|1313.9158
|32/15
|
|-
|74
|1331.9146
|69/32, 54/25
|
|-
|75
|1349.9135
|24/11
|pseudo-54/25
|-
|76
|1367.9123
|108/49
|
|-
|77
|1385.9112
|285/128, 49/22, 891/400, 20/9
|
|-
|78
|1403.91
|'''exact''' 9/4
|
|}
|}


[[Category:Edf]]
{{todo|expand}}
[[Category:Edonoi]]

Latest revision as of 19:22, 1 August 2025

← 38edf 39edf 40edf →
Prime factorization 3 × 13
Step size 17.9988 ¢ 
Octave 67\39edf (1205.92 ¢)
Twelfth 106\39edf (1907.88 ¢)
Consistency limit 3
Distinct consistency limit 3

39EDF is the equal division of the just perfect fifth into 39 parts of 17.9988 cents each, corresponding to 66.6709 edo. It is nearly identical to every third step of 200edo.

Harmonics

Approximation of harmonics in 39edf
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +5.92 +5.92 -6.15 +3.51 -6.15 -3.04 -0.23 -6.15 -8.57 +6.42 -0.23
Relative (%) +32.9 +32.9 -34.2 +19.5 -34.2 -16.9 -1.3 -34.2 -47.6 +35.6 -1.3
Steps
(reduced) 		67
(28) 		106
(28) 		133
(16) 		155
(38) 		172
(16) 		187
(31) 		200
(5) 		211
(16) 		221
(26) 		231
(36) 		239
(5)
Approximation of harmonics in 39edf
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +5.19 +2.88 -8.57 +5.69 +8.73 -0.23 -3.84 -2.65 +2.88 -5.66 +7.38
Relative (%) +28.8 +16.0 -47.6 +31.6 +48.5 -1.3 -21.3 -14.7 +16.0 -31.4 +41.0
Steps
(reduced) 		247
(13) 		254
(20) 		260
(26) 		267
(33) 		273
(0) 		278
(5) 		283
(10) 		288
(15) 		293
(20) 		297
(24) 		302
(29)

Intervals

Intervals of 39edf
degree cents value corresponding
JI intervals 		comments
0 exact 1/1
1 17.9988 100/99, 99/98, 96/95
2 35.9977 50/49, 49/48
3 53.9965 33/32
4 71.9954 (25/24), (24/23)
5 89.9942
6 107.9931 16/15
7 125.9919
8 143.9908 25/23
9 161.9896
10 179.9885 10/9
11 197.9873
12 215.9862 17/15
13 233.985 8/7
14 251.9838
15 269.9827 7/6
16 287.9815 13/11
17 305.9804 68/57
18 323.9792 6/5
19 341.9781 39/32
20 359.9769 16/13
21 377.9758 lower pseudo-5/4
22 395.9746 upper pseudo-5/4
23 413.9735 33/26
24 431.9723 9/7
25 449.9712
26 467.97
27 485.9688 45/34
28 503.9677 4/3
29 521.9665 27/20
30 539.9654
31 557.9642
32 575.9631
33 593.9619
34 611.9608 64/45
35 629.9596 (23/16), (36/25)
36 647.9585 16/11 pseudo-36/25
37 665.9573 72/49
38 683.9562 95/64, 49/33, 297/200, 40/27
39 701.955 exact 3/2 just perfect fifth
40 720.9388 50/33, 297/196, 144/95
41 737.9527 75/49, 49/32
42 755.9515 99/64
43 773.9504 25/16, 36/23
44 791.9492
45 809.9481 8/5
46 827.9469
47 845.9458 75/46
48 863.9446
49 881.9435 5/3
50 899.9423
51 917.9412 17/10
52 935.94 12/7
53 954.9388
54 971.9377 7/4
55 989.9365 39/22
56 1007.9354 34/19
57 1025.9342 9/5
58 1043.9331 117/64
59 1061.9319 24/13
60 1079.9308 lower pseudo-15/8
61 1097.9296 upper pseudo-15/8
62 1115.9285 99/52
63 1134.9273 27/14
64 1151.9261
65 1169.925 49/25
66 1187.9238 135/68
67 1205.9227 2/1
68 1223.9215 81/40
69 1241.9204
70 1259.9192
71 1277.9181
72 1295.9169
73 1313.9158 32/15
74 1331.9146 69/32, 54/25
75 1349.9135 24/11 pseudo-54/25
76 1367.9123 108/49
77 1385.9112 285/128, 49/22, 891/400, 20/9
78 1403.91 exact 9/4
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