36edf: Difference between revisions

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'''36EDF''' is the [[EDF|equal division of the just perfect fifth]] into 36 parts of 19.4988 [[cent|cents]] each, corresponding to 61.5424 [[edo]].
{{Infobox ET}}{{todo|improve synopsis}}
'''36EDF''' is the [[EDF|equal division of the just perfect fifth]] into 36 parts of 19.49875 [[cent|cents]] each, corresponding to 61.5424 [[edo]].
 
==Harmonics==
{{Harmonics in equal|36|3|2}}
{{Harmonics in equal|36|3|2|start=12|collapsed=1}}


==Intervals==
==Intervals==
{| class="wikitable"
{| class="wikitable mw-collapsible"
|+ Intervals in 36edf
|-
|-
! | degree
! | degree
Line 9: Line 15:
! | comments
! | comments
|-
|-
| | 0
| colspan="2"| 0
| | 0.0000
| | '''exact [[1/1]]'''
| | '''exact [[1/1]]'''
| |  
| |  
|-
|-
| | 1
| | 1
| | 19.4988
| | 19.49875
| | 90/89, 89/88
| | 90/89, 89/88
| |  
| |  
Line 25: Line 30:
|-
|-
| | 3
| | 3
| | 58.4963
| | 58.49625
| | 30/29
| | 30/29
| |  
| |  
|-
|-
| | 4
| | 4
| | 77.9950
| | 77.995
| |  
| |  
| |  
| |  
|-
|-
| | 5
| | 5
| | 97.4938
| | 97.49375
| | 73/69
| | 73/69
| |  
| |  
Line 45: Line 50:
|-
|-
| | 7
| | 7
| | 136.4913
| | 136.49125
| |  
| |  
| |  
| |  
|-
|-
| | 8
| | 8
| | 155.9900
| | 155.99
| |  
| |  
| |  
| |  
|-
|-
| | 9
| | 9
| | 175.4888
| | 175.48875
| | 135/122
| | 135/122
| |  
| |  
Line 65: Line 70:
|-
|-
| | 11
| | 11
| | 214.4863
| | 214.48625
| | 60/53
| | 60/53
| |  
| |  
|-
|-
| | 12
| | 12
| | 233.9850
| | 233.985
| | 87/76
| | 8/7
| |  
| |  
|-
|-
| | 13
| | 13
| | 253.4838
| | 253.48375
| | [[22/19]]
| | [[22/19]]
| |  
| |  
Line 85: Line 90:
|-
|-
| | 15
| | 15
| | 292.4813
| | 292.48125
| |  
| |32/27
| |  
| |  
|-
|-
| | 16
| | 16
| | 311.9800
| | 311.98
| |  
| | 6/5
| |  
| |  
|-
|-
| | 17
| | 17
| | 331.4788
| | 331.47875
| | 109/90
| |110/89
| |  
| |  
|-
|-
| | 18
| | 18
| | 350.9775
| | 350.9775
| | 109/89
| |11/9
| |  
| |  
|-
|-
| | 19
| | 19
| | 370.4763
| | 370.47625
| |  
| |  
| |  
| |  
|-
|-
| | 20
| | 20
| | 389.9750
| | 389.975
| |  
| | 5/4
| |  
| |  
|-
|-
| | 21
| | 21
| | 409.4738
| | 409.47375
| |  
| |  
| |  
| |  
Line 125: Line 130:
|-
|-
| | 23
| | 23
| | 448.4713
| | 448.47125
| | 57/44
| | 57/44
| |  
| |  
|-
|-
| | 24
| | 24
| | 467.9700
| | 467.97
| | 38/29
| | 38/29
| |  
| |  
|-
|-
| | 25
| | 25
| | 487.4688
| | 487.46875
| | 53/40
| | 53/40
| |  
| |  
Line 141: Line 146:
| | 26
| | 26
| | 506.9675
| | 506.9675
| | 729/544
| |243/181
| |  
| |  
|-
|-
| | 27
| | 27
| | 526.4663
| | 526.46625
| | 61/45
| | 61/45
| |  
| |  
|-
|-
| | 28
| | 28
| | 545.9650
| | 545.965
| |  
| |  
| |  
| |  
|-
|-
| | 29
| | 29
| | 565.4638
| | 565.46375
| |  
| |  
| |  
| |  
Line 165: Line 170:
|-
|-
| | 31
| | 31
| | 604.4613
| | 604.46125
| |  
| |24/17
| |  
| |  
|-
|-
| | 32
| | 32
| | 623.9600
| | 623.96
| |  
| |  
| |  
| |  
|-
|-
| | 33
| | 33
| | 643.4588
| | 643.45875
| | 29/20
| | 29/20
| |  
| |  
Line 185: Line 190:
|-
|-
| | 35
| | 35
| | 682.4563
| | 682.45625
| | 89/60
| |40/27
| |  
| |  
|-
|-
| | 36
| | 36
| | 701.9550
| | 701.955
| | '''exact [[3/2]]'''
| | '''exact [[3/2]]'''
| | just perfect fifth
| | just perfect fifth
|-
|37
|721.45375
|135/89, 267/176
|
|-
|38
|740.4525
|135/88
|
|-
|39
|760.45125
|42/59
|
|-
|40
|779.95
|
|
|-
|41
|799.44875
|73/46
|
|-
|42
|818.9475
|
|
|-
|43
|838.44625
|
|
|-
|44
|857.945
|
|
|-
|45
|877.44375
|405/244
|
|-
|46
|896.9425
|136/81
|
|-
|47
|916.44125
|90/53
|
|-
|48
|935.94
|12/7
|
|-
|49
|955.43875
|33/19
|
|-
|50
|974.9375
|72/41
|
|-
|51
|996.43625
|16/9
|
|-
|52
|1013.935
|9/5
|
|-
|53
|1032.43375
|165/89
|
|-
|54
|1052.9325
|11/6
|
|-
|55
|1072.43125
|
|
|-
|56
|1091.93
|15/8
|
|-
|57
|1110.92875
|
|
|-
|58
|1130.9275
|123/64
|
|-
|59
|1150.92625
|171/88
|
|-
|60
|1169.925
|57/29
|
|-
|61
|1189.42375
|159/80
|
|-
|62
|1208.9225
|729/362
|
|-
|63
|1228.42125
|61/30
|
|-
|64
|1247.92
|
|
|-
|65
|1267.41875
|
|
|-
|66
|1286.9175
|
|
|-
|67
|1306.41625
|36/17
|
|-
|68
|1325.915
|
|
|-
|69
|1345.41375
|87/40
|
|-
|70
|1364.9125
|11/5
|
|-
|71
|1384.41125
|20/9
|
|-
|72
|1403.91
|'''exact''' 9/4
|
|}
|}
[[Category:Edf]]
[[Category:Edonoi]]

