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This system can be approximated as 41.34495 EDO, meaning each step of 96ed5 corresponds roughly to three steps of [[124edo]], or [[124ed8]].
This system can be approximated as 41.34495 EDO, meaning each step of 96ed5 corresponds roughly to three steps of [[124edo]], or [[124ed8]].


96ed5 sets a height record on the [[The Riemann zeta function and tuning|Riemann zeta function]] with [[The Riemann zeta function and tuning#Removing primes|primes 2 and 3 removed]], approximating 41.3478 EDO. This record remains unbeaten until approximately 98.62575 EDO (~[[229ed5]]).
96ed5 sets a height record on the [[Riemann zeta function]] with [[Riemann zeta function#Removing primes|primes 2 and 3 removed]], approximating 41.3478 EDO. This record remains unbeaten until approximately 98.62575 EDO (~[[229ed5]]).


Additionally, 96ed5 is related to [[186zpi]].
Additionally, 96ed5 is related to [[186zpi]].
Line 18: Line 18:


== Intervals ==
== Intervals ==


{| class="wikitable center-1 right-2 mw-collapsible mw-collapsed"
{| class="wikitable center-1 right-2 mw-collapsible mw-collapsed"
Line 24: Line 23:
! Steps
! Steps
! Cents
! Cents
! Approximate ratios
! 8.9.5.7.11.13.17.23 ratios
|-
|-
| 0
| 0
Line 32: Line 31:
| 1
| 1
| 29
| 29
|  
| [[56/55]], [[64/63]], [[65/64]], [[117/115]], [[119/117]], [[121/119]], [[637/625]]
|-
|-
| 2
| 2
| 58
| 58
| [[30/29]], [[31/30]]
| [[65/63]], [[119/115]], [[121/117]], [[125/121]], [[175/169]]
|-
|-
| 3
| 3
| 87.1
| 87.1
| [[41/39]]
| [[81/77]], [[104/99]], [[121/115]], [[143/136]], [[343/325]], [[637/605]]
|-
|-
| 4
| 4
| 116.1
| 116.1
| [[31/29]]
| [[77/72]], [[91/85]], [[153/143]]
|-
|-
| 5
| 5
| 145.1
| 145.1
| [[25/23]], [[37/34]]
| [[25/23]]
|-
|-
| 6
| 6
| 174.1
| 174.1
| [[21/19]]
| [[72/65]]
|-
|-
| 7
| 7
| 203.2
| 203.2
|  
| [[9/8]], [[55/49]]
|-
|-
| 8
| 8
| 232.2
| 232.2
|  
| [[8/7]], [[143/125]]
|-
|-
| 9
| 9
| 261.2
| 261.2
| [[36/31]], [[43/37]]
| [[99/85]]
|-
|-
| 10
| 10
| 290.2
| 290.2
| [[13/11]]
| [[13/11]], [[77/65]]
|-
|-
| 11
| 11
Line 76: Line 75:
| 12
| 12
| 348.3
| 348.3
|  
| [[11/9]], [[104/85]], [[175/143]]
|-
|-
| 13
| 13
| 377.3
| 377.3
| [[41/33]]
|  
|-
|-
| 14
| 14
| 406.3
| 406.3
| [[43/34]]
|  
|-
|-
| 15
| 15
| 435.4
| 435.4
|  
| [[9/7]]
|-
|-
| 16
| 16
Line 96: Line 95:
| 17
| 17
| 493.4
| 493.4
|  
| [[65/49]], [[121/91]]
|-
|-
| 18
| 18
| 522.4
| 522.4
| [[23/17]]
| [[23/17]], [[169/125]]
|-
|-
| 19
| 19
| 551.5
| 551.5
|  
| [[11/8]], [[125/91]]
|-
|-
| 20
| 20
| 580.5
| 580.5
| [[7/5]]
| [[7/5]], [[169/121]]
|-
|-
| 21
| 21
| 609.5
| 609.5
| [[37/26]]
|  
|-
|-
| 22
| 22
| 638.5
| 638.5
|  
| [[13/9]], [[175/121]]
|-
|-
| 23
| 23
Line 128: Line 127:
| 25
| 25
| 725.6
| 725.6
| [[35/23]], [[38/25]]
| [[35/23]]
|-
|-
| 26
| 26
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| 28
| 28
| 812.7
| 812.7
|  
| [[8/5]]
|-
|-
| 29
| 29
| 841.7
| 841.7
|  
| [[13/8]], [[125/77]]
|-
|-
| 30
| 30
| 870.7
| 870.7
| [[38/23]], [[43/26]]
| [[91/55]]
|-
|-
| 31
| 31
| 899.7
| 899.7
| [[37/22]], [[42/25]]
|  
|-
|-
| 32
| 32
| 928.8
| 928.8
|  
| [[245/143]]
|-
|-
| 33
| 33
| 957.8
| 957.8
| [[33/19]]
| [[40/23]]
|-
|-
| 34
| 34
Line 168: Line 167:
