30edf: Difference between revisions

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{{Infobox ET}}
{{todo|improve synopsis|text=Make the synopsis longer, add a couple paragraphs about the practical music making properties of the tuning}}
'''30EDF''' is the [[EDF|equal division of the just perfect fifth]] into 30 parts of 23.3985 [[cent|cents]] each, corresponding to 51.2853 [[edo]] (practically identical to every seventh step of [[359edo]]).
'''30EDF''' is the [[EDF|equal division of the just perfect fifth]] into 30 parts of 23.3985 [[cent|cents]] each, corresponding to 51.2853 [[edo]] (practically identical to every seventh step of [[359edo]]).
==Harmonics==
{{Harmonics in equal|30|3|2|intervals=prime}}
{{Harmonics in equal|30|3|2|intervals=prime|start=12|collapsed=1}}


==Intervals==
==Intervals==
{| class="wikitable"
{| class="wikitable mw-collapsible"
|+ Intervals of 30edf
|-
|-
! | degree
! | degree
Line 9: Line 16:
! | comments
! | comments
|-
|-
| | 0
| colspan="2"| 0
| | 0.0000
| | '''exact [[1/1]]'''
| | '''exact [[1/1]]'''
| |  
| |  
Line 20: Line 26:
|-
|-
| | 2
| | 2
| | 46.7970
| | 46.797
| | 77/75
| | 77/75
| |  
| |  
Line 30: Line 36:
|-
|-
| | 4
| | 4
| | 93.5940
| | 93.594
| | [[19/18]]
| | [[19/18]]
| |  
| |  
Line 40: Line 46:
|-
|-
| | 6
| | 6
| | 140.3910
| | 140.391
| | [[13/12]]
| | [[13/12]]
| |  
| |  
Line 50: Line 56:
|-
|-
| | 8
| | 8
| | 187.1880
| | 187.188
| | 39/35
| | 39/35
| |  
| |  
Line 60: Line 66:
|-
|-
| | 10
| | 10
| | 233.9850
| | 233.985
| | [[8/7]]
| | [[8/7]]
| |  
| |  
Line 70: Line 76:
|-
|-
| | 12
| | 12
| | 280.7820
| | 280.782
| | [[20/17]]
| | [[20/17]]
| |  
| |  
Line 80: Line 86:
|-
|-
| | 14
| | 14
| | 327.5790
| | 327.579
| | 29/24
| | 29/24
| |  
| |  
Line 90: Line 96:
|-
|-
| | 16
| | 16
| | 374.3760
| | 374.376
| | 36/29
| | 36/29
| |  
| |  
Line 100: Line 106:
|-
|-
| | 18
| | 18
| | 421.1730
| | 421.173
| | [[51/40]]
| | [[51/40]]
| |  
| |  
Line 110: Line 116:
|-
|-
| | 20
| | 20
| | 467.9700
| | 467.97
| | [[21/16]]
| | [[21/16]]
| |  
| |  
Line 120: Line 126:
|-
|-
| | 22
| | 22
| | 514.7670
| | 514.767
| | 35/26
| | 35/26
| |  
| |  
Line 130: Line 136:
|-
|-
| | 24
| | 24
| | 561.5640
| | 561.564
| | [[18/13]]
| | [[18/13]]
| |  
| |  
Line 140: Line 146:
|-
|-
| | 26
| | 26
| | 608.3610
| | 608.361
| | 27/19
| | 27/19
| |  
| |  
Line 150: Line 156:
|-
|-
| | 28
| | 28
| | 655.1580
| | 655.158
| |  
| |  
| |  
| |  
Line 156: Line 162:
| | 29
| | 29
| | 678.5565
| | 678.5565
| |  
| |40/27
| |  
| |  
|-
|-
| | 30
| | 30
| | 701.9550
| | 701.955
| | '''exact [[3/2]]'''
| | '''exact [[3/2]]'''
| | just perfect fifth
| | just perfect fifth
|-
|31
|725.3535
|38/25
|
|-
|32
|748.752
|77/50
|
|-
|33
|772.1505
|25/16
|
|-
|34
|795.549
|19/12
|
|-
|35
|818.9475
|45/28
|
|-
|36
|842.346
|13/8
|
|-
|37
|865.7445
|33/20
|
|-
|38
|889.143
|117/70
|
|-
|39
|912.8415
|105/62
|
|-
|40
|935.94
|12/7
|
|-
|41
|959.3385
|87/50
|
|-
|42
|982.737
|30/17
|
|-
|43
|1006.1355
|93/52
|
|-
|44
|1028.534
|29/16
|
|-
|45
|1052.9325
|90/49, 147/80
|
|-
|46
|1076.331
|48/29
|
|-
|47
|1099.6995
|117/62
|
|-
|48
|1123.128
|153/80
|
|-
|49
|1146.5165
|
|
|-
|50
|1169.925
|63/32
|
|-
|51
|1193.3435
|
|
|-
|52
|1215.722
|105/52
|
|-
|53
|1240.1205
|45/22
|
|-
|54
|1263.519
|27/13
|
|-
|55
|1286.9175
|21/10
|
|-
|56
|1310.316
|81/38
|
|-
|57
|1333.7145
|54/25
|
|-
|58
|1357.113
|
|
|-
|59
|1380.5115
|20/9
|
|-
|60
|1403.91
|'''exact''' 9/4
|
|}
|}
[[Category:Edf]]
[[Category:Edonoi]]

