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'''45 zeta peak index''' (abbreviated '''45zpi'''), is the [[Equal-step tuning|equal-step]] [[tuning system]] obtained from the 45th [[Zeta peak index|peak]] of the [[The Riemann zeta function and tuning|Riemann zeta function]].
'''45 zeta peak index''' (abbreviated '''45zpi'''), is the [[Equal-step tuning|equal-step]] [[tuning system]] obtained from the 45th [[Zeta peak index|peak]] of the [[The Riemann zeta function and tuning|Riemann zeta function]].


{|class="wikitable"
{{ZPI
!colspan="3"|Tuning
| zpi = 45
!colspan="3"|Strength
| steps = 14.5944346577250
!colspan="2"|Closest EDO
| step size = 82.2231232756126
!colspan="2"|Integer limit
| height = 2.097730
|-
| integral = 0.344839
!ZPI
| gap = 10.594800
!Steps per octave
| edo = 15edo
!Step size (cents)
| octave = 1233.34684913419
!Height
| consistent = 2
!Integral
| distinct = 2
!Gap
}}
!EDO
!Octave (cents)
!Consistent
!Distinct
|-
|[[45zpi]]
|14.5944346577250
|82.2231232756126
|2.097730
|0.344839
|10.594800
|[[15edo]]
|1233.34684913419
|2
|2
|}


== Theory ==
== Theory ==
Line 50: Line 34:
|+ style="white-space:nowrap" | Intervals in 45zpi
|+ 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:
| colspan="3" style="text-align:left;" | JI ratios are comprised of 25-integer-limit ratios,<br>and are stylized as follows to indicate their accuracy:
* '''<u>Bold Underlined:</u>''' relative error < 8.333 %
* '''<u>Bold Underlined:</u>''' relative error < 8.333 %
* '''Bold:''' relative error < 16.667 %
* '''Bold:''' relative error < 16.667 %
Line 62: Line 46:
! Cents
! Cents
! Ratios
! Ratios
! Ups and Downs Notation
! Ups and downs notation
! Step
! Step
|-
|-
Line 73: Line 57:
| 1
| 1
| 82.223
| 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>
| '''[[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><small>[[15/14]]</small></small></small>
| ^m2
| ^m2
| 5
| 5
Line 79: Line 63:
| 2
| 2
| 164.446
| 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>
| <small><small><small>[[14/13]]</small></small></small>, <small>[[13/12]]</small>, [[25/23]], [[12/11]], '''[[23/21]]''', '''<u>[[11/10]]'''</u>, '''[[21/19]]''', [[10/9]], <small><small>[[19/17]]</small></small>, <small><small><small>[[9/8]]</small></small></small>
| vvvM2
| vvvM2
| 10
| 10
Line 85: Line 69:
| 3
| 3
| 246.669
| 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>
| <small><small>[[17/15]]</small></small>, <small>[[25/22]]</small>, [[8/7]], '''<u>[[23/20]]'''</u>, '''<u>[[15/13]]'''</u>, '''[[22/19]]''', [[7/6]], <small><small><small>[[20/17]]</small></small></small>
| ^^M2, vvm3
| ^^M2, vvm3
| 15
| 15
Line 91: Line 75:
| 4
| 4
| 328.892
| 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>
| <small><small><small>[[13/11]]</small></small></small>, <small><small>[[19/16]]</small></small>, <small>[[25/21]]</small>, '''[[6/5]]''', '''<u>[[23/19]]'''</u>, '''[[17/14]]''', [[11/9]], <small><small>[[16/13]]</small></small>, <small><small><small>[[21/17]]</small></small></small>
| ^^^m3
| ^^^m3
| 20
| 20
Line 97: Line 81:
| 5
| 5
| 411.116
| 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>
| <small>[[5/4]]</small>, '''<u>[[24/19]]'''</u>, '''<u>[[19/15]]'''</u>, '''<u>[[14/11]]'''</u>, '''[[23/18]]''', <small>[[9/7]]</small>, <small><small><small>[[22/17]]</small></small></small>
| vM3
| vM3
| 25
| 25
Line 103: Line 87:
| 6
| 6
| 493.339
| 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>
| <small><small><small>[[13/10]]</small></small></small>, <small><small>[[17/13]]</small></small>, <small>[[21/16]]</small>, [[25/19]], '''<u>[[4/3]]'''</u>, <small><small>[[23/17]]</small></small>, <small><small><small>[[19/14]]</small></small></small>
