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'''[[Ed7|Division of the 7th harmonic]] into 53 equal parts''' (53ed7) is related to [[19edo]], [[30edt]], and [[Carlos Beta]], but with the 7/1 rather than the 2/1 being just. The octave is about 7.6923 cents stretched and the step size is about 63.5628 cents. The patent val has a generally sharp tendency for harmonics up to 16, with exception for 11th harmonic.
{{Infobox ET}}
{{ED intro}}


{| class="wikitable"
== Theory ==
53ed7 is related to [[19edo]], [[30edt]], and [[Carlos Beta]], but with the 7/1 rather than the [[2/1]] being just. The octave is about 7.6923 cents stretched. Like 19edo, 53ed7 is [[consistent]] to the [[integer limit|10-integer-limit]], but the [[patent val]] has a generally sharp tendency for [[harmonic]]s up to 16, with exception for [[11/1|11th harmonic]].
 
=== Harmonics ===
{{Harmonics in equal|53|7|1|intervals=integer|columns=11}}
{{Harmonics in equal|53|7|1|intervals=integer|columns=11|start=12|collapsed=1|title=Approximation of harmonics in 53ed7 (continued)}}
 
=== Subsets and supersets ===
53ed7 is the 16th [[prime equal division|prime ed7]]. It does not contain any nontrivial subset ed7's.
 
