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'''[[Ed7|Division of the 7th harmonic]] into 30 equal parts''' (30ed7) is related to [[17edt]], but with the 7/1 rather than the 3/1 being just. The step size is about 112.2942 cents, corresponding to 10.6862 [[edo]].
{{Infobox ET}}
'''[[Ed7|Division of the 7th harmonic]] into 30 equal parts''' (30ed7) is related to [[17edt]], but with the 7/1 rather than the 3/1 being just. The step size is about 112.2942 [[cent]]s, corresponding to 10.6862 [[edo]].


{| class="wikitable"
== Intervals ==
{| class="wikitable mw-collapsible"
|+ Intervals of 30ed7
|-
|-
! | degree
! degree
! | cents value
! cents value
! | corresponding <br>JI intervals
! corresponding <br>JI intervals
! | comments
! comments
|-
|-
| | 0
| 0
| | 0.0000
| 0.0000
| | '''exact [[1/1]]'''
| '''[[1/1]]'''
| |  
|  
|-
|-
| | 1
| 1
| | 112.2942
| 112.2942
| | [[16/15]]
| [[16/15]]
| |  
|  
|-
|-
| | 2
| 2
| | 224.5884
| 224.5884
| | [[25/22]], 91/80, 57/50, 65/57
| [[25/22]], 91/80, 57/50, 65/57
| |  
|  
|-
|-
| | 3
| 3
| | 336.8826
| 336.8826
| | [[17/14]]
| [[17/14]]
| |  
|  
|-
|-
| | 4
| 4
| | 449.1768
| 449.1768
| | [[22/17]], 35/27
| [[22/17]], [[35/27]]
| |  
|  
|-
|-
| | 5
| 5
| | 561.4710
| 561.4710
| | [[18/13]]
| [[18/13]]
| |
| pseudo-[[7/5]]
|-
|-
| | 6
| 6
| | 673.7652
| 673.7652
| | [[28/19]], 96/65, 65/44, 34/23
| [[28/19]], 96/65, 65/44, 34/23
| |  
|  
|-
|-
| | 7
| 7
| | 786.0594
| 786.0594
| | 63/40
| 63/40
| |  
|  
|-
|-
| | 8
| 8
| | 898.3536
| 898.3536
| | 42/25
| 42/25
| |
| pseudo-[[5/3]]
|-
|-
| | 9
| 9
| | 1010.6478
| 1010.6478
| | 70/39
| 70/39
| |  
|  
|-
|-
| | 10
| 10
| | 1122.9420
| 1122.9420
| | 44/23, 245/128
| 44/23, 245/128
| |
|
|-
|-
| | 11
| 11
| | 1235.2362
| 1235.2362
| | [[49/48|49/24]]
| 49/24
| |
| [[49/48]] plus octave
|-
|-
| | 12
| 12
| | 1347.5304
| 1347.5304
| | [[12/11|24/11]]
| 24/11
| |
| [[12/11]] plus octave
|-
|-
| | 13
| 13
| | 1459.8246
| 1459.8246
| |  
|  
| |
| pseudo-[[7/3]]
|-
|-
| | 14
| 14
| | 1572.1188
| 1572.1188
| | 119/48
| 119/48
| |  
|  
|-
|-
| | 15
| 15
| | 1684.4130
| 1684.4130
| | 119/45, 45/17
| 119/45, 45/17
| |  
|  
|-
|-
| | 16
| 16
| | 1796.7072
| 1796.7072
| | [[24/17|48/17]]
| 48/17
| |
| [[24/17]] plus octave
|-
|-
| | 17
| 17
| | 1909.0013
| 1909.0013
| |  
|  
| | pseudo-[[3/1]]
| pseudo-[[3/1]]
|-
|-
| | 18
| 18
| | 2021.2955
| 2021.2955
| | 77/24
| 77/24
| |  
|  
|-
|-
| | 19
| 19
| | 2133.5897
| 2133.5897
| | [[12/7|24/7]]
| 24/7
| |
| [[12/7]] plus octave
|-
|-
| | 20
| 20
| | 2245.8839
| 2245.8839
| | 128/35, 161/44
| 128/35, 161/44
| |  
|  
|-
|-
| | 21
| 21
| | 2358.1781
| 2358.1781
| | 39/10
| 39/10
| |  
|  
|-
|-
| | 22
| 22
| | 2470.4723
| 2470.4723
| | [[25/24|25/6]]
| 25/6
| |
| [[25/24]] plus two octaves
|-
|-
| | 23
| 23
| | 2582.7665
| 2582.7665
| | [[10/9|40/9]]
| 40/9
| |
| [[10/9]] plus two octaves
|-
|-
| | 24
| 24
| | 2695.0607
| 2695.0607
| | 19/4
| 19/4
| |  
|  
|-
|-
| | 25
| 25
| | 2807.3549
| 2807.3549
| | 91/18
| 91/18
| | pseudo-[[5/1]]
| pseudo-[[5/1]]
|-
|-
| | 26
| 26
| | 2919.6491
| 2919.6491
| | [[27/20|27/5]]
| 27/5
| |
| [[27/20]] plus two octaves
|-
|-
| | 27
| 27
| | 3031.9433
| 3031.9433
| | 98/17
| 98/17
| |  
|  
|-
|-
| | 28
| 28
| | 3144.2375
| 3144.2375
| | [[20/13|80/13]]
| 80/13
| |
| [[20/13]] plus two octaves
|-
|-
| | 29
| 29
| | 3256.5317
| 3256.5317
| | 105/16, 46/7
| 105/16, 46/7
| |  
|  
|-
|-
| | 30
| 30
| | 3368.8259
| 3368.8259
| | '''exact [[7/1]]'''
| '''[[7/1]]'''
| | [[7/4|harmonic seventh]] plus two octaves
| [[7/4]] plus two octaves
|}
|}