| P4
| P4
| 30
| 30
Line 109: Line 93:
| 7
| 7
| 575.562
| 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>
| <small><small><small>[[15/11]]</small></small></small>, <small>[[11/8]]</small>, '''[[18/13]]''', '''<u>[[25/18]]'''</u>, '''[[7/5]]''', <small>[[24/17]]</small>, <small><small>[[17/12]]</small></small>
| v<sup>4</sup>A4
| v<sup>4</sup>A4
| 35
| 35
Line 115: Line 99:
| 8
| 8
| 657.785
| 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]]
| <small><small><small>[[10/7]]</small></small></small>, <small><small>[[23/16]]</small></small>, <small>[[13/9]]</small>, '''[[16/11]]''', '''<u>[[19/13]]'''</u>, '''<u>[[22/15]]'''</u>, '''[[25/17]]'''
| vvv5
| vvv5
| 40
| 40
Line 121: Line 105:
| 9
| 9
| 740.008
| 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>
| <small><small><small>[[3/2]]</small></small></small>, '''<u>[[23/15]]'''</u>, '''<u>[[20/13]]'''</u>, '''[[17/11]]''', <small>[[14/9]]</small>, <small><small>[[25/16]]</small></small>
| ^^5, vvm6
| ^^5, vvm6
| 45
| 45
Line 127: Line 111:
| 10
| 10
| 822.231
| 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>
| <small><small><small>[[11/7]]</small></small></small>, <small>[[19/12]]</small>, '''[[8/5]]''', '''[[21/13]]''', [[13/8]], <small><small>[[18/11]]</small></small>, <small><small><small>[[23/14]]</small></small></small>
| ^^^m6
| ^^^m6
| 50
| 50
Line 133: Line 117:
| 11
| 11
| 904.454
| 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>
| [[5/3]], '''<u>[[22/13]]'''</u>, [[17/10]], <small><small>[[12/7]]</small></small>
| vM6
| vM6
| 55
| 55
Line 139: Line 123:
| 12
| 12
| 986.677
| 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>
| <small><small><small>[[19/11]]</small></small></small>, [[7/4]], '''<u>[[23/13]]'''</u>, '''[[16/9]]''', [[25/14]], <small><small>[[9/5]]</small></small>
| m7
| m7
| 60
| 60
Line 145: Line 129:
| 13
| 13
| 1068.901
| 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>
| <small><small>[[20/11]]</small></small>, [[11/6]], '''[[24/13]]''', '''<u>[[13/7]]'''</u>, [[15/8]], <small><small>[[17/9]]</small></small>
| v<sup>4</sup>M7
| v<sup>4</sup>M7
| 65
| 65
Line 151: Line 135:
| 14
| 14
| 1151.124
| 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>
| <small><small><small>[[19/10]]</small></small></small>, <small><small>[[21/11]]</small></small>, <small>[[23/12]]</small>, [[25/13]]
| ^M7
| ^M7
| 70
| 70
Line 157: Line 141:
| 15
| 15
| 1233.347
| 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>
| <small><small>[[2/1]]</small></small>, <small><small><small>[[25/12]]</small></small></small>
| ^^1 +1 oct, vvm2 +1 oct
| ^^1 +1 oct, vvm2 +1 oct
| 75
| 75
Line 163: Line 147:
| 16
| 16
| 1315.570
| 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>
| <small><small><small>[[23/11]]</small></small></small>, <small><small>[[21/10]]</small></small>, <small>[[19/9]]</small>, '''[[17/8]]''', '''<u>[[15/7]]'''</u>, <small>[[13/6]]</small>, <small><small><small>[[24/11]]</small></small></small>
| ^^^m2 +1 oct
| ^^^m2 +1 oct
| 80
| 80
Line 169: Line 153:
| 17
| 17
| 1397.793
| 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>
| <small><small>[[11/5]]</small></small>, [[20/9]], '''<u>[[9/4]]'''</u>, <small>[[25/11]]</small>, <small><small>[[16/7]]</small></small>
| vM2 +1 oct
| vM2 +1 oct
| 85
| 85
Line 175: Line 159:
| 18
| 18
| 1480.016
| 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>
| <small><small><small>[[23/10]]</small></small></small>, '''[[7/3]]''', [[19/8]], <small><small><small>[[12/5]]</small></small></small>
| m3 +1 oct
| m3 +1 oct
| 90
| 90
Line 181: Line 165:
| 19
| 19
| 1562.239
| 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>
| <small>[[17/7]]</small>, [[22/9]], <small>[[5/2]]</small>
