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== Intervals ==
== Intervals ==
{| class="wikitable center-1 right-2 left-3 center-4 center-5"
|-
|+ style="white-space:nowrap" | Intervals in 45zpi
| colspan="3" style="text-align:left;" | JI ratios are comprised of 32-integer limit ratios,<br>and are stylized as follows to indicate their accuracy:
* '''<u>Bold Underlined:</u>''' relative error < 8.333 %
* '''Bold:''' relative error < 16.667 %
* Normal: relative error < 25 %
* <small>Small:</small> relative error < 33.333 %
* <small><small>Small Small:</small></small> relative error < 41.667 %
* <small><small><small>Small Small Small:</small></small></small> relative error < 50 %
| colspan="2" style="text-align:right;" | <center>'''⟨73 116] at every 5 steps'''</center><br>[[9/8|Whole tone]] = 13 steps<br>[[256/243|Limma]] = 4 steps<br>[[2187/2048|Apotome]] = 9 steps
|-
! Degree
! Cents
! Ratios
! Ups and Downs Notation
! Step
|-
| 0
| 0.000
|
| P1
| 0
|-
| 1
| 82.223
| <small>[[32/31]]</small>, <small>[[31/30]]</small>, <small>[[30/29]]</small>, <small>[[29/28]]</small>, [[28/27]], [[27/26]], [[26/25]], '''[[25/24]]''', '''[[24/23]]''', '''<u>[[23/22]]'''</u>, '''<u>[[22/21]]'''</u>, '''<u>[[21/20]]'''</u>, '''<u>[[20/19]]'''</u>, '''[[19/18]]''', [[18/17]], <small>[[17/16]]</small>, <small><small>[[16/15]]</small></small>, <small><small>[[31/29]]</small></small>, <small><small><small>[[15/14]]</small></small></small>
| ^m2
| 5
|-
| 2
| 164.446
| <small><small><small>[[29/27]]</small></small></small>, <small><small><small>[[14/13]]</small></small></small>, <small><small>[[27/25]]</small></small>, <small>[[13/12]]</small>, [[25/23]], [[12/11]], '''[[23/21]]''', '''<u>[[11/10]]'''</u>, '''<u>[[32/29]]'''</u>, '''[[21/19]]''', '''[[31/28]]''', [[10/9]], <small>[[29/26]]</small>, <small><small>[[19/17]]</small></small>, <small><small>[[28/25]]</small></small>, <small><small><small>[[9/8]]</small></small></small>
| vvvM2
| 10
|-
| 3
| 246.669
| <small><small><small>[[26/23]]</small></small></small>, <small><small>[[17/15]]</small></small>, <small>[[25/22]]</small>, [[8/7]], '''[[31/27]]''', '''<u>[[23/20]]'''</u>, '''<u>[[15/13]]'''</u>, '''[[22/19]]''', '''[[29/25]]''', [[7/6]], <small><small>[[27/23]]</small></small>, <small><small><small>[[20/17]]</small></small></small>
| ^^M2, vvm3
| 15
|-
| 4
| 328.892
| <small><small><small>[[13/11]]</small></small></small>, <small><small><small>[[32/27]]</small></small></small>, <small><small>[[19/16]]</small></small>, <small>[[25/21]]</small>, <small>[[31/26]]</small>, '''[[6/5]]''', '''<u>[[29/24]]'''</u>, '''<u>[[23/19]]'''</u>, '''[[17/14]]''', '''[[28/23]]''', [[11/9]], <small>[[27/22]]</small>, <small><small>[[16/13]]</small></small>, <small><small><small>[[21/17]]</small></small></small>, <small><small><small>[[26/21]]</small></small></small>
| ^^^m3
| 20
|-
| 5
| 411.116
| <small><small><small>[[31/25]]</small></small></small>, <small>[[5/4]]</small>, '''[[29/23]]''', '''<u>[[24/19]]'''</u>, '''<u>[[19/15]]'''</u>, '''<u>[[14/11]]'''</u>, '''[[23/18]]''', [[32/25]], <small>[[9/7]]</small>, <small><small>[[31/24]]</small></small>, <small><small><small>[[22/17]]</small></small></small>
| vM3
| 25
|-
| 6
| 493.339