Latest revision as of 19:21, 1 August 2025

← 35edf 36edf 37edf →
Prime factorization 22 × 32
Step size 19.4988 ¢ 
Octave 62\36edf (1208.92 ¢) (→ 31\18edf)
Twelfth 98\36edf (1910.88 ¢) (→ 49\18edf)
Consistency limit 3
Distinct consistency limit 3
Special properties

36EDF is the equal division of the just perfect fifth into 36 parts of 19.49875 cents each, corresponding to 61.5424 edo.

Harmonics

Approximation of harmonics in 36edf
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +8.92 +8.92 -1.65 +2.01 -1.65 +4.46 +7.27 -1.65 -8.57 +1.92 +7.27
Relative (%) +45.8 +45.8 -8.5 +10.3 -8.5 +22.9 +37.3 -8.5 -43.9 +9.8 +37.3
Steps
(reduced) 		62
(26) 		98
(26) 		123
(15) 		143
(35) 		159
(15) 		173
(29) 		185
(5) 		195
(15) 		204
(24) 		213
(33) 		221
(5)
Approximation of harmonics in 36edf
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +5.19 -6.12 -8.57 -3.31 +8.73 +7.27 -8.34 +0.35 -6.12 -8.66 -7.62
Relative (%) +26.6 -31.4 -43.9 -17.0 +44.8 +37.3 -42.8 +1.8 -31.4 -44.4 -39.1
Steps
(reduced) 		228
(12) 		234
(18) 		240
(24) 		246
(30) 		252
(0) 		257
(5) 		261
(9) 		266
(14) 		270
(18) 		274
(22) 		278
(26)

Intervals

Intervals in 36edf
degree cents value corresponding
JI intervals 		comments
0 exact 1/1
1 19.49875 90/89, 89/88
2 38.9975 45/44
3 58.49625 30/29
4 77.995
5 97.49375 73/69
6 116.9925
7 136.49125
8 155.99
9 175.48875 135/122
10 194.9875 272/243
11 214.48625 60/53
12 233.985 8/7
13 253.48375 22/19
14 272.9825 48/41
15 292.48125 32/27
16 311.98 6/5
17 331.47875 110/89
18 350.9775 11/9
19 370.47625
20 389.975 5/4
21 409.47375
22 428.9725 41/32
23 448.47125 57/44
24 467.97 38/29
25 487.46875 53/40
26 506.9675 243/181
27 526.46625 61/45
28 545.965
29 565.46375
30 584.9625
31 604.46125 24/17
32 623.96
33 643.45875 29/20
34 662.9575 22/15
35 682.45625 40/27
36 701.955 exact 3/2 just perfect fifth
37 721.45375 135/89, 267/176
38 740.4525 135/88
39 760.45125 42/59
40 779.95
41 799.44875 73/46
42 818.9475
43 838.44625
44 857.945
45 877.44375 405/244
46 896.9425 136/81
47 916.44125 90/53
48 935.94 12/7
49 955.43875 33/19
50 974.9375 72/41
51 996.43625 16/9
52 1013.935 9/5
53 1032.43375 165/89
54 1052.9325 11/6
55 1072.43125
56 1091.93 15/8
57 1110.92875
58 1130.9275 123/64
59 1150.92625 171/88
60 1169.925 57/29
61 1189.42375 159/80
62 1208.9225 729/362
63 1228.42125 61/30
64 1247.92
65 1267.41875
66 1286.9175
67 1306.41625 36/17
68 1325.915
69 1345.41375 87/40
70 1364.9125 11/5
71 1384.41125 20/9
72 1403.91 exact 9/4
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