| v<sup>4</sup>M3 +1 oct
| v<sup>4</sup>M3 +1 oct
| 95
| 95
Line 187: Line 171:
| 20
| 20
| 1644.462
| 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>
| [[23/9]], '''[[18/7]]''', '''[[13/5]]''', <small>[[21/8]]</small>
| ^M3 +1 oct
| ^M3 +1 oct
| 100
| 100
Line 193: Line 177:
| 21
| 21
| 1726.686
| 1726.686
| <small><small>[[8/3]]</small></small>, '''[[27/10]]''', '''<u>[[19/7]]'''</u>, '''[[30/11]]''', <small>[[11/4]]</small>
| <small><small>[[8/3]]</small></small>, '''<u>[[19/7]]'''</u>, <small>[[11/4]]</small>
| ^^4 +1 oct
| ^^4 +1 oct
| 105
| 105
Line 199: Line 183:
| 22
| 22
| 1808.909
| 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>
| <small><small><small>[[25/9]]</small></small></small>, <small>[[14/5]]</small>, '''<u>[[17/6]]'''</u>, '''[[20/7]]''', [[23/8]]
| ^^^d5 +1 oct
| ^^^d5 +1 oct
| 110
| 110
Line 211: Line 195:
| 24
| 24
| 1973.355
| 1973.355
| [[31/10]], '''[[28/9]]''', '''<u>[[25/8]]'''</u>, '''[[22/7]]''', <small>[[19/6]]</small>, <small><small><small>[[16/5]]</small></small></small>
| '''<u>[[25/8]]'''</u>, '''[[22/7]]''', <small>[[19/6]]</small>, <small><small><small>[[16/5]]</small></small></small>
| m6 +1 oct
| m6 +1 oct
| 120
| 120
Line 217: Line 201:
| 25
| 25
| 2055.578
| 2055.578
| <small><small>[[29/9]]</small></small>, [[13/4]], '''<u>[[23/7]]'''</u>, <small><small>[[10/3]]</small></small>
| [[13/4]], '''<u>[[23/7]]'''</u>, <small><small>[[10/3]]</small></small>
| v<sup>4</sup>M6 +1 oct
| v<sup>4</sup>M6 +1 oct
| 125
| 125
Line 223: Line 207:
| 26
| 26
| 2137.801
| 2137.801
| <small><small>[[27/8]]</small></small>, [[17/5]], '''<u>[[24/7]]'''</u>, '''<u>[[31/9]]'''</u>, <small><small>[[7/2]]</small></small>
| [[17/5]], '''<u>[[24/7]]'''</u>, <small><small>[[7/2]]</small></small>
| ^M6 +1 oct
| ^M6 +1 oct
| 130
| 130
Line 229: Line 213:
| 27
| 27
| 2220.024
| 2220.024
| <small>[[32/9]]</small>, [[25/7]], '''<u>[[18/5]]'''</u>, '''[[29/8]]''', <small><small>[[11/3]]</small></small>
| [[25/7]], '''<u>[[18/5]]'''</u>, <small><small>[[11/3]]</small></small>
| ^^m7 +1 oct
| ^^m7 +1 oct
| 135
| 135
Line 235: Line 219:
| 28
| 28
| 2302.247
| 2302.247
| <small><small>[[26/7]]</small></small>, [[15/4]], '''[[19/5]]''', <small>[[23/6]]</small>, <small><small><small>[[27/7]]</small></small></small>
| [[15/4]], '''[[19/5]]''', <small>[[23/6]]</small>
| vvM7 +1 oct
| vvM7 +1 oct
| 140
| 140
Line 241: Line 225:
| 29
| 29
| 2384.471
| 2384.471
| <small><small><small>[[31/8]]</small></small></small>, [[4/1]]
| [[4/1]]
| v1 +2 oct
| v1 +2 oct
| 145
| 145
Line 247: Line 231:
| 30
| 30
| 2466.694
| 2466.694
| '''<u>[[29/7]]'''</u>, '''<u>[[25/6]]'''</u>, [[21/5]], <small><small><small>[[17/4]]</small></small></small>
| '''<u>[[25/6]]'''</u>, [[21/5]], <small><small><small>[[17/4]]</small></small></small>
| m2 +2 oct
| m2 +2 oct
| 150
| 150
Line 253: Line 237:
| 31
| 31
| 2548.917
| 2548.917
| <small><small>[[30/7]]</small></small>, '''[[13/3]]''', [[22/5]], <small>[[31/7]]</small>
| '''[[13/3]]''', [[22/5]]
| v<sup>4</sup>M2 +2 oct
| v<sup>4</sup>M2 +2 oct
| 155
| 155
Line 259: Line 243:
| 32
| 32
| 2631.140
| 2631.140
| <small>[[9/2]]</small>, '''<u>[[32/7]]'''</u>, '''[[23/5]]''', <small><small><small>[[14/3]]</small></small></small>
| <small>[[9/2]]</small>, '''[[23/5]]''', <small><small><small>[[14/3]]</small></small></small>
| ^M2 +2 oct
| ^M2 +2 oct
| 160
| 160
Line 265: Line 249:
| 33
| 33
| 2713.363
| 2713.363
| [[19/4]], '''<u>[[24/5]]'''</u>, [[29/6]]
| [[19/4]], '''<u>[[24/5]]'''</u>
| ^^m3 +2 oct
| ^^m3 +2 oct
| 165
| 165
Line 277: Line 261:
| 35
| 35
| 2877.809
| 2877.809
| <small><small><small>[[31/6]]</small></small></small>, <small>[[26/5]]</small>, '''[[21/4]]''', [[16/3]]