| 35
| 35
| 1015.8
| 1015.8
|  
| [[9/5]]
|-
|-
| 36
| 36
| 1044.9
| 1044.9
| [[42/23]]
|  
|-
|-
| 37
| 37
| 1073.9
| 1073.9
| [[13/7]]
| [[13/7]], [[121/65]]
|-
|-
| 38
| 38
| 1102.9
| 1102.9
|  
| [[17/9]]
|-
|-
| 39
| 39
Line 188: Line 187:
| 40
| 40
| 1161
| 1161
| [[43/22]]
| [[45/23]], [[49/25]]
|-
|-
| 41
| 41
Line 196: Line 195:
| 42
| 42
| 1219
| 1219
|  
| [[245/121]], [[343/169]]
|-
|-
| 43
| 43
Line 208: Line 207:
| 45
| 45
| 1306.1
| 1306.1
|  
| [[17/8]], [[49/23]]
|-
|-
| 46
| 46
Line 216: Line 215:
| 47
| 47
| 1364.1
| 1364.1
| [[11/5]]
| [[11/5]], [[169/77]]
|-
|-
| 48
| 48
| 1393.2
| 1393.2
| [[38/17]]
|  
|-
|-
| 49
| 49
Line 232: Line 231:
| 51
| 51
| 1480.2
| 1480.2
|  
| [[40/17]]
|-
|-
| 52
| 52
| 1509.3
| 1509.3
|  
| [[55/23]]
|-
|-
| 53
| 53
| 1538.3
| 1538.3
| [[17/7]]
| [[17/7]], [[56/23]]
|-
|-
| 54
| 54
| 1567.3
| 1567.3
| [[42/17]]
| [[121/49]]
|-
|-
| 55
| 55
Line 252: Line 251:
| 56
| 56
| 1625.3
| 1625.3
|  
| [[23/9]], [[125/49]]
|-
|-
| 57
| 57
Line 260: Line 259:
| 58
| 58
| 1683.4
| 1683.4
| [[37/14]]
| [[45/17]]
|-
|-
| 59
| 59
Line 268: Line 267:
| 60
| 60
| 1741.4
| 1741.4
| [[41/15]]
| [[63/23]]
|-
|-
| 61
| 61
| 1770.5
| 1770.5
|  
| [[25/9]], [[64/23]]
|-
|-
| 62
| 62
| 1799.5
| 1799.5
|  
| [[65/23]]
|-
|-
| 63
| 63
| 1828.5
| 1828.5
|  
| [[23/8]], [[49/17]]
|-
|-
| 64
| 64
| 1857.5
| 1857.5
| [[38/13]]
| [[143/39]]
|-
|-
| 65
| 65
Line 292: Line 291:
| 66
| 66
| 1915.6
| 1915.6
|  
| [[275/91]]
|-
|-
| 67
| 67
| 1944.6
| 1944.6
| [[43/14]]
| [[40/13]], [[77/25]], [[169/55]]
|-
|-
| 68
| 68
| 1973.6
| 1973.6
|  
| [[25/8]], [[72/23]]
|-
|-
| 69
| 69
Line 308: Line 307:
| 70
| 70
| 2031.7
| 2031.7
| [[42/13]]
| [[55/17]]
|-
|-
| 71
| 71
| 2060.7
| 2060.7
| [[23/7]]
| [[23/7]], [[56/17]]
|-
|-
| 72
| 72
| 2089.7
| 2089.7
|  
| [[77/23]]
|-
|-
| 73
| 73
Line 324: Line 323:
| 74
| 74
| 2147.8
| 2147.8
| [[38/11]]
| [[45/13]], [[121/35]], [[169/49]]
|-
|-
| 75
| 75
| 2176.8
| 2176.8
|  
| [[81/23]]
|-
|-
| 76
| 76
Line 336: Line 335:
| 77
| 77
| 2234.9
| 2234.9
|  
| [[40/11]], [[91/25]]
|-
|-
| 78
| 78
| 2263.9
| 2263.9
| [[37/10]]
| [[63/17]], [[85/23]]
|-
|-
| 79
| 79
| 2292.9
| 2292.9
|  
| [[49/13]], [[64/17]]
|-
|-
| 80
| 80
| 2321.9
| 2321.9
| [[42/11]]
| [[65/17]]
|-
|-
| 81
| 81
| 2351
| 2351
|  
| [[35/9]]
|-
|-
| 82
| 82
| 2380
| 2380
|  
| [[91/23]]
|-
|-
| 83
| 83
Line 364: Line 363:
| 84
| 84
| 2438
| 2438
|  
| [[45/11]], [[143/35]]
|-
|-
| 85
| 85
Line 372: Line 371:
| 86
| 86
| 2496.1
| 2496.1
|  
| [[55/13]], [[72/17]]
|-
|-
| 87
| 87
| 2525.1
| 2525.1
| [[43/10]]
| [[56/13]], [[99/23]]
|-
|-
| 88
| 88
| 2554.1
| 2554.1
|  
| [[35/8]]
|-
|-
| 89
| 89
| 2583.1
| 2583.1
|  
| [[40/9]], [[49/11]]
|-
|-
| 90
| 90
| 2612.2
| 2612.2
|  
| [[77/17]], [[104/23]]
|-
|-
| 91
| 91
Line 400: Line 399:
| 93
| 93
| 2699.2
| 2699.2
|  
| [[81/17]]
|-
|-
| 94
| 94
| 2728.3
| 2728.3
| [[29/6]]
| [[63/13]], [[121/25]], [[169/35]]
|-
|-
| 95
| 95
| 2757.3
| 2757.3
|  
| [[64/13]]
|-
|-
| 96
| 96
| 2786.3
| 2786.3
| [[5/1]]
| [[5/1]]
|}{{Todo|replace auto-generated table of intervals with manually curated table}}
|}


== Optimization ==
== Optimization ==
Retrieved from "https://en.xen.wiki/w/96ed5"