== Intervals ==
{| class="wikitable center-1 right-2 mw-collapsible"
|-
|-
! | degree
! #
! | cents value
! Cents
! | corresponding <br>JI intervals
! Approximate ratios
! | comments
|-
|-
| | 0
| 0
| | 0.0000
| 0.0
| | '''exact [[1/1]]'''
| [[1/1]]
| |
|-
|-
| | 1
| 1
| | 63.5628
| 63.6
| | [[28/27]], [[27/26]]
| [[21/20]], [[25/24]], [[27/26]], [[28/27]]
| |
|-
|-
| | 2
| 2
| | 127.1255
| 127.1
| | [[14/13]]
| [[13/12]], [[14/13]], [[15/14]], [[16/15]]
| |
|-
|-
| | 3
| 3
| | 190.6883
| 190.7
| | [[19/17]]
| [[9/8]], [[10/9]]
| |
|-
|-
| | 4
| 4
| | 254.2510
| 254.3
| | [[22/19]]
| [[7/6]], [[8/7]]
| |
|-
|-
| | 5
| 5
| | 317.8138
| 317.8
| | [[6/5]], 77/64
| [[6/5]]
| |
|-
|-
| | 6
| 6
| | 381.3765
| 381.4
| | 96/77
| [[5/4]]
| |
|-
|-
| | 7
| 7
| | 444.9393
| 444.9
| | [[22/17]]
| [[9/7]]
| |
|-
|-
| | 8
| 8
| | 508.5020
| 508.5
| |
| [[4/3]]
| |
|-
|-
| | 9
| 9
| | 572.0648
| 572.1
| | [[32/23]]
| [[7/5]], [[18/13]]
| |
|-
|-
| | 10
| 10
| | 635.6275
| 635.6
| | [[13/9]]
| [[10/7]], [[13/9]]
| |
|-
|-
| | 11
| 11
| | 699.1903
| 699.2
| | [[3/2]]
| [[3/2]]
| |
|-
|-
| | 12
| 12
| | 762.7530
| 762.8
| | [[14/9]]
| [[14/9]]
| |
|-
|-
| | 13
| 13
| | 826.3158
| 826.3
| |
| [[8/5]], [[13/8]]
| |
|-
|-
| | 14
| 14
| | 889.8785
| 889.9
| | 77/46
| [[5/3]]
| |
|-
|-
| | 15
| 15
| | 953.4413
| 953.4
| | [[26/15]]
| [[7/4]], [[12/7]]
| |
|-
|-
| | 16
| 16
| | 1017.0040
| 1017.0
| | [[9/5]]
| [[9/5]]
| |
|-
|-
| | 17
| 17
| | 1080.5668
| 1080.6
| | [[28/15]]
| [[15/8]]
| |
|-
|-
| | 18
| 18
| | 1144.1296
| 1144.1
| | 64/33
| [[27/14]], [[35/18]]
| |
|-
|-
| | 19
| 19
| | 1207.6923
| 1207.7
| | 161/80
| [[2/1]]
| | pseudo-[[octave]]
|-
|-
| | 20
| 20
| | 1271.2551
| 1271.3
| | [[25/24|25/12]]
| [[21/10]], [[25/12]]
| |
|-
|-
| | 21
| 21
| | 1334.8178
| 1334.8
| | [[27/25|54/25]]
| [[13/6]]
| |
|-
|-
| | 22
| 22
| | 1398.3806
| 1398.4
| | 56/25, 110/49
| [[9/4]]
| |
|-
|-
| | 23
| 23
| | 1461.9433
| 1461.9
| |
| [[7/3]]
| |
|-
|-
| | 24
| 24
| | 1525.5061
| 1525.5
| |
| [[12/5]]
| |
|-
|-
| | 25
| 25
| | 1589.0688
| 1589.1
| | [[5/2]]
| [[5/2]]
| |
|-
|-
| | 26
| 26
| | 1652.6316
| 1652.6
| | [[13/5]]
| [[13/5]]
| |
|-
|-
| | 27
| 27
| | 1716.1943
| 1716.2
| | 35/13
| [[8/3]]
| |
|-
|-
| | 28
| 28
| | 1779.7571
| 1779.8
| | [[14/5]]
| [[14/5]]
| |
|-
|-
| | 29
| 29
| | 1843.3198
| 1843.3
| |
| [[20/7]], [[26/9]]
| |
|-
|-
| | 30
| 30
| | 1906.8826
| 1906.9
| |
| [[3/1]]
| | pseudo-[[3/1]]
|-
|-
| | 31
| 31
| | 1970.4453
| 1970.4
| | [[25/16|25/8]]
| [[25/8]], [[28/9]]
| |
|-
|-
| | 32
| 32
| | 2034.0081
| 2034.0
| | 68/21
| [[13/4]]
| |
|-
|-
| | 33
| 33
| | 2097.5708
| 2097.6
| | [[42/25|84/25]]
| [[10/3]]
| |
|-
|-
| | 34
| 34
| | 2161.1336
| 2161.1
| | 80/23
| [[7/2]]
| |
|-
|-
| | 35
| 35
| | 2224.6964
| 2224.7
| | 76/21
| [[18/5]]
| |
|-
|-
| | 36
| 36
| | 2288.2591
| 2288.3
| | [[15/4]]
| [[15/4]]
| |
|-
|-
| | 37
| 37
| | 2351.8219
| 2351.8
| | 35/9
| [[35/9]]
| |
|-
|-
| | 38
| 38
| | 2415.3846
| 2415.4
| | 105/26
| [[4/1]]
| | pseudo-[[4/1]]
|-
|-
| | 39
| 39
| | 2478.9474
| 2478.9
| | 46/11, [[22/21|88/21]]
| [[21/5]], [[25/6]]
| |
|-
|-
| | 40
| 40
| | 2542.5101
| 2542.5
| | 100/23
| [[13/3]]
| |
|-
|-
| | 41
| 41
| | 2606.0729
| 2606.1
| | [[9/2]]
| [[9/2]]
| |
|-
|-
| | 42
| 42
| | 2669.6356
| 2669.6
| | [[14/3]]
| [[14/3]]
| |
|-
|-
| | 43
| 43
| | 2733.1984
| 2733.2
| | 63/13
| [[24/5]]
| |
|-
|-
| | 44
| 44
| | 2796.7611
| 2796.8
| | 161/32
| [[5/1]]
| | pseudo-[[5/1]]
|-
|-
| | 45
| 45
| | 2860.3239
| 2860.3
| |
| [[21/4]], [[26/5]]
| |
|-
|-
| | 46
| 46
| | 2923.8866
| 2923.9
| | 119/22
| [[16/3]]
| |
|-
|-
| | 47
| 47
| | 2987.4494
| 2987.4
| |
| [[28/5]]
| |
|-
|-
| | 48
| 48
| | 3051.0121
| 3051.0
| | 64/11, 35/6
| [[35/6]]
| |
|-
|-
| | 49
| 49
| | 3114.5749
| 3114.6
| | 133/22
| [[6/1]]
| | pseudo-[[6/1]]
|-
|-
| | 50
| 50
| | 3178.1376
| 3178.1
| | 119/19
| [[50/8]], [[56/9]]
| |
|-
|-
| | 51
| 51
| | 3241.7004
| 3241.7
| | [[13/2]]
| [[13/2]]
| |
|-
|-
| | 52
| 52
| | 3305.2632
| 3305.3
| | [[27/16|27/4]]
| [[27/4]]
| |
|-
|-
| | 53
| 53
| | 3368.8259
| 3368.8
| | '''exact [[7/1]]'''
| [[7/1]]
| | [[7/4|harmonic seventh]] plus two octaves
|}
|}