| '''[[21/4]]''', [[16/3]]
| v4 +2 oct
| v4 +2 oct
| 175
| 175
Line 283: Line 267:
| 36
| 36
| 2960.032
| 2960.032
| <small><small><small>[[27/5]]</small></small></small>, '''[[11/2]]''', <small>[[28/5]]</small>
| '''[[11/2]]'''
| ^<sup>4</sup>4 +2 oct
| ^<sup>4</sup>4 +2 oct
| 180
| 180
Line 289: Line 273:
| 37
| 37
| 3042.256
| 3042.256
| <small><small><small>[[17/3]]</small></small></small>, [[23/4]], '''<u>[[29/5]]'''</u>
| <small><small><small>[[17/3]]</small></small></small>, [[23/4]]
| v<sup>4</sup>5 +2 oct
| v<sup>4</sup>5 +2 oct
| 185
| 185
Line 295: Line 279:
| 38
| 38
| 3124.479
| 3124.479
| <small>[[6/1]]</small>, <small><small>[[31/5]]</small></small>
| <small>[[6/1]]</small>
| ^5 +2 oct
| ^5 +2 oct
| 190
| 190
Line 301: Line 285:
| 39
| 39
| 3206.702
| 3206.702
| <small><small>[[25/4]]</small></small>, '''[[19/3]]''', '''[[32/5]]''', <small><small>[[13/2]]</small></small>
| <small><small>[[25/4]]</small></small>, '''[[19/3]]''', <small><small>[[13/2]]</small></small>
| ^^m6 +2 oct
| ^^m6 +2 oct
| 195
| 195
Line 307: Line 291:
| 40
| 40
| 3288.925
| 3288.925
| '''<u>[[20/3]]'''</u>, [[27/4]]
| '''<u>[[20/3]]'''</u>
| vvM6 +2 oct
| vvM6 +2 oct
| 200
| 200
Line 319: Line 303:
| 42
| 42
| 3453.371
| 3453.371
| <small>[[29/4]]</small>, '''<u>[[22/3]]'''</u>, <small><small><small>[[15/2]]</small></small></small>
| '''<u>[[22/3]]'''</u>, <small><small><small>[[15/2]]</small></small></small>
| ^<sup>4</sup>m7 +2 oct
| ^<sup>4</sup>m7 +2 oct
| 210
| 210
Line 325: Line 309:
| 43
| 43
| 3535.594
| 3535.594
| '''[[23/3]]''', '''[[31/4]]'''
| '''[[23/3]]'''
| M7 +2 oct
| M7 +2 oct
| 215
| 215
Line 337: Line 321:
| 45
| 45
| 3700.041
| 3700.041
| <small><small>[[25/3]]</small></small>, '''<u>[[17/2]]'''</u>, <small><small><small>[[26/3]]</small></small></small>
| <small><small>[[25/3]]</small></small>, '''<u>[[17/2]]'''</u>
| ^^m2 +3 oct
| ^^m2 +3 oct
| 225
| 225
Line 349: Line 333:
| 47
| 47
| 3864.487
| 3864.487
| '''<u>[[28/3]]'''</u>, <small><small>[[19/2]]</small></small>
| <small><small>[[19/2]]</small></small>
| vm3 +3 oct
| vm3 +3 oct
| 235
| 235
Line 355: Line 339:
| 48
| 48
| 3946.710
| 3946.710
| [[29/3]], <small><small><small>[[10/1]]</small></small></small>
| <small><small><small>[[10/1]]</small></small></small>
| ^<sup>4</sup>m3 +3 oct
| ^<sup>4</sup>m3 +3 oct
| 240
| 240
Line 361: Line 345:
| 49
| 49
| 4028.933
| 4028.933
| [[31/3]]
|  
| M3 +3 oct
| M3 +3 oct
| 245
| 245
Line 367: Line 351:
| 50
| 50
| 4111.156
| 4111.156
| <small><small><small>[[21/2]]</small></small></small>, '''[[32/3]]''', <small><small><small>[[11/1]]</small></small></small>
| <small><small><small>[[21/2]]</small></small></small>, <small><small><small>[[11/1]]</small></small></small>
| ^4 +3 oct
| ^4 +3 oct
| 250
| 250
Line 397: Line 381:
| 55
| 55
| 4522.272
| 4522.272
| [[27/2]]
|  
| M6 +3 oct
| M6 +3 oct
| 275
| 275
Line 403: Line 387:
| 56
| 56
| 4604.495
| 4604.495
| <small><small><small>[[14/1]]</small></small></small>, <small>[[29/2]]</small>
| <small><small><small>[[14/1]]</small></small></small>
| ^m7 +3 oct
| ^m7 +3 oct
| 280
| 280
Line 415: Line 399:
| 58
| 58
| 4768.941
| 4768.941
| <small>[[31/2]]</small>, <small><small>[[16/1]]</small></small>
| <small><small>[[16/1]]</small></small>
| ^^M7 +3 oct, vv1 +4 oct
| ^^M7 +3 oct, vv1 +4 oct
| 290
| 290
Line 478: Line 462:
| ^m6 +4 oct
| ^m6 +4 oct
| 340
| 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
|}
|}


Line 514: Line 468:
=== Interval mappings ===
=== Interval mappings ===


The following tables show how 32-integer-limit intervals are represented in 45zpi. Prime harmonics are in '''bold'''; inconsistent intervals are in ''italics''.
