25edf: Difference between revisions

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'''25EDF''' is the [[EDF|equal division of the just perfect fifth]] into 25 parts of 28.0782 [[cent|cents]] each, corresponding to 42.7378 [[edo]] (similar to every fourth step of [[171edo]]). It is related to the regular temperament which tempers out 703125/702464 and 5250987/5242880 in the 7-limit, which is supported by [[43edo]], [[128edo]], [[171edo]], [[214edo]], [[299edo]], and [[385edo]].
{{Infobox ET}}
{{ED intro}} It corresponds to 42.7378 [[edo]] (similar to every fourth step of [[171edo]]).  
 
It is related to the regular temperament which tempers out 703125/702464 and 5250987/5242880 in the 7-limit, which is supported by [[43edo]], [[128edo]], [[171edo]], [[214edo]], [[299edo]], and [[385edo]].


Lookalikes: [[43edo]], [[68edt]]
Lookalikes: [[43edo]], [[68edt]]


==Intervals==
== Harmonics ==
{| class="wikitable"
{{Harmonics in equal|25|3|2|intervals=prime}}
{{Harmonics in equal|25|3|2|start=12|collapsed=1|intervals=prime}}
 
== Intervals ==
{| class="wikitable mw-collapsible"
|+ style="font-size: 105%;" | Intervals of 25edf
|-
! Degree
! Cents
! Corresponding<br />JI intervals
! Comments
|-
| colspan="2" | 0
| '''exact [[1/1]]'''
|
|-
| 1
| 28.0782
| 51/50
|
|-
| 2
| 56.1564
| 26/25
|
|-
| 3
| 84.2346
| [[21/20]]
|
|-
| 4
| 112.3128
| [[16/15]]
|
|-
| 5
| 140.391
| 13/12
|
|-
| 6
| 168.4692
|
|
|-
| 7
| 196.5474
| [[28/25]]
|
|-
| 8
| 224.6256
| 8/7
|
|-
| 9
| 252.7038
|
|
|-
| 10
| 280.782
| [[20/17]]
|
|-
| 11
| 308.8602
|
| pseudo-[[6/5]]
|-
| 12
| 336.9384
|
|
|-
| 13
| 365.0166
|
|
|-
| 14
| 393.0948
|
| pseudo-[[5/4]]
|-
| 15
| 421.173
| 51/40
|
|-
| 16
| 449.2512
|
|
|-
| 17
| 477.3294
|
|
|-
| 18
| 505.4076
| 75/56
| pseudo-[[4/3]]
|-
| 19
| 533.4858
|
|
|-
| 20
| 561.564
|
|
|-
| 21
| 589.6422
| [[45/32]]
|
|-
| 22
| 617.7204
| [[10/7]]
|
|-
| 23
| 645.7986
|
|
|-
|-
! | degree
| 24
! | cents value
| 673.8768
! | corresponding <br>JI intervals
|  
! | comments
|  
|-
|-
| | 0
| 25
| | 0.0000
| 701.955
| | '''exact [[1/1]]'''
| '''exact [[3/2]]'''
| |
| just perfect fifth
|-
|-
| | 1
| 26
| | 28.0782
| 730.033
| |
| 153/100
| |  
|  
|-
|-
| | 2
| 27
| | 56.1564
| 757.1114
| |
| 39/25
| |  
|  
|-
|-
| | 3
| 28
| | 84.2346
| 786.1896
| | [[21/20]]
| 63/40
| |  
|  
|-
|-
| | 4
| 29
| | 112.3128
| 814.2678
| | [[16/15]]
| 8/5
| |  
|  
|-
|-
| | 5
| 30
| | 140.3910
| 842.346
| |
| 13/8
| |  
|  
|-
|-
| | 6
| 31
| | 168.4692
| 870.2452
| |  
|  
| |  
|  
|-
|-
| | 7
| 32
| | 196.5474
| 898.5024
| | [[28/25]]
| 42/25
| |  
|  
|-
|-
| | 8
| 33
| | 224.6256
| 926.5806
| |
| 12/7
| |  
|  
|-
|-
| | 9
| 34
| | 252.7038
| 954.6588
| |  
|  
| |  
|  
|-
|-
| | 10
| 35
| | 280.7820
| 982.737
| | [[20/17]]
| 30/17
| |  
|  
|-
|-
| | 11
| 36
| | 308.8602
| 1010.8152
| |  
|  
| | pseudo-[[6/5]]
| pseudo-9/5
|-
|-
| | 12
| 37
| | 336.9384
| 1038.8934
| |  
|  
| |  
|  
|-
|-
| | 13
| 38
| | 365.0166
| 1066.9716
| |  
|  
| |  
|  
|-
|-
| | 14
| 39
| | 393.0948
| 1095.0498
| |  
|  
| | pseudo-[[5/4]]
| pseudo-15/8
|-
|-
| | 15
| 40
| | 421.1730
| 1123.128
| | 51/40
| 153/80
| |  
|  
|-
|-
| | 16
| 41
| | 449.2512
| 1151.2062
| |  
|  
| |  
|  
|-
|-
| | 17
| 42
| | 477.3294
| 1179.2844
| |  
|  
| |  
|  
|-
|-
| | 18
| 43
| | 505.4076
| 1207.3526
| | 75/56
| 225/112
| | pseudo-[[4/3]]
| pseudo-2/1
|-
|-
| | 19
| 44
| | 533.4858
| 1235.4408
| |  
|  
| |  
|  
|-
|-
| | 20
| 45
| | 561.5640
| 1263.519
| |  
|  
| |  
|  
|-
|-
| | 21
| 46
| | 589.6422
| 1291.5972
| | [[45/32]]
| 135/64
| |  
|  
|-
|-
| | 22
| 47
| | 617.7204
| 1319.6754
| | [[10/7]]
| 15/7
| |  
|  
|-
|-
| | 23
| 48
| | 645.7986
| 1347.7536
| |  
|  
| |  
|  
|-
|-
| | 24
| 49
| | 673.8768
| 1375.8318
| |  
|  
| |  
|  
|-
|-
| | 25
| 50
| | 701.9550
| 1403.91
| | '''exact [[3/2]]'''
| '''exact''' 9/4
| | just perfect fifth
|  
|}
|}


