96ed7: Difference between revisions

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'''[[Ed7|Division of the 7th harmonic]] into 96 equal parts''' (96ed7) is related to the [[Carlos Gamma]], but with the 7/1 rather than the 3/2 being just. The step size is about 35.0919 cents, similar to every fifth step of 171edo.
{{Infobox ET}}
'''[[Ed7|Division of the 7th harmonic]] into 96 equal parts''' (96ed7) is related to the [[Carlos Gamma]], but with the 7/1 rather than the 3/2 being just. The step size is about 35.0919 cents, corresponding to every fifth step of [[171edo]].


{| class="wikitable"
== Intervals ==
{| class="wikitable mw-collapsible"
|+ Intervals of 96ed7
|-
|-
! | degree
! | degree
Line 15: Line 18:
| | 1
| | 1
| | 35.0919
| | 35.0919
| |  
| | [[50/49]], [[49/48]]
| |  
| |  
|-
|-
| | 2
| | 2
| | 70.1839
| | 70.1839
| | 25/24
| | [[25/24]]
| |  
| |  
|-
|-
| | 3
| | 3
| | 105.2758
| | 105.2758
| |  
| | [[17/16]]
| |  
| |  
|-
|-
Line 45: Line 48:
| | 7
| | 7
| | 245.6436
| | 245.6436
| | 144/125
| | [[144/125]]
| |  
| |  
|-
|-
| | 8
| | 8
| | 280.7355
| | 280.7355
| |  
| | [[20/17]]
| |  
| |  
|-
|-
Line 70: Line 73:
| | 12
| | 12
| | 421.1032
| | 421.1032
| |  
| | [[51/40]]
| |  
| |  
|-
|-
Line 95: Line 98:
| | 17
| | 17
| | 596.5629
| | 596.5629
| |  
| | [[24/17]]
| |  
| |  
|-
|-
Line 105: Line 108:
| | 19
| | 19
| | 666.7468
| | 666.7468
| |  
| | [[72/49]]
| |  
| |  
|-
|-
Line 125: Line 128:
| | 23
| | 23
| | 807.1145
| | 807.1145
| |  
| | 51/32
| |  
| |  
|-
|-
Line 145: Line 148:
| | 27
| | 27
| | 947.4823
| | 947.4823
| | 216/125
| | 216/125, 140/81
| |  
| |  
|-
|-
| | 28
| | 28
| | 982.5742
| | 982.5742
| |  
| | [[30/17]]
| |  
| |  
|-
|-
Line 185: Line 188:
| | 35
| | 35
| | 1228.2178
| | 1228.2178
| |  
| | [[64/63|128/63]]
| |  
| |  
|-
|-
| | 36
| | 36
| | 1263.3097
| | 1263.3097
| | 1296/625
| | [[648/625|1296/625]], [[28/27|56/27]]
| |  
| |  
|-
|-
| | 37
| | 37
| | 1298.4017
| | 1298.4017
| |  
| | [[18/17|36/17]]
| |  
| |  
|-
|-
| | 38
| | 38
| | 1333.4936
| | 1333.4936
| | 54/25
| | [[27/25|54/25]]
| |  
| |  
|-
|-
Line 245: Line 248:
| | 47
| | 47
| | 1649.3210
| | 1649.3210
| |  
| | 70/27
| |  
| |  
|-
|-
| | 48
| | 48
| | 1684.4130
| | 1684.4130
| |  
| | 119/45, 45/17
| |  
| |  
|-
|-
| | 49
| | 49
| | 1719.5049
| | 1719.5049
| |  
| | [[27/20|27/10]]
| |  
| |  
|-
|-
Line 265: Line 268:
| | 51
| | 51
| | 1789.6888
| | 1789.6888
| |  
| | [[45/32|45/16]]
| |  
| |  
|-
|-
Line 285: Line 288:
| | 55
| | 55
| | 1930.0565
| | 1930.0565
| |  
| | [[32/21|64/21]]
| |  
| |  
|-
|-
Line 310: Line 313:
| | 60
| | 60
| | 2105.5162
| | 2105.5162
| |  
| | [[27/16|27/8]]
| |  
| |  
|-
|-
Line 350: Line 353:
| | 68
| | 68
| | 2386.2517
| | 2386.2517
| |  
| | 119/30
| |  
| |  
|-
|-
| | 69
| | 69
| | 2421.3436
| | 2421.3436
| |  
| | [[81/80|81/20]]
| |  
| |  
|-
|-
Line 385: Line 388:
| | 75
| | 75
| | 2631.8952
| | 2631.8952
| |  
| | [[8/7|32/7]]
| |  
| |  
|-
|-
Line 430: Line 433:
| | 84
| | 84
| | 2947.7227
| | 2947.7227
| |  
| | [[48/35|192/35]]
| |  
| |  
|-
|-
Line 440: Line 443:
| | 86
| | 86
| | 3017.9065
| | 3017.9065
| |  
| | [[10/7|40/7]]
| |  
| |  
|-
|-
| | 87
| | 87
| | 3052.9985
| | 3052.9985
| | 35/6
| | [[35/24|35/6]]
| |  
| |  
|-
|-
| | 88
| | 88
| | 3088.0904
| | 3088.0904
| |  
| | 119/20
| |  
| |  
|-
|-
Line 480: Line 483:
| | 94
| | 94
| | 3298.6420
| | 3298.6420
| |  
| | 168/25
| |  
| |  
|-
|-
| | 95
| | 95
| | 3333.7340
| | 3333.7340
| |  
| | [[12/7|48/7]]
| |  
| |  
|-
|-
Line 494: Line 497:
|}
|}