The following tables show how 25-integer-limit intervals are represented in 45zpi. Prime harmonics are in '''bold'''; inconsistent intervals are in ''italics''.


{| class="wikitable center-1 right-2 right-3 mw-collapsible mw-collapsed"
{| class="wikitable center-1 right-2 right-3 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | 32-integer-limit intervals in 45zpi (by direct approximation)
|+ style="white-space: nowrap;" | 25-integer-limit intervals in 45zpi (by direct approximation)
|-
|-
! Ratio
! Ratio
Line 526: Line 480:
| +0.002
| +0.002
| +0.003
| +0.003
|- style="background-color: #cccccc;"
| ''[[32/7]]''
| ''-0.034''
| ''-0.042''
|-
|-
| '''[[19/1]]'''
| '''[[19/1]]'''
Line 550: Line 500:
| +0.800
| +0.800
| +0.973
| +0.973
|-
| [[29/5]]
| -1.008
| -1.226
|-
|-
| [[23/13]]
| [[23/13]]
Line 562: Line 508:
| -1.072
| -1.072
| -1.303
| -1.303
|- style="background-color: #cccccc;"
| ''[[29/24]]''
| ''+1.270''
| ''+1.545''
|- style="background-color: #cccccc;"
| ''[[31/12]]''
| ''+1.382''
| ''+1.681''
|- style="background-color: #cccccc;"
| ''[[27/16]]''
| ''-1.411''
| ''-1.716''
|-
|-
| '''[[23/1]]'''
| '''[[23/1]]'''
Line 594: Line 528:
| +1.871
| +1.871
| +2.276
| +2.276
|- style="background-color: #cccccc;"
| ''[[32/19]]''
| ''+1.967''
| ''+2.393''
|-
|-
| [[19/7]]
| [[19/7]]
Line 610: Line 540:
| ''-2.278''
| ''-2.278''
| ''-2.771''
| ''-2.771''
|- style="background-color: #cccccc;"
| ''[[32/1]]''
| ''+2.288''
| ''+2.783''
|-
|-
| '''[[7/1]]'''
| '''[[7/1]]'''
| '''+2.322'''
| '''+2.322'''
| '''+2.824'''
| '''+2.824'''
|- style="background-color: #cccccc;"
| ''[[28/3]]''
| ''-2.384''
| ''-2.900''
|-
|-
| [[18/5]]
| [[18/5]]
| +2.428
| +2.428
| +2.953
| +2.953
|- style="background-color: #cccccc;"
| ''[[32/13]]''
| ''+2.767''
| ''+3.365''
|-
|-
| [[13/7]]
| [[13/7]]
| -2.801
| -2.801
| -3.407
| -3.407
|-
| [[31/9]]
| -3.324
| -4.043
|-
| [[30/17]]
| +3.364
| +4.092
|-
| [[29/18]]
| -3.436
| -4.179
|- style="background-color: #cccccc;"
| ''[[32/23]]''
| ''+3.836''
| ''+4.666''
|- style="background-color: #cccccc;"
| ''[[32/15]]''
| ''+3.839''
| ''+4.669''
|-
|-
| [[23/7]]
| [[23/7]]
Line 670: Line 568:
| +4.008
| +4.008
| +4.875
| +4.875
|-
| [[26/17]]
| +4.436
| +5.395
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[20/3]]''
| ''[[20/3]]''
Line 710: Line 604:
| +5.908
| +5.908
| +7.186
| +7.186
|-
| [[29/7]]
| +5.942
| +7.227
|- style="background-color: #cccccc;"
| ''[[32/29]]''
| ''-5.977''
| ''-7.269''
|- style="background-color: #cccccc;"
| ''[[31/16]]''
| ''+6.088''
| ''+7.404''
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[9/4]]''
| ''[[9/4]]''
Line 762: Line 644:
| +6.953
| +6.953
| +8.456
| +8.456
|- style="background-color: #cccccc;"
| ''[[32/5]]''
| ''-6.984''
| ''-8.495''
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[24/1]]''
| ''[[24/1]]''
Line 774: Line 652:
| ''+7.028''
| ''+7.028''
| ''+8.548''
| ''+8.548''
|- style="background-color: #cccccc;"
| ''[[27/10]]''
| ''+7.134''
| ''+8.677''
|-
|-
| [[22/19]]
| [[22/19]]
Line 790: Line 664:
| ''+7.473''
| ''+7.473''
| ''+9.089''
| ''+9.089''
|-
| [[31/27]]
| +7.499
| +9.120
|-
| [[27/11]]
| +7.692
| +9.355
|-
| [[29/19]]