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

Latest revision as of 19:21, 1 August 2025

← 24edf 25edf 26edf →
Prime factorization 52
Step size 28.0782 ¢ 
Octave 43\25edf (1207.36 ¢)
Twelfth 68\25edf (1909.32 ¢)
Consistency limit 3
Distinct consistency limit 3

25 equal divisions of the perfect fifth (abbreviated 25edf or 25ed3/2) is a nonoctave tuning system that divides the interval of 3/2 into 25 equal parts of about 28.1 ¢ each. Each step represents a frequency ratio of (3/2)1/25, or the 25th root of 3/2. It corresponds to 42.7378 edo (similar to every fourth step of 171edo).

It is related to the regular temperament which tempers out 703125/702464 and 5250987/5242880 in the 7-limit, which is supported by 43edo, 128edo, 171edo, 214edo, 299edo, and 385edo.

Lookalikes: 43edo, 68edt

Harmonics

Approximation of prime harmonics in 25edf
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +7.4 +7.4 -6.6 +0.6 +4.3 -4.2 +8.7 +12.7 -9.2 +10.7 +7.5
Relative (%) +26.2 +26.2 -23.4 +2.0 +15.2 -14.9 +31.1 +45.3 -32.7 +38.1 +26.9
Steps
(reduced) 		43
(18) 		68
(18) 		99
(24) 		120
(20) 		148
(23) 		158
(8) 		175
(0) 		182
(7) 		193
(18) 		208
(8) 		212
(12)
Approximation of prime harmonics in 25edf
Harmonic 37 41 43 47 53 59 61 67 71 73 79
Error Absolute (¢) +10.1 +0.8 +2.6 -11.0 +5.7 -11.5 -13.1 -7.1 +4.9 +12.9 -11.5
Relative (%) +36.0 +3.0 +9.3 -39.1 +20.1 -41.1 -46.7 -25.1 +17.3 +46.1 -41.0
Steps
(reduced) 		223
(23) 		229
(4) 		232
(7) 		237
(12) 		245
(20) 		251
(1) 		253
(3) 		259
(9) 		263
(13) 		265
(15) 		269
(19)

Intervals

Intervals of 25edf
Degree Cents Corresponding
JI intervals 		Comments
0 exact 1/1
1 28.0782 51/50
2 56.1564 26/25
3 84.2346 21/20
4 112.3128 16/15
5 140.391 13/12
6 168.4692
7 196.5474 28/25
8 224.6256 8/7
9 252.7038
10 280.782 20/17
11 308.8602 pseudo-6/5
12 336.9384
13 365.0166
14 393.0948 pseudo-5/4
15 421.173 51/40
16 449.2512
17 477.3294
18 505.4076 75/56 pseudo-4/3
19 533.4858
20 561.564
21 589.6422 45/32
22 617.7204 10/7
23 645.7986
24 673.8768
25 701.955 exact 3/2 just perfect fifth
26 730.033 153/100
27 757.1114 39/25
28 786.1896 63/40
29 814.2678 8/5
30 842.346 13/8
31 870.2452
32 898.5024 42/25
33 926.5806 12/7
34 954.6588
35 982.737 30/17
36 1010.8152 pseudo-9/5
37 1038.8934
38 1066.9716
39 1095.0498 pseudo-15/8
40 1123.128 153/80
41 1151.2062
42 1179.2844
43 1207.3526 225/112 pseudo-2/1
44 1235.4408
45 1263.519
46 1291.5972 135/64
47 1319.6754 15/7
48 1347.7536
49 1375.8318
50 1403.91 exact 9/4
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