49ed7: Difference between revisions

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Divides the seventh harmonics into 49 equal steps. It is similar to every second step of [[35edo|35edo]].
{{Infobox ET}}
'''49ED7''' is the [[Ed7|equal division of the 7th harmonic]] into 49 parts of 68.7515 [[cent|cents]] each. It is similar to every second step of [[35edo]].


49
== Intervals ==
{| class="wikitable mw-collapsible"
|+ Intervals of 49ed7
|-
! | degree
! | cents value
! | corresponding <br>JI intervals
! | comments
|-
| | 0
| | 0.00000
| | '''exact [[1/1]]'''
| |
|-
| | 1
| | 68.75155
| | [[26/25]], [[25/24]]
| |
|-
| | 2
| | 137.50310
| | [[13/12]]
| |
|-
| | 3
| | 206.25465
| | [[9/8]]
| |
|-
| | 4
| | 275.00620
| | 27/23
| |
|-
| | 5
| | 343.75775
| | 39/32
| |
|-
| | 6
| | 412.50929
| | 33/26
| |
|-
| | 7
| | 481.26084
| | 33/25, 119/90
| |
|-
| | 8
| | 550.01239
| | [[11/8]]
| |
|-
| | 9
| | 618.76394
| | [[10/7]], 63/44
| |
|-
| | 10
| | 687.51549
| | 49/33
| |
|-
| | 11
| | 756.26704
| | 161/104
| |
|-
| | 12
| | 825.01859
| | 161/100
| |
|-
| | 13
| | 893.77014
| | 77/46, 161/96
| |
|-
| | 14
| | 962.52169
| | 68/39
| |
|-
| | 15
| | 1031.27324
| | 49/27
| |
|-
| | 16
| | 1100.02479
| | [[17/9]]
| |
|-
| | 17
| | 1168.77633
| | 100/51, 51/26, 108/55, 55/28, 112/57
| |
|-
| | 18
| | 1237.52788
| | [[50/49|100/49]], [[49/48|49/24]], [[45/44|45/22]]
| |
|-
| | 19
| | 1306.27943
| | [[17/16|17/8]]
| |
|-
| | 20
| | 1375.03098
| | 133/60
| |
|-
| | 21
| | 1443.78253
| | 23/10
| |
|-
| | 22
| | 1512.53408
| | [[12/5]]
| |
|-
| | 23
| | 1581.28563
| |
| |
|-
| | 24
| | 1650.03718
| | 70/27
| |
|-
| | 25
| | 1718.78873
| | [[27/20|27/10]]
| |
|-
| | 26
| | 1787.54028
| | 160/57
| |
|-
| | 27
| | 1856.29183
| | 35/12
| |
|-
| | 28
| | 1925.04338
| | 70/23
| |
|-
| | 29
| | 1993.79492
| | [[30/19|60/19]]
| |
|-
| | 30
| | 2062.54647
| | 23/7
| |
|-
| | 31
| | 2131.29802
| | [[12/7|24/7]]
| |
|-
| | 32
| | 2200.04957
| | 57/16
| |
|-
| | 33
| | 2268.80112
| | 63/17
| |
|-
| | 34
| | 2337.55267
| | 27/7
| |
|-
| | 35
| | 2406.30422
| | 273/68
| |
|-
| | 36
| | 2475.05577
| | 96/23, 46/11
| |
|-
| | 37
| | 2543.80732
| | 100/23
| |
|-
| | 38
| | 2612.55887
| | 104/23
| |
|-
| | 39
| | 2681.31042
| | 33/7
| |
|-
| | 40
| | 2750.06196
| | [[11/9|44/9]], [[49/40|49/10]]
| |
|-
| | 41
| | 2818.81351
| | [[14/11|56/11]]
| |
|-
| | 42
| | 2887.56506
| | 90/17, 175/33
| |
|-
| | 43
| | 2956.31661
| |
| |
|-
| | 44
| | 3025.06816
| |
| |
|-
| | 45
| | 3093.81971
| | 161/27
| |
|-
| | 46
| | 3162.57126
| | [[14/9|56/9]]
| |
|-
| | 47
| | 3231.32281
| | [[21/13|84/13]]
| |
|-
| | 48
| | 3300.07436
| | [[42/25|168/25]], 175/26
| |
|-
| | 49
| | 3368.82591
| | '''exact [[7/1]]'''
| | [[7/4|harmonic seventh]] plus two octaves
|}


!
== Harmonics ==
 
{{Harmonics in equal|49|7|1}}
68.75155
{{Harmonics in equal|49|7|1|collapsed=1|start=12}}
 