| +7.944
| +9.661
|-
|-
| [[21/13]]
| [[21/13]]
| -8.022
| -8.022
| -9.756
| -9.756
|-
| '''[[29/1]]'''
| '''+8.265'''
| '''+10.051'''
|- style="background-color: #cccccc;"
| ''[[28/9]]''
| ''+8.439''
| ''+10.264''
|-
|-
| [[21/1]]
| [[21/1]]
Line 834: Line 688:
| ''+8.714''
| ''+8.714''
| ''+10.599''
| ''+10.599''
|-
| [[29/13]]
| +8.744
| +10.634
|-
|-
| [[21/19]]
| [[21/19]]
Line 854: Line 704:
| -9.137
| -9.137
| -11.113
| -11.113
|- style="background-color: #cccccc;"
| ''[[26/11]]''
| ''-9.194''
| ''-11.181''
|-
|-
| '''[[5/1]]'''
| '''[[5/1]]'''
Line 874: Line 720:
| ''-9.413''
| ''-9.413''
| ''-11.448''
| ''-11.448''
|- style="background-color: #cccccc;"
| ''[[31/4]]''
| ''-9.441''
| ''-11.483''
|- style="background-color: #cccccc;"
| ''[[29/8]]''
| ''-9.553''
| ''-11.618''
|-
|-
| [[13/5]]
| [[13/5]]
| -9.751
| -9.751
| -11.860
| -11.860
|-
| [[29/23]]
| +9.813
| +11.934
|-
| [[29/15]]
| +9.815
| +11.937
|-
|-
| [[25/17]]
| [[25/17]]
| -9.887
| -9.887
| -12.025
| -12.025
|- style="background-color: #cccccc;"
| ''[[30/11]]''
| ''-10.265''
| ''-12.485''
|-
| [[29/25]]
| -10.280
| -12.503
|-
|-
| [[13/3]]
| [[13/3]]
Line 914: Line 736:
| ''+10.615''
| ''+10.615''
| ''+12.909''
| ''+12.909''
|- style="background-color: #cccccc;"
| ''[[32/21]]''
| ''+10.789''
| ''+13.122''
|-
|-
| [[23/5]]
| [[23/5]]
Line 938: Line 756:
| ''+11.551''
| ''+11.551''
| ''+14.048''
| ''+14.048''
|- style="background-color: #cccccc;"
| ''[[28/15]]''
| ''-11.657''
| ''-14.177''
|- style="background-color: #cccccc;"
| ''[[28/23]]''
| ''-11.659''
| ''-14.180''
|-
|-
| [[18/1]]
| [[18/1]]
| +11.701
| +11.701
| +14.230
| +14.230
|- style="background-color: #cccccc;"
| ''[[31/28]]''
| ''-11.763''
| ''-14.307''
|-
|-
| [[18/13]]
| [[18/13]]
| +12.180
| +12.180
| +14.813
| +14.813
|- style="background-color: #cccccc;"
| ''[[28/13]]''
| ''-12.728''
| ''-15.480''
|- style="background-color: #cccccc;"
| ''[[32/3]]''
| ''+13.111''
| ''+15.946''
|-
|-
| [[7/3]]
| [[7/3]]
| +13.145
| +13.145
| +15.987
| +15.987
|- style="background-color: #cccccc;"
| ''[[28/1]]''
| ''-13.207''
| ''-16.063''
|-
|-
| [[23/18]]
| [[23/18]]
Line 982: Line 776:
| +13.251
| +13.251
| +16.116
| +16.116
|- style="background-color: #cccccc;"
| ''[[28/19]]''
| ''-13.528''
| ''-16.453''
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[17/11]]''
| ''[[17/11]]''
Line 1,002: Line 792:
| ''+13.981''
| ''+13.981''
| ''+17.004''
| ''+17.004''
|- style="background-color: #cccccc;"
| ''[[27/14]]''
| ''+14.085''
| ''+17.130''
|-
| [[31/3]]
| -14.148
| -17.206
|-
|-
| [[17/10]]
| [[17/10]]
| -14.187
| -14.187
| -17.255
| -17.255
|-
| [[29/6]]
| -14.259
| -17.342
|-
| [[26/25]]
| +14.323
| +17.420
|- style="background-color: #cccccc;"
| ''[[29/20]]''
| ''+14.522''
| ''+17.661''
|- style="background-color: #cccccc;"
| ''[[31/10]]''
| ''+14.633''
| ''+17.797''
|-
|-
| [[25/2]]
| [[25/2]]
Line 1,042: Line 808:
| ''+15.050''
| ''+15.050''
| ''+18.304''
| ''+18.304''
|-
| [[29/22]]
| +15.079
| +18.340
|-
| [[31/11]]
| +15.191
| +18.475
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[20/9]]''
| ''[[20/9]]''
Line 1,074: Line 832:
| +16.223
| +16.223
| +19.730
| +19.730
