23edt: Difference between revisions

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{{Infobox ET}}
'''23EDT''' is the [[Edt|equal division of the third harmonic]] into 23 parts of 82.6937 [[cent|cents]] each, corresponding to 14.5114 [[edo]] (similar to every second step of [[29edo]]).
'''23EDT''' is the [[Edt|equal division of the third harmonic]] into 23 parts of 82.6937 [[cent|cents]] each, corresponding to 14.5114 [[edo]] (similar to every second step of [[29edo]]).


== Intervals ==
{| class="wikitable"
{| class="wikitable"
|-
|-
! | degree
! | degree
! | cents value
! | cents value
! | corresponding <br>JI intervals
!hekts
! | corresponding JI intervals
! | comments
! | comments
|-
|-
| | 0
! colspan="3" | 0
| | 0.0000
| | '''exact [[1/1]]'''
| | '''exact [[1/1]]'''
| |  
| |  
Line 15: Line 17:
| | 1
| | 1
| | 82.6937
| | 82.6937
|56.522
| | 150/143
| | 150/143
| |  
| |  
Line 20: Line 23:
| | 2
| | 2
| | 165.3874
| | 165.3874
|113.0435
| | [[11/10]]
| | [[11/10]]
| |  
| |  
Line 25: Line 29:
| | 3
| | 3
| | 248.0811
| | 248.0811
|169.565
| | [[15/13]]
| | [[15/13]]
| |  
| |  
Line 30: Line 35:
| | 4
| | 4
| | 330.7748
| | 330.7748
|226.087
| | 23/19
| | 23/19
| |  
| |  
Line 35: Line 41:
| | 5
| | 5
| | 413.4685
| | 413.4685
|282.609
| | 33/26, 80/63
| | 33/26, 80/63
| |  
| |  
Line 40: Line 47:
| | 6
| | 6
| | 496.1622
| | 496.1622
|339.13
| | ([[4/3]])
| | ([[4/3]])
| |  
| |  
Line 45: Line 53:
| | 7
| | 7
| | 578.8559
| | 578.8559
|395.652
| | 88/63, 95/68
| | 88/63, 95/68
| |  
| |pseudo-[[7/5]]
|-
|-
| | 8
| | 8
| | 661.5496
| | 661.5496
| |  
|452.174
| |63/43
| |  
| |  
|-
|-
| | 9
| | 9
| | 744.2433
| | 744.2433
| |  
|508.696
| |135/88
| |  
| |  
|-
|-
| | 10
| | 10
| | 826.9370
| | 826.937
| | 50/31
|565.217
| | 50/31, 408/253, 129/80, 108/67
| |  
| |  
|-
|-
| | 11
| | 11
| | 909.6307
| | 909.6307
| |  
|621.739
| |(27/16)
| | pseudo-[[5/3]]
| | pseudo-[[5/3]]
|-
|-
| | 12
| | 12
| | 992.3243
| | 992.3243
| |  
|678.261
| |(16/9)
| |  
| |  
|-
|-
| | 13
| | 13
| | 1075.0180
| | 1075.018
|734.783
| | 93/50, 253/136, 80/43, 67/36
| | 93/50, 253/136, 80/43, 67/36
| |  
| |  
Line 80: Line 95:
| | 14
| | 14
| | 1157.7117
| | 1157.7117
| |  
|791.304
| |88/45
| |  
| |  
|-
|-
| | 15
| | 15
| | 1240.4054
| | 1240.4054
| |  
|847.826
| |43/21
| |  
| |  
|-
|-
| | 16
| | 16
| | 1323.0991
| | 1323.0991
| |  
|904.348
| |189/88, 204/95
| |  
| |  
|-
|-
| | 17
| | 17
| | 1405.7928
| | 1405.7928
|960.87
| | ([[9/4]])
| | ([[9/4]])
| |  
| |  
Line 100: Line 119:
| | 18
| | 18
| | 1488.4865
| | 1488.4865
| | [[13/11|26/11]]
|1017.391
| | [[13/11|26/11]], 189/80
| | pseudo-[[7/3]]
| | pseudo-[[7/3]]
|-
|-
| | 19
| | 19
| | 1571.1802
| | 1571.1802
|1073.913
| | 57/23
| | 57/23
| |  
| |  
Line 110: Line 131:
| | 20
| | 20
| | 1653.8739
| | 1653.8739
|1130.435.
| | [[13/5]]
| | [[13/5]]
| |  
| |  
Line 115: Line 137:
| | 21
| | 21
| | 1736.5676
| | 1736.5676
|1186.9565
| | [[15/11|30/11]]
| | [[15/11|30/11]]
| |  
| |  
Line 120: Line 143:
| | 22
| | 22
| | 1819.2613
| | 1819.2613
|1243.478
| | 143/50
| | 143/50
| |  
| |  
Line 125: Line 149:
| | 23
| | 23
| | 1901.9550
| | 1901.9550
|1300
| | '''exact [[3/1]]'''
| | '''exact [[3/1]]'''
| | [[3/2|just perfect fifth]] plus an octave
| | [[3/2|just perfect fifth]] plus an octave
|}
|}


