29edf: Difference between revisions

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'''29EDF''' is the [[EDF|equal division of the just perfect fifth]] into 29 parts of 24.2053 [[cent|cents]] each, corresponding to 49.5758 [[edo]]. It is related to the [[Hemimean clan|sengagen temperament]], which tempers out 3136/3125 and 420175/419904 in the 7-limit.
{{Infobox ET}}
'''29EDF''' is the [[EDF|equal division of the just perfect fifth]] into 29 parts of 24.2053 [[cent|cents]] each, corresponding to 49.5758 [[edo]]. It is related to the [[Hemimean clan#Sengagen|sengagen temperament]], which tempers out 3136/3125 and 420175/419904 in the 7-limit.


{| class="wikitable"
== Harmonics ==
{{Harmonics in equal|29|3|2}}
{{Harmonics in equal|29|3|2|start=12|collapsed=1}}
 
== Intervals ==
{| class="wikitable mw-collapsible"
|+ Intervals of 29edf
|-
|-
! | degree
! | degree
Line 8: Line 15:
! | comments
! | comments
|-
|-
| | 0
| colspan="2"| 0
| | 0.0000
| | '''exact [[1/1]]'''
| | '''exact [[1/1]]'''
| |  
| |  
Line 15: Line 21:
| | 1
| | 1
| | 24.2053
| | 24.2053
| |  
| | 72/71
| |  
| |  
|-
|-
Line 25: Line 31:
| | 3
| | 3
| | 72.6160
| | 72.6160
| |  
| | [[24/23]]
| |  
| |  
|-
|-
| | 4
| | 4
| | 96.8214
| | 96.8214
| |  
| | 37/35, 55/52
| |  
| |  
|-
|-
Line 40: Line 46:
| | 6
| | 6
| | 145.2321
| | 145.2321
| |  
| | 25/23, 37/34
| |  
| |  
|-
|-
Line 60: Line 66:
| | 10
| | 10
| | 242.0534
| | 242.0534
| |  
| | [[23/20]]
| |  
| |  
|-
|-
Line 70: Line 76:
| | 12
| | 12
| | 290.4641
| | 290.4641
| |  
| | 71/60
| |  
| |  
|-
|-
Line 80: Line 86:
| | 14
| | 14
| | 338.8748
| | 338.8748
| |  
| | 45/37
| |  
| |  
|-
|-
| | 15
| | 15
| | 363.0802
| | 363.0802
| |  
| | 37/30
| |  
| |  
|-
|-
Line 95: Line 101:
| | 17
| | 17
| | 411.4909
| | 411.4909
| |  
| | 90/71
| |  
| |  
|-
|-
Line 105: Line 111:
| | 19
| | 19
| | 459.9016
| | 459.9016
| |  
| | [[30/23]]
| |  
| |  
|-
|-
| | 20
| | 20
| | 484.1069
| | 484.1069
| |  
| | 45/34
| |  
| |  
|-
|-
| | 21
| | 21
| | 508.3122
| | 508.3122
| |  
| | 51/38
| |  
| |  
|-
|-
Line 140: Line 146:
| | 26
| | 26
| | 629.3390
| | 629.3390
| |  
| | [[23/16]]
| |  
| |  
|-
|-
Line 156: Line 162:
| | 701.9550
| | 701.9550
| | '''exact [[3/2]]'''
| | '''exact [[3/2]]'''
| | just major third plus two octaves
| | just perfect fifth
|-
|30
|726.16035
|
|
|-
|31
|750.3657
|
|
|-
|32
|774.5710
|
|
|-
|33
|798.7764
|
|
|-
|34
|822.9817
|45/28
|
|-
|35
|847.1871
|
|
|-
|36
|871.3924
|81/49
|
|-
|37
|895.5978
|57/34
|
|-
|38
|919.8031
|17/10
|
|-
|39
|944.00845
|
|
|-
|40
|968.2138
|7/4
|
|-
|41
|992.4191
|16/9
|
|-
|42
|1016.6245
|9/5
|
|-
|43
|1040.8298
|
|
|-
|44
|1065.0352
|
|
|-
|45
|1089.2405
|15/8
|
|-
|46
|1113.4459
|
|
|-
|47
|1137.6512
|56/29
|
|-
|48
|1161.8566
|
|
|-
|49
|1186.0619
|(2/1-)
|
|-
|50
|1210.2672
|(2/1+)
|
|-
|51
|1234.4726
|49/24
|
|-
|52
|1258.6779
|29/14
|
|-
|53
|1282.8833
|21/10
|
|-
|54
|1307.0886
|17/8
|
|-
|55
|1331.2940
|41/19
|
|-
|56
|1355.4993
|35/16
|
|-
|57
|1379.7047
|20/9
|
|-
|58
|1403.9100
|exact 9/4
|
|}
|}