|- style="background-color: #cccccc;"
| ''[[32/25]]''
| ''-16.257''
| ''-19.772''
|- style="background-color: #cccccc;"
| ''[[27/2]]''
| ''+16.407''
| ''+19.954''
|-
| [[31/21]]
| -16.470
| -20.030
|-
|-
| [[18/17]]
| [[18/17]]
| -16.731
| -16.731
| -20.349
| -20.349
|-
| [[29/21]]
| +16.766
| +20.390
|- style="background-color: #cccccc;"
| ''[[27/26]]''
| ''+16.886''
| ''+20.537''
|- style="background-color: #cccccc;"
| ''[[27/4]]''
| ''-16.940''
| ''-20.603''
|-
|-
| [[25/14]]
| [[25/14]]
Line 1,126: Line 860:
| ''-17.957''
| ''-17.957''
| ''-21.840''
| ''-21.840''
|-
| [[31/22]]
| -18.156
| -22.081
|-
|-
| [[25/19]]
| [[25/19]]
Line 1,146: Line 876:
| +18.545
| +18.545
| +22.554
| +22.554
|- style="background-color: #cccccc;"
| ''[[31/20]]''
| ''-18.714''
| ''-22.760''
|-
|-
| [[25/13]]
| [[25/13]]
| +19.024
| +19.024
| +23.137
| +23.137
|-
| [[29/3]]
| +19.088
| +23.215
|-
|-
| [[17/5]]
| [[17/5]]
| +19.160
| +19.160
| +23.302
| +23.302
|- style="background-color: #cccccc;"
| ''[[28/27]]''
| ''+19.262''
| ''+23.427''
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[23/8]]''
| ''[[23/8]]''
Line 1,190: Line 908:
| +20.098
| +20.098
| +24.443
| +24.443
|-
| [[29/17]]
| -20.167
| -24.528
|-
|-
| [[7/6]]
| [[7/6]]
Line 1,206: Line 920:
| +21.167
| +21.167
| +25.744
| +25.744
|- style="background-color: #cccccc;"
| ''[[27/17]]''
| ''+21.322''
| ''+25.931''
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[24/17]]''
| ''[[24/17]]''
| ''-21.438''
| ''-21.438''
| ''-26.073''
| ''-26.073''
|- style="background-color: #cccccc;"
| ''[[29/28]]''
| ''+21.472''
| ''+26.114''
|- style="background-color: #cccccc;"
| ''[[31/14]]''
| ''+21.583''
| ''+26.250''
|-
|-
| [[9/1]]
| [[9/1]]
Line 1,234: Line 936:
| -22.203
| -22.203
| -27.003
| -27.003
|- style="background-color: #cccccc;"
| ''[[28/5]]''
| ''-22.480''
| ''-27.340''
|-
|-
| [[6/1]]
| [[6/1]]
Line 1,254: Line 952:
| -23.003
| -23.003
| -27.976
| -27.976
|-
| [[31/15]]
| -23.420
| -28.483
|-
| [[31/23]]
| -23.422
| -28.486
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[25/11]]''
| ''[[25/11]]''
| ''-23.516''
| ''-23.516''
| ''-28.601''
| ''-28.601''
|-
| [[30/29]]
| +23.532
| +28.619
|-
| [[26/5]]
| +23.595
| +28.697
|- style="background-color: #cccccc;"
| ''[[29/4]]''
| ''+23.794''
| ''+28.938''
|- style="background-color: #cccccc;"
| ''[[31/2]]''
| ''+23.906''
| ''+29.074''
|- style="background-color: #cccccc;"
| ''[[32/9]]''
| ''+23.934''
| ''+29.109''
|-
|-
| [[9/7]]
| [[9/7]]
Line 1,302: Line 972:
| ''+24.244''
| ''+24.244''
| ''+29.486''
| ''+29.486''
|- style="background-color: #cccccc;"
| ''[[31/26]]''
| ''+24.385''
| ''+29.657''
|-
| [[31/13]]
| -24.492
| -29.787
|-
| [[29/26]]
| -24.603
| -29.923
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[11/4]]''
| ''[[11/4]]''
Line 1,330: Line 988:
| ''-24.908''
| ''-24.908''
| ''-30.293''
| ''-30.293''
|-
| '''[[31/1]]'''
| '''-24.971'''
| '''-30.369'''
|-
| [[29/2]]
| -25.082
| -30.505
|-
| [[31/19]]
| -25.291
| -30.759
|-
|-
| [[25/22]]
| [[25/22]]
| +25.360
| +25.360
| +30.843
| +30.843
|- style="background-color: #cccccc;"
| ''[[31/30]]''
| ''+25.456''
| ''+30.960''
|-
| [[27/22]]
| -25.655