137.50310
 
206.25465
 
275.00620
 
343.75775
 
412.50929
 
481.26084
 
550.01239
 
618.76394
 
687.51549
 
756.26704
 
825.01859
 
893.77014
 
962.52169
 
1031.27324
 
1100.02479
 
1168.77633
 
1237.52788
 
1306.27943
 
1375.03098
 
1443.78253
 
1512.53408
 
1581.28563
 
1650.03718
 
1718.78873
 
1787.54028
 
1856.29183
 
1925.04338
 
1993.79492
 
2062.54647
 
2131.29802
 
2200.04957
 
2268.80112
 
2337.55267
 
2406.30422
 
2475.05577
 
2543.80732
 
2612.55887
 
2681.31042
 
2750.06196
 
2818.81351
 
2887.56506
 
2956.31661
 
3025.06816
 
3093.81971
 
3162.57126
 
3231.32281
 
3300.07436
 
7/1


== Music ==
== Music ==
* [http://soundcloud.com/ahornberg/sets/49ed7 49ed7] by Ahornberg
* [http://soundcloud.com/ahornberg/sets/49ed7 49ed7] by [[Ahornberg]]


[[Category:Ed7]]
{{todo|expand}}
[[Category:Listening]]
[[Category:Listen]]

Latest revision as of 19:23, 1 August 2025

← 48ed7 49ed7 50ed7 →
Prime factorization 72
Step size 68.7515 ¢ 
Octave 17\49ed7 (1168.78 ¢)
Twelfth 28\49ed7 (1925.04 ¢) (→ 4\7ed7)
Consistency limit 2
Distinct consistency limit 2

49ED7 is the equal division of the 7th harmonic into 49 parts of 68.7515 cents each. It is similar to every second step of 35edo.

Intervals

Intervals of 49ed7
degree cents value corresponding
JI intervals 		comments
0 0.00000 exact 1/1
1 68.75155 26/25, 25/24
2 137.50310 13/12
3 206.25465 9/8
4 275.00620 27/23
5 343.75775 39/32
6 412.50929 33/26
7 481.26084 33/25, 119/90
8 550.01239 11/8
9 618.76394 10/7, 63/44
10 687.51549 49/33
11 756.26704 161/104
12 825.01859 161/100
13 893.77014 77/46, 161/96
14 962.52169 68/39
15 1031.27324 49/27
16 1100.02479 17/9
17 1168.77633 100/51, 51/26, 108/55, 55/28, 112/57
18 1237.52788 100/49, 49/24, 45/22
19 1306.27943 17/8
20 1375.03098 133/60
21 1443.78253 23/10
22 1512.53408 12/5
23 1581.28563
24 1650.03718 70/27
25 1718.78873 27/10
26 1787.54028 160/57
27 1856.29183 35/12
28 1925.04338 70/23
29 1993.79492 60/19
30 2062.54647 23/7
31 2131.29802 24/7
32 2200.04957 57/16
33 2268.80112 63/17
34 2337.55267 27/7
35 2406.30422 273/68
36 2475.05577 96/23, 46/11
37 2543.80732 100/23
38 2612.55887 104/23
39 2681.31042 33/7
40 2750.06196 44/9, 49/10
41 2818.81351 56/11
42 2887.56506 90/17, 175/33
43 2956.31661
44 3025.06816
45 3093.81971 161/27
46 3162.57126 56/9
47 3231.32281 84/13
48 3300.07436 168/25, 175/26
49 3368.82591 exact 7/1 harmonic seventh plus two octaves

Harmonics

Approximation of harmonics in 49ed7
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -31.2 +23.1 +6.3 +32.5 -8.1 +0.0 -24.9 -22.6 +1.3 -26.2 +29.4
Relative (%) -45.4 +33.6 +9.2 +47.3 -11.8 +0.0 -36.2 -32.8 +1.9 -38.1 +42.8
Steps
(reduced) 		17
(17) 		28
(28) 		35
(35) 		41
(41) 		45
(45) 		49
(0) 		52
(3) 		55
(6) 		58
(9) 		60
(11) 		63
(14)
Approximation of harmonics in 49ed7
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +28.3 -31.2 -13.2 +12.6 -23.6 +15.0 -9.9 -29.9 +23.1 +11.3 +3.1
Relative (%) +41.2 -45.4 -19.1 +18.3 -34.3 +21.7 -14.4 -43.6 +33.6 +16.4 +4.5
Steps
(reduced) 		65
(16) 		66
(17) 		68
(19) 		70
(21) 		71
(22) 		73
(24) 		74
(25) 		75
(26) 		77
(28) 		78
(29) 		79
(30)

Music

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