[[Category:Ed7]]
== Harmonics ==
[[Category:Edonoi]]
{{Harmonics in equal|96|7|1|intervals=prime}}
{{Harmonics in equal|96|7|1|intervals=prime|collapsed=1|start=12}}
 
 
{{stub}}

Latest revision as of 19:24, 1 August 2025

← 95ed7 96ed7 97ed7 →
Prime factorization 25 × 3
Step size 35.0919 ¢ 
Octave 34\96ed7 (1193.13 ¢) (→ 17\48ed7)
Twelfth 54\96ed7 (1894.96 ¢) (→ 9\16ed7)
Consistency limit 7
Distinct consistency limit 7

Division of the 7th harmonic into 96 equal parts (96ed7) is related to the Carlos Gamma, but with the 7/1 rather than the 3/2 being just. The step size is about 35.0919 cents, corresponding to every fifth step of 171edo.

Intervals

Intervals of 96ed7
degree cents value corresponding
JI intervals 		comments
0 0.0000 exact 1/1
1 35.0919 50/49, 49/48
2 70.1839 25/24
3 105.2758 17/16
4 140.3677
5 175.4597
6 210.5516
7 245.6436 144/125
8 280.7355 20/17
9 315.8274 6/5
10 350.9194
11 386.0113 5/4
12 421.1032 51/40
13 456.1952 125/96
14 491.2871
15 526.3790
16 561.4710
17 596.5629 24/17
18 631.6549 36/25
19 666.7468 72/49
20 701.8387 3/2
21 736.9307
22 772.0226 25/16
23 807.1145 51/32
24 842.2065
25 877.2984
26 912.3903
27 947.4823 216/125, 140/81
28 982.5742 30/17
29 1017.6662 9/5
30 1052.7581
31 1087.8500 15/4
32 1122.9420
33 1158.0339 125/64
34 1193.1258
35 1228.2178 128/63
36 1263.3097 1296/625, 56/27
37 1298.4017 36/17
38 1333.4936 54/25
39 1368.5855
40 1403.6775 9/4
41 1438.7694
42 1473.8613 225/96
43 1508.9533
44 1544.0452
45 1579.1371
46 1614.2291
47 1649.3210 70/27
48 1684.4130 119/45, 45/17
49 1719.5049 27/10
50 1754.5968
51 1789.6888 45/16
52 1824.7807
53 1859.8726
54 1894.9646
55 1930.0565 64/21
56 1965.1484 28/9
57 2000.2404
58 2035.3323
59 2070.4243
60 2105.5162 27/8
61 2140.6081
62 2175.7001
63 2210.7920
64 2245.8839
65 2280.9759 28/15
66 2316.0678
67 2351.1597 35/9
68 2386.2517 119/30
69 2421.3436 81/20
70 2456.4356
71 2491.5275
72 2526.6194
73 2961.7114
74 2596.8033 112/25
75 2631.8952 32/7
76 2666.9872 14/3
77 2702.0791
78 2737.1710 175/36
79 2772.2630
80 2807.3549
81 2842.4469
82 2877.5388
83 2912.6307
84 2947.7227 192/35
85 2982.8146 28/5
86 3017.9065 40/7
87 3052.9985 35/6
88 3088.0904 119/20
89 3123.1824
90 3158.2743
91 3193.3662
92 3228.4582
93 3263.5501
94 3298.6420 168/25
95 3333.7340 48/7
96 3368.8259 exact 7/1 harmonic seventh plus two octaves

Harmonics

Approximation of prime harmonics in 96ed7
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) -6.9 -7.0 -14.1 +0.0 -10.5 +16.1 +7.9 -9.2 +11.0 -4.3 -14.5
Relative (%) -19.6 -19.9 -40.0 +0.0 -29.8 +46.0 +22.6 -26.2 +31.3 -12.3 -41.3
Steps
(reduced) 		34
(34) 		54
(54) 		79
(79) 		96
(0) 		118
(22) 		127
(31) 		140
(44) 		145
(49) 		155
(59) 		166
(70) 		169
(73)
Approximation of prime harmonics in 96ed7
Harmonic 37 41 43 47 53 59 61 67 71 73 79
Error Absolute (¢) -5.0 -7.2 +15.6 +2.0 +4.5 -5.7 +6.8 -15.3 -10.4 +11.7 +15.3
Relative (%) -14.2 -20.6 +44.4 +5.6 +12.9 -16.2 +19.3 -43.5 -29.6 +33.3 +43.7
Steps
(reduced) 		178
(82) 		183
(87) 		186
(90) 		190
(94) 		196
(4) 		201
(9) 		203
(11) 		207
(15) 		210
(18) 		212
(20) 		216
(24)


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