23edf: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
Wikispaces>FREEZE
No edit summary
Fredg999 category edits (talk | contribs)
autopatrolled, Bots
4,330 edits
m Removing from Category:Edf using Cat-a-lot
 
(6 intermediate revisions by 5 users not shown)
Line 1: Line 1:
Twenty-three equal divisions of the perfect fifth (23ed3/2)
{{Infobox ET}}
'''23EDF''' is the [[EDF|equal division of the just perfect fifth]] into 23 parts of 30.5198 [[cents]] each, corresponding to 39.3188 [[edo]] (similar to every third step of [[118edo]]).


Rank 1 scale with step size of 30.52 cents.
==History==
A proponent of 23edf is [[Petr Pařízek]]. The first to write about 23edf on this wiki was [[Todd Harrop]] in 2015.


Close to 39ed2 and/or 62ed3, however, the respective
==Theory==
23edf is close to [[39edo]] and/or [[62edt]], however, the respective [[octave]] and [[tritave|twelfth]] would need to be nearly 10 cents flat.


octave and twelfth would need to be nearly 10 cents flat.
Some intervals in table below, selected on the basis of single-use of [[prime]]s (for most cases):
 
A proponent of this scale is Petr Pařízek.
 
Some intervals in table below, selected on the basis of
 
single-use of primes (for most cases):


{| class="wikitable"
{| class="wikitable"
Line 85: Line 82:
| style="text-align:center;" | 7/2
| style="text-align:center;" | 7/2
| style="text-align:center;" | –1.9¢
| style="text-align:center;" | –1.9¢
|}
=== Harmonics ===
{{Harmonics in equal|23|3|2}}
{{Harmonics in equal|23|3|2|start=12|collapsed=1}}
== Intervals ==
{| class="wikitable mw-collapsible"
|+ Intervals of 23edf
|-
!Step number
!Size (cents)
|-
|1
|30.5198
|-
|2
|61.0296
|-
|3
|91.55935
|-
|4
|122.0791
|-
|5
|152.5989
|-
|6
|183.1187
|-
|7
|213.6385
|-
|8
|244.1583
|-
|9
|274.678
|-
|10
|305.1978
|-
|11
|335.7176
|-
|12
|366.2374
|-
|13
|396.7572
|-
|14
|427.277
|-
|15
|457.7967
|-
|16
|488.3165
|-
|17
|518.8363
|-
|18
|549.3561
|-
|19
|579.8759
|-
|20
|610.39565
|-
|21
|640.9154
|-
|22
|671.4352
|-
|23
|701.955
|-
|24
|732.4748
|-
|25
|762.9946
|-
|26
|793.51435
|-
|27
|824.0341
|-
|28
|854.5539
|-
|29
|885.0737
|-
|-
| style="text-align:center;" |  
|30
| style="text-align:center;" |  
|915.5935
| style="text-align:center;" |  
|-
| style="text-align:center;" |  
|31
|946.1133
|-
|32
|976.633
|-
|33
|1007.1529
|-
|34
|1037.6726
|-
|35
|1068.1924
|-
|36
|1098.7122
|-
|37
|1129.232
|-
|38
|1159.7517
|-
|39
|1190.2715
|-
|40
|1220.7913
|-
|41
|1251.3111
|-
|42
|1281.8309
|-
|43
|1312.35065
|-
|44
|1342.8704
|-
|45
|1373.3902
|-
|46
|1403.91
|}
|}
–Todd Harrop (June 2015)
{{todo|inline=1|complete table|text=Add at least one more column, showing what the notes are named, what JI they approximate, or anything else interesting about them individually.}}
[[Category:31edo]]
 
[[Category:edf]]
 
{{todo|expand}}
[[Category:nonoctave]]
[[Category:nonoctave]]
[[Category:what_is]]
[[Category:wiki]]

Latest revision as of 19:00, 1 August 2025

← 22edf 23edf 24edf →
Prime factorization 23 (prime)
Step size 30.5198 ¢ 
Octave 39\23edf (1190.27 ¢)
Twelfth 62\23edf (1892.23 ¢)
Consistency limit 3
Distinct consistency limit 3

23EDF is the equal division of the just perfect fifth into 23 parts of 30.5198 cents each, corresponding to 39.3188 edo (similar to every third step of 118edo).

History

A proponent of 23edf is Petr Pařízek. The first to write about 23edf on this wiki was Todd Harrop in 2015.

Theory

23edf is close to 39edo and/or 62edt, however, the respective octave and twelfth would need to be nearly 10 cents flat.

Some intervals in table below, selected on the basis of single-use of primes (for most cases):

Step Size

(cents)

Approx.

(JI) ratio

Error from

ratio (cents)

19 579.9 7/5 –2.6¢
23 702 3/2
24 732.5 29/19 +0.4¢
29 885.1 5/3 +0.7¢
31 946.1 19/11 –0.1¢
35 1068 13/7 –3.5¢
46 1404 9/4
48 1465 7/3 –1.9¢
52 1587 5/2 +0.7¢
55 1679 29/11 +0.3¢
58 1770 25/9 +1.4¢
71 2167 7/2 –1.9¢

Harmonics

Approximation of harmonics in 23edf
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -9.7 -9.7 +11.1 -9.0 +11.1 -11.6 +1.3 +11.1 +11.8 -0.6 +1.3
Relative (%) -31.9 -31.9 +36.2 -29.5 +36.2 -38.2 +4.4 +36.2 +38.6 -2.1 +4.4
Steps
(reduced) 		39
(16) 		62
(16) 		79
(10) 		91
(22) 		102
(10) 		110
(18) 		118
(3) 		125
(10) 		131
(16) 		136
(21) 		141
(3)
Approximation of harmonics in 23edf
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -15.2 +9.1 +11.8 -8.4 +8.7 +1.3 -0.7 +2.0 +9.1 -10.4 +4.2
Relative (%) -49.7 +30.0 +38.6 -27.5 +28.6 +4.4 -2.3 +6.7 +30.0 -33.9 +13.9
Steps
(reduced) 		145
(7) 		150
(12) 		154
(16) 		157
(19) 		161
(0) 		164
(3) 		167
(6) 		170
(9) 		173
(12) 		175
(14) 		178
(17)

Intervals

Intervals of 23edf
Step number Size (cents)
1 30.5198
2 61.0296
3 91.55935
4 122.0791
5 152.5989
6 183.1187
7 213.6385
8 244.1583
9 274.678
10 305.1978
11 335.7176
12 366.2374
13 396.7572
14 427.277
15 457.7967
16 488.3165
17 518.8363
18 549.3561
19 579.8759
20 610.39565
21 640.9154
22 671.4352
23 701.955
24 732.4748
25 762.9946
26 793.51435
27 824.0341
28 854.5539
29 885.0737
30 915.5935
31 946.1133
32 976.633
33 1007.1529
34 1037.6726
35 1068.1924
36 1098.7122
37 1129.232
38 1159.7517
39 1190.2715
40 1220.7913
41 1251.3111
42 1281.8309
43 1312.35065
44 1342.8704
45 1373.3902
46 1403.91
Todo: complete table

Add at least one more column, showing what the notes are named, what JI they approximate, or anything else interesting about them individually.

Retrieved from "https://en.xen.wiki/index.php?title=23edf&oldid=205891"