22edf: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
VisualWikitext
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
4,516 edits
Created page with "'''22EDF''' is the equal division of the just perfect fifth into 22 parts of 31.9070 cents each, corresponding to 37.6092 edo (similar to every fifth step..."
 
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
18,452 edits
m →Intervals: title row
 
(6 intermediate revisions by 4 users not shown)
Line 1: Line 1:
'''22EDF''' is the [[EDF|equal division of the just perfect fifth]] into 22 parts of 31.9070 [[cent|cents]] each, corresponding to 37.6092 [[edo]] (similar to every fifth step of [[188edo]]).
{{Infobox ET}}
'''22EDF''' is the [[EDF|equal division of the just perfect fifth]] into 22 parts of 31.907 [[cents]] each, corresponding to 37.6092 [[edo]] (similar to every fifth step of [[188edo]]).
 
==Harmonics==
{{Harmonics in equal|22|3|2}}
{{Harmonics in equal|22|3|2|start=12|collapsed=1}}


==Intervals==
==Intervals==
{| class="wikitable"
{| class="wikitable mw-collapsible"
|+ Intervals of 22edf
|-
|-
! | degree
! | degree
Line 9: Line 15:
! | comments
! | comments
|-
|-
| | 0
| colspan="2"| 0
| | 0.0000
| | '''exact [[1/1]]'''
| | '''exact [[1/1]]'''
| |  
| |  
|-
|-
| | 1
| | 1
| | 31.9070
| | 31.907
| | [[55/54]]
| | [[55/54]]
| |  
| |  
Line 46: Line 51:
| | 7
| | 7
| | 223.3493
| | 223.3493
| |  
| |8/7
| |  
| |  
|-
|-
Line 56: Line 61:
| | 9
| | 9
| | 287.1634
| | 287.1634
| |  
| |13/11
| |  
| |  
|-
|-
| | 10
| | 10
| | 319.0705
| | 319.0705
| |  
| |6/5
| |  
| |  
|-
|-
Line 71: Line 76:
| | 12
| | 12
| | 382.8845
| | 382.8845
| |  
| |5/4
| |  
| |  
|-
|-
| | 13
| | 13
| | 414.7916
| | 414.7916
| |  
| |14/11
| |  
| |  
|-
|-
Line 106: Line 111:
| | 19
| | 19
| | 606.2339
| | 606.2339
| |  
| |64/45
| |  
| |  
|-
|-
Line 115: Line 120:
|-
|-
| | 21
| | 21
| | 670.0480
| | 670.048
| | 81/55
| | 81/55
| |  
| |  
|-
|-
| | 22
| | 22
| | 701.9550
| | 701.955
| | '''exact [[3/2]]'''
| | '''exact [[3/2]]'''
| | just perfect fifth
| | just perfect fifth
|-
|23
|733.862
|55/36
|
|-
|24
|765.7691
|14/9, 81/52
|
|-
|25
|797.6761
|
|
|-
|26
|828.5732
|21/13
|
|-
|27
|861.4902
|171/104
|
|-
|28
|893.3973
|
|
|-
|29
|925.3043
|12/7
|
|-
|30
|956.2114
|
|
|-
|31
|988.1184
|39/22
|
|-
|32
|1020.0255
|9/5
|
|-
|33
|1052.9235
|90/49, 147/80
|
|-
|34
|1084.8395
|15/8
|
|-
|35
|1116.7466
|21/11
|
|-
|36
|1148.6536
|
|
|-
|37
|1180.5607
|
|
|-
|38
|1211.4677
|
|
|-
|39
|1244.3748
|39/19
|
|-
|40
|1276.2816
|117/56
|
|-
|41
|1308.1889
|32/15
|
|-
|42
|1340.0959
|13/6
|
|-
|43
|1372.003
|243/110
|
|-
|44
|1403.91
|'''exact''' 9/4
|
|}
|}


[[Category:Edf]]
 
[[Category:Edonoi]]
{{stub}}

Latest revision as of 08:27, 19 December 2024

← 21edf 22edf 23edf →
Prime factorization 2 × 11
Step size 31.907 ¢ 
Octave 38\22edf (1212.47 ¢) (→ 19\11edf)
Twelfth 60\22edf (1914.42 ¢) (→ 30\11edf)
Consistency limit 3
Distinct consistency limit 3

22EDF is the equal division of the just perfect fifth into 22 parts of 31.907 cents each, corresponding to 37.6092 edo (similar to every fifth step of 188edo).

Harmonics

Approximation of harmonics in 22edf
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +12.5 +12.5 -7.0 -10.4 -7.0 +13.3 +5.5 -7.0 +2.1 -3.4 +5.5
Relative (%) +39.1 +39.1 -21.8 -32.6 -21.8 +41.7 +17.2 -21.8 +6.5 -10.7 +17.2
Steps
(reduced) 		38
(16) 		60
(16) 		75
(9) 		87
(21) 		97
(9) 		106
(18) 		113
(3) 		119
(9) 		125
(15) 		130
(20) 		135
(3)
Approximation of harmonics in 22edf
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -5.4 -6.1 +2.1 -13.9 +8.7 +5.5 +7.6 +14.5 -6.1 +9.1 -4.1
Relative (%) -17.1 -19.2 +6.5 -43.7 +27.4 +17.2 +23.9 +45.6 -19.2 +28.4 -12.8
Steps
(reduced) 		139
(7) 		143
(11) 		147
(15) 		150
(18) 		154
(0) 		157
(3) 		160
(6) 		163
(9) 		165
(11) 		168
(14) 		170
(16)

Intervals

Intervals of 22edf
degree cents value corresponding
JI intervals 		comments
0 exact 1/1
1 31.907 55/54
2 63.8141 (28/27), (27/26)
3 95.7211
4 127.6282 14/13
5 159.5352 57/52
6 191.4423
7 223.3493 8/7
8 255.2564
9 287.1634 13/11
10 319.0705 6/5
11 350.9775 60/49, 49/40
12 382.8845 5/4
13 414.7916 14/11
14 446.6986
15 478.6057
16 510.5127
17 542.4198 26/19
18 574.3268 39/28
19 606.2339 64/45
20 638.1409 (13/9)
21 670.048 81/55
22 701.955 exact 3/2 just perfect fifth
23 733.862 55/36
24 765.7691 14/9, 81/52
25 797.6761
26 828.5732 21/13
27 861.4902 171/104
28 893.3973
29 925.3043 12/7
30 956.2114
31 988.1184 39/22
32 1020.0255 9/5
33 1052.9235 90/49, 147/80
34 1084.8395 15/8
35 1116.7466 21/11
36 1148.6536
37 1180.5607
38 1211.4677
39 1244.3748 39/19
40 1276.2816 117/56
41 1308.1889 32/15
42 1340.0959 13/6
43 1372.003 243/110
44 1403.91 exact 9/4


This page is a stub. You can help the Xenharmonic Wiki by expanding it.
Retrieved from "https://en.xen.wiki/index.php?title=22edf&oldid=171792"