38edf: Difference between revisions

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'''[[EDF|Division of the just perfect fifth]] into 38 equal parts''' (38EDF) is related to [[65edo|65 edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 0.7125 cents stretched and the step size is about 18.4725 cents.
{{Infobox ET}}
'''[[EDF|Division of the just perfect fifth]] into 38 equal parts''' (38EDF) is related to [[65edo]], but with the [[3/2]] rather than the [[2/1]] being [[just]]. The [[octave]] is [[Octave stretch|stretched]] by about 0.7125 [[cents]] and the step size is about 18.4725 cents.


Lookalikes: [[65edo]], [[103edt]]
Lookalikes: [[65edo]], [[103edt]]


[[Category:Edf]]
== Harmonics ==
[[Category:Edonoi]]
{{Harmonics in equal|38|3|2|intervals=prime}}
 
== Intervals ==
{| class="wikitable mw-collapsible"
|+ Intervals of 38edf
|-
! Step number
! Cents value
|-
| style="text-align:center;" |1
| style="text-align:right;" |18.4725
|-
| style="text-align:center;" |2
| style="text-align:right;" |36.945
|-
| style="text-align:center;" |3
| style="text-align:right;" |55.4175
|-
| style="text-align:center;" |4
| style="text-align:right;" |73.89
|-
| style="text-align:center;" |5
| style="text-align:right;" |92.3625
|-
| style="text-align:center;" |6
| style="text-align:right;" |110.835
|-
| style="text-align:center;" |7
| style="text-align:right;" |129.3075
|-
| style="text-align:center;" |8
| style="text-align:right;" |147.78
|-
| style="text-align:center;" |9
| style="text-align:right;" |166.2525
|-
| style="text-align:center;" |10
| style="text-align:right;" |184.725
|-
| style="text-align:center;" |11
| style="text-align:right;" |203.1975
|-
| style="text-align:center;" |12
| style="text-align:right;" |221.67
|-
| style="text-align:center;" |13
| style="text-align:right;" |240.1425
|-
| style="text-align:center;" |14
| style="text-align:right;" |258.615
|-
| style="text-align:center;" |15
| style="text-align:right;" |277.0875
|-
| style="text-align:center;" |16
| style="text-align:right;" |295.56
|-
| style="text-align:center;" |17
| style="text-align:right;" |314.0325
|-
| style="text-align:center;" |18
| style="text-align:right;" |332.505
|-
| style="text-align:center;" |19
| style="text-align:right;" |350.9775
|-
| style="text-align:center;" |20
| style="text-align:right;" |369.45
|-
| style="text-align:center;" |21
| style="text-align:right;" |387.9225
|-
| style="text-align:center;" |22
| style="text-align:right;" |406.395
|-
| style="text-align:center;" |23
| style="text-align:right;" |424.8675
|-
| style="text-align:center;" |24
| style="text-align:right;" |443.34
|-
| style="text-align:center;" |25
| style="text-align:right;" |461.8125
|-
| style="text-align:center;" |26
| style="text-align:right;" |480.285
|-
| style="text-align:center;" |27
| style="text-align:right;" |498.7575
|-
| style="text-align:center;" |28
| style="text-align:right;" |517.23
|-
| style="text-align:center;" |29
| style="text-align:right;" |535.7025
|-
| style="text-align:center;" |30
| style="text-align:right;" |553.175
|-
| style="text-align:center;" |31
| style="text-align:right;" |572.6475
|-
| style="text-align:center;" |32
| style="text-align:right;" |591.12
|-
| style="text-align:center;" |33
| style="text-align:right;" |609.5925
|-
| style="text-align:center;" |34
| style="text-align:right;" |628.065
|-
| style="text-align:center;" |35
| style="text-align:right;" |646.5375
|-
| style="text-align:center;" |36
| style="text-align:right;" |664.01
|-
| style="text-align:center;" |37
| style="text-align:right;" |683.4825
|-
| style="text-align:center;" |38
| style="text-align:right;" |701.955
|-
| style="text-align:center;" |39
| style="text-align:right;" |720.4275
|-
| style="text-align:center;" |40
| style="text-align:right;" |738.9
|-
| style="text-align:center;" |41
| style="text-align:right;" |757.3725
|-
| style="text-align:center;" |42
| style="text-align:right;" |775.845
|-
| style="text-align:center;" |43
| style="text-align:right;" |794.3175
|-
| style="text-align:center;" |44
| style="text-align:right;" |812.79
|-
| style="text-align:center;" |45
| style="text-align:right;" |831.2625
|-
| style="text-align:center;" |46
| style="text-align:right;" |849.735
|-
| style="text-align:center;" |47
| style="text-align:right;" |868.2075
|-
| style="text-align:center;" |48
| style="text-align:right;" |886.605
|-
| style="text-align:center;" |49
| style="text-align:right;" |905.1525
|-
| style="text-align:center;" |50
| style="text-align:right;" |923.625
|-
| style="text-align:center;" |51
| style="text-align:right;" |942.0975
|-
| style="text-align:center;" |52
| style="text-align:right;" |960.57
|-
| style="text-align:center;" |53
| style="text-align:right;" |979.0425
|-
| style="text-align:center;" |54
| style="text-align:right;" |997.515
|-
| style="text-align:center;" |55
| style="text-align:right;" |1015.9875
|-
| style="text-align:center;" |56
| style="text-align:right;" |1034.46
|-
| style="text-align:center;" |57
| style="text-align:right;" |1052.9235
|-
| style="text-align:center;" |58
| style="text-align:right;" |1071.405
|-
| style="text-align:center;" |59
| style="text-align:right;" |1089.8775
|-
| style="text-align:center;" |60
| style="text-align:right;" |1108.35
|-
| style="text-align:center;" |61
| style="text-align:right;" |1126.8225
|-
| style="text-align:center;" |62
| style="text-align:right;" |1145.295
|-
| style="text-align:center;" |63
| style="text-align:right;" |1163.7675
|-
| style="text-align:center;" |64
| style="text-align:right;" |1182.24
|-
| style="text-align:center;" |65
| style="text-align:right;" |1200.7125
|-
| style="text-align:center;" | 66
| style="text-align:right;" | 1219.185
|-
| style="text-align:center;" | 67
| style="text-align:right;" | 1237.6575
|-
| style="text-align:center;" | 68
| style="text-align:right;" | 1256.13
|-
| style="text-align:center;" | 69
| style="text-align:right;" | 1274.6025
|-
| style="text-align:center;" | 70
| style="text-align:right;" | 1293.075
|-
| style="text-align:center;" | 71
| style="text-align:right;" | 1311.5775
|-
| style="text-align:center;" | 72
| style="text-align:right;" | 1330.02
|-
| style="text-align:center;" | 73
| style="text-align:right;" | 1348.4925
|-
| style="text-align:center;" | 74
| style="text-align:right;" | 1366.965
|-
| style="text-align:center;" | 75
| style="text-align:right;" | 1385.4375
|-
| style="text-align:center;" | 76
| style="text-align:right;" | 1403.91
|}
 