[[Category:Edt]]
== Harmonics ==
[[Category:Edonoi]]
{{Harmonics in equal
| steps = 23
| num = 3
| denom = 1
| intervals = integer
}}
{{Harmonics in equal
| steps = 23
| num = 3
| denom = 1
| start = 12
| collapsed = 1
| intervals = integer
}}
 
 
{{stub}}

Latest revision as of 19:20, 1 August 2025

← 22edt 23edt 24edt →
Prime factorization 23 (prime)
Step size 82.6937 ¢ 
Octave 15\23edt (1240.41 ¢)
Consistency limit 3
Distinct consistency limit 3

23EDT is the equal division of the third harmonic into 23 parts of 82.6937 cents each, corresponding to 14.5114 edo (similar to every second step of 29edo).

Intervals

degree cents value hekts corresponding JI intervals comments
0 exact 1/1
1 82.6937 56.522 150/143
2 165.3874 113.0435 11/10
3 248.0811 169.565 15/13
4 330.7748 226.087 23/19
5 413.4685 282.609 33/26, 80/63
6 496.1622 339.13 (4/3)
7 578.8559 395.652 88/63, 95/68 pseudo-7/5
8 661.5496 452.174 63/43
9 744.2433 508.696 135/88
10 826.937 565.217 50/31, 408/253, 129/80, 108/67
11 909.6307 621.739 (27/16) pseudo-5/3
12 992.3243 678.261 (16/9)
13 1075.018 734.783 93/50, 253/136, 80/43, 67/36
14 1157.7117 791.304 88/45
15 1240.4054 847.826 43/21
16 1323.0991 904.348 189/88, 204/95
17 1405.7928 960.87 (9/4)
18 1488.4865 1017.391 26/11, 189/80 pseudo-7/3
19 1571.1802 1073.913 57/23
20 1653.8739 1130.435. 13/5
21 1736.5676 1186.9565 30/11
22 1819.2613 1243.478 143/50
23 1901.9550 1300 exact 3/1 just perfect fifth plus an octave

Harmonics

Approximation of harmonics in 23edt
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +40.4 +0.0 -1.9 +25.3 +40.4 +21.6 +38.5 +0.0 -17.0 -16.6 -1.9
Relative (%) +48.9 +0.0 -2.3 +30.6 +48.9 +26.1 +46.6 +0.0 -20.6 -20.1 -2.3
Steps
(reduced) 		15
(15) 		23
(0) 		29
(6) 		34
(11) 		38
(15) 		41
(18) 		44
(21) 		46
(0) 		48
(2) 		50
(4) 		52
(6)
Approximation of harmonics in 23edt
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +24.9 -20.7 +25.3 -3.8 -26.0 +40.4 +29.5 +23.4 +21.6 +23.8 +29.5
Relative (%) +30.1 -25.0 +30.6 -4.6 -31.5 +48.9 +35.7 +28.3 +26.1 +28.7 +35.7
Steps
(reduced) 		54
(8) 		55
(9) 		57
(11) 		58
(12) 		59
(13) 		61
(15) 		62
(16) 		63
(17) 		64
(18) 		65
(19) 		66
(20)


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