| <small><small><small>[[13/10]]</small></small></small>, <small><small>[[30/23]]</small></small>, <small><small>[[17/13]]</small></small>, <small>[[21/16]]</small>, [[25/19]], [[29/22]], '''<u>[[4/3]]'''</u>, <small>[[31/23]]</small>, <small>[[27/20]]</small>, <small><small>[[23/17]]</small></small>, <small><small><small>[[19/14]]</small></small></small>
| P4
| 30
|-
| 7
| 575.562
| <small><small><small>[[15/11]]</small></small></small>, <small><small>[[26/19]]</small></small>, <small>[[11/8]]</small>, [[29/21]], '''[[18/13]]''', '''<u>[[25/18]]'''</u>, '''<u>[[32/23]]'''</u>, '''[[7/5]]''', [[31/22]], <small>[[24/17]]</small>, <small><small>[[17/12]]</small></small>, <small><small>[[27/19]]</small></small>
| v<sup>4</sup>A4
| 35
|-
| 8
| 657.785
| <small><small><small>[[10/7]]</small></small></small>, <small><small>[[23/16]]</small></small>, <small>[[13/9]]</small>, [[29/20]], '''[[16/11]]''', '''<u>[[19/13]]'''</u>, '''<u>[[22/15]]'''</u>, '''[[25/17]]''', '''[[28/19]]''', [[31/21]]
| vvv5
| 40
|-
| 9
| 740.008
| <small><small><small>[[3/2]]</small></small></small>, '''[[32/21]]''', '''[[29/19]]''', '''<u>[[26/17]]'''</u>, '''<u>[[23/15]]'''</u>, '''<u>[[20/13]]'''</u>, '''[[17/11]]''', [[31/20]], <small>[[14/9]]</small>, <small><small>[[25/16]]</small></small>
| ^^5, vvm6
| 45
|-
| 10
| 822.231
| <small><small><small>[[11/7]]</small></small></small>, <small><small>[[30/19]]</small></small>, <small>[[19/12]]</small>, <small>[[27/17]]</small>, '''[[8/5]]''', '''<u>[[29/18]]'''</u>, '''[[21/13]]''', [[13/8]], <small>[[31/19]]</small>, <small><small>[[18/11]]</small></small>, <small><small><small>[[23/14]]</small></small></small>
| ^^^m6
| 50
|-
| 11
| 904.454
| <small><small><small>[[28/17]]</small></small></small>, [[5/3]], '''<u>[[32/19]]'''</u>, '''<u>[[27/16]]'''</u>, '''<u>[[22/13]]'''</u>, [[17/10]], [[29/17]], <small><small>[[12/7]]</small></small>, <small><small><small>[[31/18]]</small></small></small>
| vM6
| 55
|-
| 12
| 986.677
| <small><small><small>[[19/11]]</small></small></small>, <small><small><small>[[26/15]]</small></small></small>, [[7/4]], '''<u>[[30/17]]'''</u>, '''<u>[[23/13]]'''</u>, '''[[16/9]]''', [[25/14]], <small><small>[[9/5]]</small></small>
| m7
| 60
|-
| 13
| 1068.901
| <small><small><small>[[29/16]]</small></small></small>, <small><small>[[20/11]]</small></small>, <small><small>[[31/17]]</small></small>, [[11/6]], '''[[24/13]]''', '''<u>[[13/7]]'''</u>, '''[[28/15]]''', [[15/8]], <small>[[32/17]]</small>, <small><small>[[17/9]]</small></small>
| v<sup>4</sup>M7
| 65
|-
| 14
| 1151.124
| <small><small><small>[[19/10]]</small></small></small>, <small><small>[[21/11]]</small></small>, <small>[[23/12]]</small>, [[25/13]], [[27/14]], '''[[29/15]]''', '''<u>[[31/16]]'''</u>
| ^M7
| 70
|-
| 15
| 1233.347
| <small><small>[[2/1]]</small></small>, <small>[[31/15]]</small>, <small>[[29/14]]</small>, <small><small>[[27/13]]</small></small>, <small><small><small>[[25/12]]</small></small></small>
| ^^1 +1 oct, vvm2 +1 oct
| 75
|-
| 16
| 1315.570
| <small><small><small>[[23/11]]</small></small></small>, <small><small>[[21/10]]</small></small>, <small>[[19/9]]</small>, '''[[17/8]]''', '''<u>[[32/15]]'''</u>, '''<u>[[15/7]]'''</u>, '''[[28/13]]''', <small>[[13/6]]</small>, <small><small><small>[[24/11]]</small></small></small>