{{todo|inline=1|complete table|text=Add a third column that comments on the intervals, either what [[JI]] they approximate, what they are named, or how they can be used musically.}}
 
 
{{todo|expand}}

Latest revision as of 19:21, 1 August 2025

← 37edf 38edf 39edf →
Prime factorization 2 × 19
Step size 18.4725 ¢ 
Octave 65\38edf (1200.71 ¢)
Twelfth 103\38edf (1902.67 ¢)
Consistency limit 6
Distinct consistency limit 6

Division of the just perfect fifth into 38 equal parts (38EDF) is related to 65edo, but with the 3/2 rather than the 2/1 being just. The octave is stretched by about 0.7125 cents and the step size is about 18.4725 cents.

Lookalikes: 65edo, 103edt

Harmonics

Approximation of prime harmonics in 38edf
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.71 +0.71 +3.03 -6.83 +4.99 -7.13 +8.73 +0.90 +2.64 +7.73 +3.11
Relative (%) +3.9 +3.9 +16.4 -37.0 +27.0 -38.6 +47.3 +4.9 +14.3 +41.9 +16.8
Steps
(reduced) 		65
(27) 		103
(27) 		151
(37) 		182
(30) 		225
(35) 		240
(12) 		266
(0) 		276
(10) 		294
(28) 		316
(12) 		322
(18)

Intervals

Intervals of 38edf
Step number Cents value
1 18.4725
2 36.945
3 55.4175
4 73.89
5 92.3625
6 110.835
7 129.3075
8 147.78
9 166.2525
10 184.725
11 203.1975
12 221.67
13 240.1425
14 258.615
15 277.0875
16 295.56
17 314.0325
18 332.505
19 350.9775
20 369.45
21 387.9225
22 406.395
23 424.8675
24 443.34
25 461.8125
26 480.285
27 498.7575
28 517.23
29 535.7025
30 553.175
31 572.6475
32 591.12
33 609.5925
34 628.065
35 646.5375
36 664.01
37 683.4825
38 701.955
39 720.4275
40 738.9
41 757.3725
42 775.845
43 794.3175
44 812.79
45 831.2625
46 849.735
47 868.2075
48 886.605
49 905.1525
50 923.625
51 942.0975
52 960.57
53 979.0425
54 997.515
55 1015.9875
56 1034.46
57 1052.9235
58 1071.405
59 1089.8775
60 1108.35
61 1126.8225
62 1145.295
63 1163.7675
64 1182.24
65 1200.7125
66 1219.185
67 1237.6575
68 1256.13
69 1274.6025
70 1293.075
71 1311.5775
72 1330.02
73 1348.4925
74 1366.965
75 1385.4375
76 1403.91
Todo: complete table

Add a third column that comments on the intervals, either what JI they approximate, what they are named, or how they can be used musically.

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