Latest revision as of 19:21, 1 August 2025

← 29edf 30edf 31edf →
Prime factorization 2 × 3 × 5
Step size 23.3985 ¢ 
Octave 51\30edf (1193.32 ¢) (→ 17\10edf)
Twelfth 81\30edf (1895.28 ¢) (→ 27\10edf)
Consistency limit 3
Distinct consistency limit 3

30EDF is the equal division of the just perfect fifth into 30 parts of 23.3985 cents each, corresponding to 51.2853 edo (practically identical to every seventh step of 359edo).

Harmonics

Approximation of prime harmonics in 30edf
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) -6.7 -6.7 -1.9 +0.6 -9.8 +5.2 +8.7 +3.4 +0.2 -3.4 -1.8
Relative (%) -28.5 -28.5 -8.1 +2.4 -41.8 +22.2 +37.3 +14.4 +0.8 -14.3 -7.8
Steps
(reduced) 		51
(21) 		81
(21) 		119
(29) 		144
(24) 		177
(27) 		190
(10) 		210
(0) 		218
(8) 		232
(22) 		249
(9) 		254
(14)
Approximation of prime harmonics in 30edf
Harmonic 37 41 43 47 53 59 61 67 71 73 79
Error Absolute (¢) -3.9 +5.5 -6.7 +3.1 +5.7 +7.2 -3.7 -2.4 -9.2 -10.5 -6.8
Relative (%) -16.9 +23.6 -28.8 +13.1 +24.2 +30.7 -16.0 -10.1 -39.2 -44.7 -29.2
Steps
(reduced) 		267
(27) 		275
(5) 		278
(8) 		285
(15) 		294
(24) 		302
(2) 		304
(4) 		311
(11) 		315
(15) 		317
(17) 		323
(23)

Intervals

Intervals of 30edf
degree cents value corresponding
JI intervals 		comments
0 exact 1/1
1 23.3985 76/75
2 46.797 77/75
3 70.1955 25/24
4 93.594 19/18
5 116.9925 15/14
6 140.391 13/12
7 163.7895 11/10
8 187.188 39/35
9 210.5865 35/31
10 233.985 8/7
11 257.3835 29/25
12 280.782 20/17
13 304.1805 31/26
14 327.579 29/24
15 350.9775 60/49, 49/40
16 374.376 36/29
17 397.7745 39/31
18 421.173 51/40
19 444.5715
20 467.97 21/16
21 491.3685
22 514.767 35/26
23 538.1655 15/11
24 561.564 18/13
25 584.9625 7/5
26 608.361 27/19
27 631.7595 36/25
28 655.158
29 678.5565 40/27
30 701.955 exact 3/2 just perfect fifth
31 725.3535 38/25
32 748.752 77/50
33 772.1505 25/16
34 795.549 19/12
35 818.9475 45/28
36 842.346 13/8
37 865.7445 33/20
38 889.143 117/70
39 912.8415 105/62
40 935.94 12/7
41 959.3385 87/50
42 982.737 30/17
43 1006.1355 93/52
44 1028.534 29/16
45 1052.9325 90/49, 147/80
46 1076.331 48/29
47 1099.6995 117/62
48 1123.128 153/80
49 1146.5165
50 1169.925 63/32
51 1193.3435
52 1215.722 105/52
53 1240.1205 45/22
54 1263.519 27/13
55 1286.9175 21/10
56 1310.316 81/38
57 1333.7145 54/25
58 1357.113
59 1380.5115 20/9
60 1403.91 exact 9/4
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