[[Category:Ed7]]
== See also ==
[[Category:Edonoi]]
* [[11edf]] – relative edf
* [[19edo]] – relative edo
* [[30edt]] – relative edt
* [[49ed6]] – relative ed6
* [[68ed12]] – relative ed12
* [[93ed30]] – relative ed30

Latest revision as of 16:24, 30 March 2025

← 52ed7 53ed7 54ed7 →
Prime factorization 53 (prime)
Step size 63.5628 ¢ 
Octave 19\53ed7 (1207.69 ¢)
Twelfth 30\53ed7 (1906.88 ¢)
Consistency limit 10
Distinct consistency limit 7

53 equal divisions of the 7th harmonic (abbreviated 53ed7) is a nonoctave tuning system that divides the interval of 7/1 into 53 equal parts of about 63.6 ¢ each. Each step represents a frequency ratio of 71/53, or the 53rd root of 7.

Theory

53ed7 is related to 19edo, 30edt, and Carlos Beta, but with the 7/1 rather than the 2/1 being just. The octave is about 7.6923 cents stretched. Like 19edo, 53ed7 is consistent to the 10-integer-limit, but the patent val has a generally sharp tendency for harmonics up to 16, with exception for 11th harmonic.

Harmonics

Approximation of harmonics in 53ed7
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +7.7 +4.9 +15.4 +10.4 +12.6 +0.0 +23.1 +9.9 +18.1 -19.7 +20.3
Relative (%) +12.1 +7.8 +24.2 +16.4 +19.9 +0.0 +36.3 +15.5 +28.5 -31.1 +32.0
Steps
(reduced) 		19
(19) 		30
(30) 		38
(38) 		44
(44) 		49
(49) 		53
(0) 		57
(4) 		60
(7) 		63
(10) 		65
(12) 		68
(15)
Approximation of harmonics in 53ed7 (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +8.9 +7.7 +15.4 +30.8 -10.6 +17.5 -12.5 +25.8 +4.9 -12.0 -25.4
Relative (%) +13.9 +12.1 +24.2 +48.4 -16.7 +27.6 -19.7 +40.6 +7.8 -19.0 -40.0
Steps
(reduced) 		70
(17) 		72
(19) 		74
(21) 		76
(23) 		77
(24) 		79
(26) 		80
(27) 		82
(29) 		83
(30) 		84
(31) 		85
(32)

Subsets and supersets

53ed7 is the 16th prime ed7. It does not contain any nontrivial subset ed7's.

Intervals

# Cents Approximate ratios
0 0.0 1/1
1 63.6 21/20, 25/24, 27/26, 28/27
2 127.1 13/12, 14/13, 15/14, 16/15
3 190.7 9/8, 10/9
4 254.3 7/6, 8/7
5 317.8 6/5
6 381.4 5/4
7 444.9 9/7
8 508.5 4/3
9 572.1 7/5, 18/13
10 635.6 10/7, 13/9
11 699.2 3/2
12 762.8 14/9
13 826.3 8/5, 13/8
14 889.9 5/3
15 953.4 7/4, 12/7
16 1017.0 9/5
17 1080.6 15/8
18 1144.1 27/14, 35/18
19 1207.7 2/1
20 1271.3 21/10, 25/12
21 1334.8 13/6
22 1398.4 9/4
23 1461.9 7/3
24 1525.5 12/5
25 1589.1 5/2
26 1652.6 13/5
27 1716.2 8/3
28 1779.8 14/5
29 1843.3 20/7, 26/9
30 1906.9 3/1
31 1970.4 25/8, 28/9
32 2034.0 13/4
33 2097.6 10/3
34 2161.1 7/2
35 2224.7 18/5
36 2288.3 15/4
37 2351.8 35/9
38 2415.4 4/1
39 2478.9 21/5, 25/6
40 2542.5 13/3
41 2606.1 9/2
42 2669.6 14/3
43 2733.2 24/5
44 2796.8 5/1
45 2860.3 21/4, 26/5
46 2923.9 16/3
47 2987.4 28/5
48 3051.0 35/6
49 3114.6 6/1
50 3178.1 50/8, 56/9
51 3241.7 13/2
52 3305.3 27/4
53 3368.8 7/1

See also

Retrieved from "https://en.xen.wiki/index.php?title=53ed7&oldid=188934"