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{{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]].
'''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]].


{| class="wikitable"
== Intervals ==
{| class="wikitable mw-collapsible"
|+ Intervals of 49ed7
|-
|-
! | degree
! | degree
Line 9: Line 12:
|-
|-
| | 0
| | 0
| | 0.0000
| | 0.00000
| | '''exact [[1/1]]'''
| | '''exact [[1/1]]'''
| |  
| |  
Line 15: Line 18:
| | 1
| | 1
| | 68.75155
| | 68.75155
| | [[26/25]] ~ [[25/24]]
| | [[26/25]], [[25/24]]
| |  
| |  
|-
|-
Line 40: Line 43:
| | 6
| | 6
| | 412.50929
| | 412.50929
| |  
| | 33/26
| |  
| |  
|-
|-
| | 7
| | 7
| | 481.26084
| | 481.26084
| |  
| | 33/25, 119/90
| |  
| |  
|-
|-
Line 55: Line 58:
| | 9
| | 9
| | 618.76394
| | 618.76394
| | [[10/7]]
| | [[10/7]], 63/44
| |  
| |  
|-
|-
| | 10
| | 10
| | 687.51549
| | 687.51549
| |  
| | 49/33
| |  
| |  
|-
|-
| | 11
| | 11
| | 756.26704
| | 756.26704
| |  
| | 161/104
| |  
| |  
|-
|-
| | 12
| | 12
| | 825.01859
| | 825.01859
| |  
| | 161/100
| |  
| |  
|-
|-
| | 13
| | 13
| | 893.77014
| | 893.77014
| |  
| | 77/46, 161/96
| |  
| |  
|-
|-
| | 14
| | 14
| | 962.52169
| | 962.52169
| |  
| | 68/39
| |  
| |  
|-
|-
Line 95: Line 98:
| | 17
| | 17
| | 1168.77633
| | 1168.77633
| | 100/51 ~ 51/26 ~ 108/55 ~ 55/28 ~ 112/57
| | 100/51, 51/26, 108/55, 55/28, 112/57
| |  
| |  
|-
|-
| | 18
| | 18
| | 1237.52788
| | 1237.52788
| | [[50/49|100/49]] ~ [[49/48|49/24]] ~ [[45/44|45/22]]
| | [[50/49|100/49]], [[49/48|49/24]], [[45/44|45/22]]
| |  
| |  
|-
|-
Line 110: Line 113:
| | 20
| | 20
| | 1375.03098
| | 1375.03098
| |  
| | 133/60
| |  
| |  
|-
|-
Line 140: Line 143:
| | 26
| | 26
| | 1787.54028
| | 1787.54028
| |  
| | 160/57
| |  
| |  
|-
|-
| | 27
| | 27
| | 1856.29183
| | 1856.29183
| |  
| | 35/12
| |  
| |  
|-
|-
| | 28
| | 28
| | 1925.04338
| | 1925.04338
| |  
| | 70/23
| |  
| |  
|-
|-
Line 175: Line 178:
| | 33
| | 33
| | 2268.80112
| | 2268.80112
| |  
| | 63/17
| |  
| |  
|-
|-
Line 185: Line 188:
| | 35
| | 35
| | 2406.30422
| | 2406.30422
| |  
| | 273/68
| |  
| |  
|-
|-
| | 36
| | 36
| | 2475.05577
| | 2475.05577
| | 96/23 ~ 46/11
| | 96/23, 46/11
| |  
| |  
|-
|-
Line 205: Line 208:
| | 39
| | 39
| | 2681.31042
| | 2681.31042
| |  
| | 33/7
| |  
| |  
|-
|-
| | 40
| | 40
| | 2750.06196
| | 2750.06196
| | [[49/40|49/10]]
| | [[11/9|44/9]], [[49/40|49/10]]
| |  
| |  
|-
|-
Line 220: Line 223:
| | 42
| | 42
| | 2887.56506
| | 2887.56506
| |  
| | 90/17, 175/33
| |  
| |  
|-
|-
Line 235: Line 238:
| | 45
| | 45
| | 3093.81971
| | 3093.81971
| |  
| | 161/27
| |  
| |  
|-
|-
Line 250: Line 253:
| | 48
| | 48
| | 3300.07436
| | 3300.07436
| | [[42/25|168/25]] ~ 175/26
| | [[42/25|168/25]], 175/26
| |  
| |  
|-
|-
Line 258: Line 261:
| | [[7/4|harmonic seventh]] plus two octaves
| | [[7/4|harmonic seventh]] plus two octaves
|}
|}
== Harmonics ==
{{Harmonics in equal|49|7|1}}
{{Harmonics in equal|49|7|1|collapsed=1|start=12}}


== 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:Edonoi]]
[[Category:Listen]]
[[Category:Listening]]

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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