Line 164: Line 315:
*[[Carlos Gamma|Carlos Gamma (20 EDF)]]
*[[Carlos Gamma|Carlos Gamma (20 EDF)]]


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

Latest revision as of 19:21, 1 August 2025

← 28edf 29edf 30edf →
Prime factorization 29 (prime)
Step size 24.2053 ¢ 
Octave 50\29edf (1210.27 ¢)
Twelfth 79\29edf (1912.22 ¢)
Consistency limit 3
Distinct consistency limit 3

29EDF is the equal division of the just perfect fifth into 29 parts of 24.2053 cents each, corresponding to 49.5758 edo. It is related to the sengagen temperament, which tempers out 3136/3125 and 420175/419904 in the 7-limit.

Harmonics

Approximation of harmonics in 29edf
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +10.3 +10.3 -3.7 -2.7 -3.7 -4.3 +6.6 -3.7 +7.6 +12.0 +6.6
Relative (%) +42.4 +42.4 -15.2 -11.2 -15.2 -17.7 +27.3 -15.2 +31.3 +49.6 +27.3
Steps
(reduced) 		50
(21) 		79
(21) 		99
(12) 		115
(28) 		128
(12) 		139
(23) 		149
(4) 		157
(12) 		165
(20) 		172
(27) 		178
(4)
Approximation of harmonics in 29edf
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -10.9 +6.0 +7.6 -7.3 +8.7 +6.6 +9.8 -6.4 +6.0 -1.9 -6.3
Relative (%) -45.2 +24.7 +31.3 -30.3 +36.1 +27.3 +40.5 -26.3 +24.7 -8.0 -25.9
Steps
(reduced) 		183
(9) 		189
(15) 		194
(20) 		198
(24) 		203
(0) 		207
(4) 		211
(8) 		214
(11) 		218
(15) 		221
(18) 		224
(21)

Intervals

Intervals of 29edf
degree cents value corresponding
JI intervals 		comments
0 exact 1/1
1 24.2053 72/71
2 48.4107 36/35
3 72.6160 24/23
4 96.8214 37/35, 55/52
5 121.0267 15/14
6 145.2321 25/23, 37/34
7 169.4374 54/49
8 193.6428 19/17
9 217.8481 17/15
10 242.0534 23/20
11 266.2588 7/6
12 290.4641 71/60
13 314.6695 6/5
14 338.8748 45/37
15 363.0802 37/30
16 387.2855 5/4
17 411.4909 90/71
18 435.6962 9/7
19 459.9016 30/23
20 484.1069 45/34
21 508.3122 51/38
22 532.5176 49/36
23 556.7229
24 580.9283 7/5
25 605.1336
26 629.3390 23/16
27 653.5443 35/24
28 677.7497
29 701.9550 exact 3/2 just perfect fifth
30 726.16035
31 750.3657
32 774.5710
33 798.7764
34 822.9817 45/28
35 847.1871
36 871.3924 81/49
37 895.5978 57/34
38 919.8031 17/10
39 944.00845
40 968.2138 7/4
41 992.4191 16/9
42 1016.6245 9/5
43 1040.8298
44 1065.0352
45 1089.2405 15/8
46 1113.4459
47 1137.6512 56/29
48 1161.8566
49 1186.0619 (2/1-)
50 1210.2672 (2/1+)
51 1234.4726 49/24
52 1258.6779 29/14
53 1282.8833 21/10
54 1307.0886 17/8
55 1331.2940 41/19
56 1355.4993 35/16
57 1379.7047 20/9
58 1403.9100 exact 9/4

See also

Retrieved from "https://en.xen.wiki/index.php?title=29edf&oldid=205985"