[[Category:Ed7]]
== Harmonics ==
[[Category:Edonoi]]
{{Harmonics in equal|30|7|1}}
{{Harmonics in equal|30|7|1|collapsed=1|start=12}}
 
 
{{stub}}

Latest revision as of 19:21, 1 August 2025

← 29ed7 30ed7 31ed7 →
Prime factorization 2 × 3 × 5
Step size 112.294 ¢ 
Octave 11\30ed7 (1235.24 ¢)
Twelfth 17\30ed7 (1909 ¢)
Consistency limit 3
Distinct consistency limit 3

Division of the 7th harmonic into 30 equal parts (30ed7) is related to 17edt, but with the 7/1 rather than the 3/1 being just. The step size is about 112.2942 cents, corresponding to 10.6862 edo.

Intervals

Intervals of 30ed7
degree cents value corresponding
JI intervals 		comments
0 0.0000 1/1
1 112.2942 16/15
2 224.5884 25/22, 91/80, 57/50, 65/57
3 336.8826 17/14
4 449.1768 22/17, 35/27
5 561.4710 18/13 pseudo-7/5
6 673.7652 28/19, 96/65, 65/44, 34/23
7 786.0594 63/40
8 898.3536 42/25 pseudo-5/3
9 1010.6478 70/39
10 1122.9420 44/23, 245/128
11 1235.2362 49/24 49/48 plus octave
12 1347.5304 24/11 12/11 plus octave
13 1459.8246 pseudo-7/3
14 1572.1188 119/48
15 1684.4130 119/45, 45/17
16 1796.7072 48/17 24/17 plus octave
17 1909.0013 pseudo-3/1
18 2021.2955 77/24
19 2133.5897 24/7 12/7 plus octave
20 2245.8839 128/35, 161/44
21 2358.1781 39/10
22 2470.4723 25/6 25/24 plus two octaves
23 2582.7665 40/9 10/9 plus two octaves
24 2695.0607 19/4
25 2807.3549 91/18 pseudo-5/1
26 2919.6491 27/5 27/20 plus two octaves
27 3031.9433 98/17
28 3144.2375 80/13 20/13 plus two octaves
29 3256.5317 105/16, 46/7
30 3368.8259 7/1 7/4 plus two octaves

Harmonics

Approximation of harmonics in 30ed7
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +35.2 +7.0 -41.8 +21.0 +42.3 +0.0 -6.6 +14.1 -56.0 +3.6 -34.8
Relative (%) +31.4 +6.3 -37.2 +18.7 +37.7 +0.0 -5.9 +12.5 -49.9 +3.2 -31.0
Steps
(reduced) 		11
(11) 		17
(17) 		21
(21) 		25
(25) 		28
(28) 		30
(0) 		32
(2) 		34
(4) 		35
(5) 		37
(7) 		38
(8)
Approximation of harmonics in 30ed7
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +51.2 +35.2 +28.1 +28.7 +36.0 +49.3 -44.3 -20.8 +7.0 +38.8 -38.2
Relative (%) +45.6 +31.4 +25.0 +25.5 +32.0 +43.9 -39.4 -18.5 +6.3 +34.6 -34.0
Steps
(reduced) 		40
(10) 		41
(11) 		42
(12) 		43
(13) 		44
(14) 		45
(15) 		45
(15) 		46
(16) 		47
(17) 		48
(18) 		48
(18)


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