| ^^^m2 +1 oct
| 80
|-
| 17
| 1397.793
| <small><small>[[11/5]]</small></small>, <small>[[31/14]]</small>, [[20/9]], '''[[29/13]]''', '''<u>[[9/4]]'''</u>, <small>[[25/11]]</small>, <small><small>[[16/7]]</small></small>
| vM2 +1 oct
| 85
|-
| 18
| 1480.016
| <small><small><small>[[23/10]]</small></small></small>, <small><small>[[30/13]]</small></small>, '''[[7/3]]''', '''[[26/11]]''', [[19/8]], <small>[[31/13]]</small>, <small><small><small>[[12/5]]</small></small></small>
| m3 +1 oct
| 90
|-
| 19
| 1562.239
| <small><small><small>[[29/12]]</small></small></small>, <small>[[17/7]]</small>, [[22/9]], '''[[27/11]]''', '''<u>[[32/13]]'''</u>, <small>[[5/2]]</small>
| v<sup>4</sup>M3 +1 oct
| 95
|-
| 20
| 1644.462
| <small>[[28/11]]</small>, [[23/9]], '''[[18/7]]''', '''<u>[[31/12]]'''</u>, '''[[13/5]]''', <small>[[21/8]]</small>, <small><small>[[29/11]]</small></small>
| ^M3 +1 oct
| 100
|-
| 21
| 1726.686
| <small><small>[[8/3]]</small></small>, '''[[27/10]]''', '''<u>[[19/7]]'''</u>, '''[[30/11]]''', <small>[[11/4]]</small>
| ^^4 +1 oct
| 105
|-
| 22
| 1808.909
| <small><small><small>[[25/9]]</small></small></small>, <small>[[14/5]]</small>, [[31/11]], '''<u>[[17/6]]'''</u>, '''[[20/7]]''', [[23/8]], <small><small>[[26/9]]</small></small>, <small><small><small>[[29/10]]</small></small></small>, <small><small><small>[[32/11]]</small></small></small>
| ^^^d5 +1 oct
| 110
|-
| 23
| 1891.132
| '''[[3/1]]'''
| v5 +1 oct
| 115
|-
| 24
| 1973.355
| [[31/10]], '''[[28/9]]''', '''<u>[[25/8]]'''</u>, '''[[22/7]]''', <small>[[19/6]]</small>, <small><small><small>[[16/5]]</small></small></small>
| m6 +1 oct
| 120
|-
| 25
| 2055.578
| <small><small>[[29/9]]</small></small>, [[13/4]], '''<u>[[23/7]]'''</u>, <small><small>[[10/3]]</small></small>
| v<sup>4</sup>M6 +1 oct
| 125
|-
| 26
| 2137.801
| <small><small>[[27/8]]</small></small>, [[17/5]], '''<u>[[24/7]]'''</u>, '''<u>[[31/9]]'''</u>, <small><small>[[7/2]]</small></small>
| ^M6 +1 oct
| 130
|-
| 27
| 2220.024
| <small>[[32/9]]</small>, [[25/7]], '''<u>[[18/5]]'''</u>, '''[[29/8]]''', <small><small>[[11/3]]</small></small>
| ^^m7 +1 oct
| 135
|-
| 28
| 2302.247
| <small><small>[[26/7]]</small></small>, [[15/4]], '''[[19/5]]''', <small>[[23/6]]</small>, <small><small><small>[[27/7]]</small></small></small>
| vvM7 +1 oct
| 140
|-
| 29
| 2384.471
| <small><small><small>[[31/8]]</small></small></small>, [[4/1]]
| v1 +2 oct
| 145
|-
| 30
| 2466.694
| '''<u>[[29/7]]'''</u>, '''<u>[[25/6]]'''</u>, [[21/5]], <small><small><small>[[17/4]]</small></small></small>
| m2 +2 oct
| 150
|-
| 31
| 2548.917
| <small><small>[[30/7]]</small></small>, '''[[13/3]]''', [[22/5]], <small>[[31/7]]</small>
| v<sup>4</sup>M2 +2 oct
| 155
|-
| 32
| 2631.140
| <small>[[9/2]]</small>, '''<u>[[32/7]]'''</u>, '''[[23/5]]''', <small><small><small>[[14/3]]</small></small></small>
| ^M2 +2 oct
| 160
|-
| 33
| 2713.363
| [[19/4]], '''<u>[[24/5]]'''</u>, [[29/6]]
| ^^m3 +2 oct
| 165
|-
| 34
| 2795.586
| '''[[5/1]]'''
| vvM3 +2 oct
| 170
|-
| 35
| 2877.809
| <small><small><small>[[31/6]]</small></small></small>, <small>[[26/5]]</small>, '''[[21/4]]''', [[16/3]]
| v4 +2 oct
| 175
|-
| 36
| 2960.032
| <small><small><small>[[27/5]]</small></small></small>, '''[[11/2]]''', <small>[[28/5]]</small>
