61ed7: Difference between revisions

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'''[[Ed7|Division of the 7th harmonic]] into 61 equal parts''' (61ed7) is related to the [[Hemifamity temperaments|alphaquarter temperament]], which tempers out 3025/3024, 4000/3993, and 5120/5103 in the 11-limit; 325/324, 364/363, 1001/1000, and 4096/4095 in the 13-limit. The step size is about 55.2267 cents, corresponding to 21.7286 [[edo]].
{{Infobox ET}}
'''[[Ed7|Division of the 7th harmonic]] into 61 equal parts''' (61ed7) is related to the [[Escapade family#Alphaquarter|alphaquarter temperament]], which tempers out 3025/3024, 4000/3993, and 5120/5103 in the 11-limit; 325/324, 364/363, 1001/1000, and 4096/4095 in the 13-limit. The step size is about 55.2267 cents, corresponding to 21.7286 [[edo]].


{| class="wikitable"
== Intervals ==
{| class="wikitable mw-collapsible"
|+ Intervals of 61ed7
|-
|-
! | degree
! | degree
Line 35: Line 38:
| | 5
| | 5
| | 276.1333
| | 276.1333
| |  
| | 88/75
| |  
| |  
|-
|-
| | 6
| | 6
| | 331.3599
| | 331.3599
| |  
| | 40/33
| |  
| |  
|-
|-
Line 50: Line 53:
| | 8
| | 8
| | 441.8132
| | 441.8132
| |  
| | (49/38)
| |  
| |  
|-
|-
Line 65: Line 68:
| | 11
| | 11
| | 607.4932
| | 607.4932
| | 91/64, [[64/45]]
| | (91/64), [[64/45]]
| |  
| |  
|-
|-
Line 75: Line 78:
| | 13
| | 13
| | 717.9465
| | 717.9465
| |  
| | 50/33
| |  
| |  
|-
|-
Line 140: Line 143:
| | 26
| | 26
| | 1435.8930
| | 1435.8930
| |  
| | 55/24
| |  
| |  
|-
|-
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| | 29
| | 29
| | 1601.5730
| | 1601.5730
| |  
| | [[63/50|63/25]]
| |  
| |  
|-
|-
Line 210: Line 213:
| | 40
| | 40
| | 2209.0662
| | 2209.0662
| | [[34/19|68/19]]
| | ([[34/19|68/19]])
| |  
| |  
|-
|-
| | 41
| | 41
| | 2264.2928
| | 2264.2928
| | [[50/27|100/27]]
| | 100/27
| |  
| |  
|-
|-
Line 230: Line 233:
| | 44
| | 44
| | 2429.9728
| | 2429.9728
| | 57/14, [[56/55|224/55]], [[55/54|110/27]]
| | (57/14), [[56/55|224/55]], 110/27
| |  
| |  
|-
|-
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| | 50
| | 50
| | 2761.3327
| | 2761.3327
| | [[16/13|64/13]]
| | ([[16/13|64/13]])
| |  
| |  
|-
|-
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| | 53
| | 53
| | 2927.0127
| | 2927.0127
| | [[19/14|38/7]]
| | ([[19/14|38/7]])
| |  
| |  
|-
|-
Line 295: Line 298:
| | 57
| | 57
| | 3147.9193
| | 3147.9193
| | [[20/13|80/13]]
| | ([[20/13|80/13]])
| |  
| |  
|-
|-
Line 310: Line 313:
| | 60
| | 60
| | 3313.5993
| | 3313.5993
| | [[22/13|88/13]]
| | ([[22/13|88/13]])
| |  
| |  
|-
|-
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|}
|}


[[Category:Ed7]]
== Harmonics ==
[[Category:Edonoi]]
{{Harmonics in equal|61|7|1}}
{{Harmonics in equal|61|7|1|collapsed=1|start=12}}
 
== Music ==
* [https://www.youtube.com/watch?v=FcF2wKqBiCs A Gift (a day late, i am ashamed)] by [[Nicolai Pulley]]
 
{{todo|expand}}

Latest revision as of 19:23, 1 August 2025

← 60ed7 61ed7 62ed7 →
Prime factorization 61 (prime)
Step size 55.2267 ¢ 
Octave 22\61ed7 (1214.99 ¢)
Twelfth 34\61ed7 (1877.71 ¢)
Consistency limit 2
Distinct consistency limit 2

Division of the 7th harmonic into 61 equal parts (61ed7) is related to the alphaquarter temperament, which tempers out 3025/3024, 4000/3993, and 5120/5103 in the 11-limit; 325/324, 364/363, 1001/1000, and 4096/4095 in the 13-limit. The step size is about 55.2267 cents, corresponding to 21.7286 edo.

Intervals

Intervals of 61ed7
degree cents value corresponding
JI intervals 		comments
0 0.0000 exact 1/1
1 55.2267 33/32
2 110.4533 16/15
3 165.6800 11/10
4 220.9066 25/22
5 276.1333 88/75
6 331.3599 40/33
7 386.5866 5/4
8 441.8132 (49/38)
9 497.0399 4/3
10 552.2665 11/8
11 607.4932 (91/64), 64/45
12 662.7199 22/15
13 717.9465 50/33
14 773.1732 25/16
15 828.3998
16 883.6265 5/3
17 938.8531 55/32
18 994.0798 16/9
19 1049.3064 11/6
20 1104.5331
21 1159.7597
22 1214.9864
23 1270.2130 25/12
24 1325.4397
25 1380.6664 20/9
26 1435.8930 55/24
27 1491.1197
28 1546.3463
29 1601.5730 63/25
30 1656.7996
31 1712.0263
32 1767.2529 25/9
33 1822.4796
34 1877.7062
35 1932.9329
36 1988.1596
37 2043.3862 88/27
38 2098.6129 84/25
39 2153.8395
40 2209.0662 (68/19)
41 2264.2928 100/27
42 2319.5195 42/11
43 2374.7461 63/16
44 2429.9728 (57/14), 224/55, 110/27
45 2485.1994 21/5
46 2540.4261 (13/3)
47 2595.6527
48 2650.8794
49 2706.1061 105/22
50 2761.3327 (64/13)
51 2816.5594 56/11
52 2871.7860 21/4
53 2927.0127 (38/7)
54 2982.2393 28/5
55 3037.4660 (52/9)
56 3092.6926
57 3147.9193 (80/13)
58 3203.1459 70/11
59 3258.3726 105/16
60 3313.5993 (88/13)
61 3368.8259 exact 7/1 harmonic seventh plus two octaves

Harmonics

Approximation of harmonics in 61ed7
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +15.0 -24.2 -25.3 -25.0 -9.3 +0.0 -10.3 +6.7 -10.0 -9.3 +5.7
Relative (%) +27.1 -43.9 -45.7 -45.2 -16.8 +0.0 -18.6 +12.2 -18.1 -16.9 +10.4
Steps
(reduced) 		22
(22) 		34
(34) 		43
(43) 		50
(50) 		56
(56) 		61
(0) 		65
(4) 		69
(8) 		72
(11) 		75
(14) 		78
(17)
Approximation of harmonics in 61ed7
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -22.4 +15.0 +6.0 +4.7 +10.2 +21.7 -16.7 +5.0 -24.2 +5.7 -16.1
Relative (%) -40.6 +27.1 +10.9 +8.5 +18.5 +39.3 -30.2 +9.0 -43.9 +10.3 -29.1
Steps
(reduced) 		80
(19) 		83
(22) 		85
(24) 		87
(26) 		89
(28) 		91
(30) 		92
(31) 		94
(33) 		95
(34) 		97
(36) 		98
(37)

Music

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