15edf: Difference between revisions

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=15edf=
{{Infobox ET}}
'''15EDF''' is the [[EDF|equal division of the just perfect fifth]] into 15 parts of 46.797 [[cent|cents]] each, corresponding to 25.6427 [[edo]] (similar to every third step of [[77edo]]). The [[3edf]]~[[5edo]] correspondence has completely collapsed by this point, with this EDF being closer to [[26edo]] than [[25edo]].


0: 1/1 0.000 unison, perfect prime
Lookalikes: [[26edo]], [[41edt]]


1: 46.797 cents 46.797
==Harmonics==
{{Harmonics in equal|15|3|2}}
{{Harmonics in equal|15|3|2|start=12|collapsed=1}}


2: 93.594 cents 93.594
==Intervals==
{| class="wikitable mw-collapsible"
|+ Intervals of 15edf
|-
! | degree
! | cents value
! | corresponding <br>JI intervals
! | comments
|-
! colspan="2" | 0
| | '''exact [[1/1]]'''
| |
|-
| | 1
| | 46.797
| |
| |
|-
| | 2
| | 93.594
| | [[19/18]]
| |
|-
| | 3
| | 140.391
| | [[13/12]]
| |
|-
| | 4
| | 187.188
| | [[10/9]]
| |
|-
| | 5
| | 233.985
| | [[8/7]]
| |
|-
| | 6
| | 280.782
| | [[20/17]]
| |
|-
| | 7
| | 327.579
| |
| |
|-
| | 8
| | 374.376
| |
| |
|-
| | 9
| | 421.173
| | 51/40
| |
|-
| | 10
| | 467.97
| | [[21/16]]
| |
|-
| | 11
| | 514.767
| | [[27/20]]
| |
|-
| | 12
| | 561.564
| | [[18/13]]
| |
|-
| | 13
| | 608.361
| | 27/19
| |
|-
| | 14
| | 655.158
| |
| |
|-
| | 15
| | 701.955
| | '''exact [[3/2]]'''
| | just perfect fifth
|-
|16
|748.752
|
|
|-
|17
|795.549
|19/12
|
|-
|18
|842.346
|13/8
|
|-
|19
|889.143
|5/3
|
|-
|20
|935.94
|12/7
|
|-
|21
|982.737
|30/17
|
|-
|22
|1029.534
|
|
|-
|23
|1076.331
|
|
|-
|24
|1123.128
|153/80
|
|-
|25
|1168.925
|63/32
|
|-
|26
|1216.722
|81/40
|
|-
|27
|1263.519
|27/13
|
|-
|28
|1310.316
|81/38
|
|-
|29
|1357.113
|
|
|-
|30
|1403.91
|'''exact''' 9/4
|
|}


3: 140.391 cents 140.391


4: 187.188 cents 187.188
{{stub}}
 
5: 233.985 cents 233.985
 
6: 280.782 cents 280.782
 
7: 327.579 cents 327.579
 
8: 374.376 cents 374.376
 
9: 421.173 cents 421.173
 
10: 467.970 cents 467.970
 
11: 514.767 cents 514.767
 
12: 561.564 cents 561.564
 
13: 608.361 cents 608.361
 
14: 655.158 cents 655.158
 
15: 3/2 701.955 perfect fifth
 
Lookalikes: [[26edo|26edo]]
 
*this is an interesting one

Latest revision as of 03:29, 21 December 2024

← 14edf 15edf 16edf →
Prime factorization 3 × 5
Step size 46.797 ¢ 
Octave 26\15edf (1216.72 ¢)
Twelfth 41\15edf (1918.68 ¢)
Consistency limit 3
Distinct consistency limit 3

15EDF is the equal division of the just perfect fifth into 15 parts of 46.797 cents each, corresponding to 25.6427 edo (similar to every third step of 77edo). The 3edf~5edo correspondence has completely collapsed by this point, with this EDF being closer to 26edo than 25edo.

Lookalikes: 26edo, 41edt

Harmonics

Approximation of harmonics in 15edf
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +16.7 +16.7 -13.4 +21.5 -13.4 +0.6 +3.4 -13.4 -8.6 +13.6 +3.4
Relative (%) +35.7 +35.7 -28.5 +46.0 -28.5 +1.2 +7.2 -28.5 -18.3 +29.1 +7.2
Steps
(reduced) 		26
(11) 		41
(11) 		51
(6) 		60
(0) 		66
(6) 		72
(12) 		77
(2) 		81
(6) 		85
(10) 		89
(14) 		92
(2)
Approximation of harmonics in 15edf
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +5.2 +17.3 -8.6 +20.1 +8.7 +3.4 +3.4 +8.2 +17.3 -16.5 +0.2
Relative (%) +11.1 +36.9 -18.3 +42.9 +18.7 +7.2 +7.2 +17.4 +36.9 -35.2 +0.4
Steps
(reduced) 		95
(5) 		98
(8) 		100
(10) 		103
(13) 		105
(0) 		107
(2) 		109
(4) 		111
(6) 		113
(8) 		114
(9) 		116
(11)

Intervals

Intervals of 15edf
degree cents value corresponding
JI intervals 		comments
0 exact 1/1
1 46.797
2 93.594 19/18
3 140.391 13/12
4 187.188 10/9
5 233.985 8/7
6 280.782 20/17
7 327.579
8 374.376
9 421.173 51/40
10 467.97 21/16
11 514.767 27/20
12 561.564 18/13
13 608.361 27/19
14 655.158
15 701.955 exact 3/2 just perfect fifth
16 748.752
17 795.549 19/12
18 842.346 13/8
19 889.143 5/3
20 935.94 12/7
21 982.737 30/17
22 1029.534
23 1076.331
24 1123.128 153/80
25 1168.925 63/32
26 1216.722 81/40
27 1263.519 27/13
28 1310.316 81/38
29 1357.113
30 1403.91 exact 9/4


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