| ^<sup>4</sup>4 +2 oct
| 180
|-
| 37
| 3042.256
| <small><small><small>[[17/3]]</small></small></small>, [[23/4]], '''<u>[[29/5]]'''</u>
| v<sup>4</sup>5 +2 oct
| 185
|-
| 38
| 3124.479
| <small>[[6/1]]</small>, <small><small>[[31/5]]</small></small>
| ^5 +2 oct
| 190
|-
| 39
| 3206.702
| <small><small>[[25/4]]</small></small>, '''[[19/3]]''', '''[[32/5]]''', <small><small>[[13/2]]</small></small>
| ^^m6 +2 oct
| 195
|-
| 40
| 3288.925
| '''<u>[[20/3]]'''</u>, [[27/4]]
| vvM6 +2 oct
| 200
|-
| 41
| 3371.148
| '''<u>[[7/1]]'''</u>
| vm7 +2 oct
| 205
|-
| 42
| 3453.371
| <small>[[29/4]]</small>, '''<u>[[22/3]]'''</u>, <small><small><small>[[15/2]]</small></small></small>
| ^<sup>4</sup>m7 +2 oct
| 210
|-
| 43
| 3535.594
| '''[[23/3]]''', '''[[31/4]]'''
| M7 +2 oct
| 215
|-
| 44
| 3617.817
| [[8/1]]
| ^1 +3 oct
| 220
|-
| 45
| 3700.041
| <small><small>[[25/3]]</small></small>, '''<u>[[17/2]]'''</u>, <small><small><small>[[26/3]]</small></small></small>
| ^^m2 +3 oct
| 225
|-
| 46
| 3782.264
| <small>[[9/1]]</small>
| vvM2 +3 oct
| 230
|-
| 47
| 3864.487
| '''<u>[[28/3]]'''</u>, <small><small>[[19/2]]</small></small>
| vm3 +3 oct
| 235
|-
| 48
| 3946.710
| [[29/3]], <small><small><small>[[10/1]]</small></small></small>
| ^<sup>4</sup>m3 +3 oct
| 240
|-
| 49
| 4028.933
| [[31/3]]
| M3 +3 oct
| 245
|-
| 50
| 4111.156
| <small><small><small>[[21/2]]</small></small></small>, '''[[32/3]]''', <small><small><small>[[11/1]]</small></small></small>
| ^4 +3 oct
| 250
|-
| 51
| 4193.379
| <small><small><small>[[23/2]]</small></small></small>
| vvvA4 +3 oct
| 255
|-
| 52
| 4275.602
| <small>[[12/1]]</small>
| vv5 +3 oct
| 260
|-
| 53
| 4357.826
| [[25/2]]
| vm6 +3 oct
| 265
|-
| 54
| 4440.049
| '''<u>[[13/1]]'''</u>
| ^<sup>4</sup>m6 +3 oct
| 270
|-
| 55
| 4522.272
| [[27/2]]
| M6 +3 oct
| 275
|-
| 56
| 4604.495
| <small><small><small>[[14/1]]</small></small></small>, <small>[[29/2]]</small>
| ^m7 +3 oct
| 280
|-
| 57
| 4686.718
| '''<u>[[15/1]]'''</u>
| vvvM7 +3 oct
| 285
|-
| 58
| 4768.941
| <small>[[31/2]]</small>, <small><small>[[16/1]]</small></small>
| ^^M7 +3 oct, vv1 +4 oct
| 290
|-
| 59
| 4851.164
|
| vm2 +4 oct
| 295
|-
| 60
| 4933.387
| <small><small>[[17/1]]</small></small>
| ^<sup>4</sup>m2 +4 oct
| 300
|-
| 61
| 5015.611
| '''[[18/1]]'''
| M2 +4 oct
| 305
|-
| 62
| 5097.834
| '''<u>[[19/1]]'''</u>
| ^m3 +4 oct
| 310
|-
| 63
| 5180.057
| '''<u>[[20/1]]'''</u>
| vvvM3 +4 oct
| 315
|-
| 64
| 5262.280
| '''[[21/1]]'''
| ^^M3 +4 oct, vv4 +4 oct
| 320
|-
| 65
| 5344.503
| '''<u>[[22/1]]'''</u>
| ^^^4 +4 oct
| 325
|-
| 66
| 5426.726
| '''<u>[[23/1]]'''</u>
| ^<sup>4</sup>d5 +4 oct
| 330
|-
| 67
| 5508.949
| '''[[24/1]]'''
| P5 +4 oct
| 335
|-
| 68
| 5591.172
| [[25/1]]
| ^m6 +4 oct
| 340
|-
| 69
| 5673.396
| <small><small>[[26/1]]</small></small>, <small><small>[[27/1]]</small></small>
| vvvM6 +4 oct
| 345
|-
| 70
| 5755.619
| '''[[28/1]]'''
| ^^M6 +4 oct, vvm7 +4 oct
| 350
|-
| 71
| 5837.842
| '''[[29/1]]'''
| ^^^m7 +4 oct
| 355
|-
| 72
| 5920.065
| <small><small>[[30/1]]</small></small>, <small>[[31/1]]</small>
| vM7 +4 oct
| 360
|-
| 73
| 6002.288
| '''<u>[[32/1]]'''</u>
| P1 +5 oct
| 365
|}


== Approximation to JI ==
== Approximation to JI ==
Retrieved from "https://en.xen.wiki/w/45zpi"