| -31.201
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[13/12]]''
| ''[[13/12]]''
Line 1,362: Line 1,000:
| +26.110
| +26.110
| +31.755
| +31.755
|- style="background-color: #cccccc;"
| ''[[32/17]]''
| ''-26.144''
| ''-31.796''
|- style="background-color: #cccccc;"
| ''[[27/20]]''
| ''-26.213''
| ''-31.880''
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[21/8]]''
| ''[[21/8]]''
Line 1,386: Line 1,016:
| ''+26.673''
| ''+26.673''
| ''+32.440''
| ''+32.440''
|- style="background-color: #cccccc;"
| ''[[28/11]]''
| ''+26.955''
| ''+32.782''
|-
|-
| [[25/21]]
| [[25/21]]
Line 1,398: Line 1,024:
| ''+27.230''
| ''+27.230''
| ''+33.117''
| ''+33.117''
|- style="background-color: #cccccc;"
| ''[[32/31]]''
| ''+27.259''
| ''+33.152''
|-
| [[31/7]]
| -27.293
| -33.194
|-
| [[29/14]]
| -27.404
| -33.329
|-
|-
| [[17/12]]
| [[17/12]]
| -27.439
| -27.439
| -33.371
| -33.371
|- style="background-color: #cccccc;"
| ''[[26/9]]''
| ''-27.709''
| ''-33.700''
|-
|-
| [[19/17]]
| [[19/17]]
Line 1,438: Line 1,048:
| ''-28.781''
| ''-28.781''
| ''-35.003''
| ''-35.003''
|- style="background-color: #cccccc;"
| ''[[31/17]]''
| ''+28.820''
| ''+35.052''
|-
|-
| [[17/13]]
| [[17/13]]
Line 1,454: Line 1,060:
| +29.368
| +29.368
| +35.718
| +35.718
|-
| [[30/7]]
| +29.474
| +35.846
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[16/15]]''
| ''[[16/15]]''
Line 1,466: Line 1,068:
| ''+29.511''
| ''+29.511''
| ''+35.891''
| ''+35.891''
|-
| [[29/9]]
| +29.911
| +36.378
|-
|-
| [[23/17]]
| [[23/17]]
Line 1,482: Line 1,080:
| ''-30.361''
| ''-30.361''
| ''-36.925''
| ''-36.925''
|-
| [[26/7]]
| +30.546
| +37.150
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[16/13]]''
| ''[[16/13]]''
Line 1,494: Line 1,088:
| -30.919
| -30.919
| -37.604
| -37.604
|-
| [[27/23]]
| -30.921
| -37.607
|-
|-
| [[7/2]]
| [[7/2]]
Line 1,510: Line 1,100:
| ''+31.103''
| ''+31.103''
| ''+37.827''
| ''+37.827''
|- style="background-color: #cccccc;"
| ''[[27/25]]''
| ''+31.209''
| ''+37.956''
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[19/16]]''
| ''[[19/16]]''
| ''+31.379''
| ''+31.379''
| ''+38.164''
| ''+38.164''
|-
| [[30/19]]
| +31.476
| +38.281
|-
|-
| [[21/11]]
| [[21/11]]
| +31.661
| +31.661
| +38.506
| +38.506
|- style="background-color: #cccccc;"
| ''[[28/25]]''
| ''-31.752''
| ''-38.617''
|-
| [[30/1]]
| +31.796
| +38.671
|- style="background-color: #cccccc;"
| ''[[27/8]]''
| ''+31.936''
| ''+38.841''
|- style="background-color: #cccccc;"
| ''[[31/24]]''
| ''-31.965''
| ''-38.876''
|-
| [[27/13]]
| -31.990
| -38.907
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[17/9]]''
| ''[[17/9]]''
| ''-32.145''
| ''-32.145''
| ''-39.095''
| ''-39.095''
|-
| [[30/13]]
| +32.275
| +39.253
|-
| [[27/1]]
| -32.469
| -39.489
|-
| [[26/19]]
| +32.547
| +39.584
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[25/16]]''
| ''[[25/16]]''
Line 1,570: Line 1,120:
| ''+32.789''
| ''+32.789''
| ''+39.878''
| ''+39.878''
|-
| [[27/19]]
| -32.790
| -39.879
|-
| [[26/1]]
| +32.868
| +39.974
|-
|-
| [[19/2]]
| [[19/2]]
| -33.026
| -33.026
| -40.167
| -40.167
|-
| [[31/29]]
| -33.235
| -40.421
|-
| [[30/23]]
| +33.344
| +40.554
|-
|-
| '''[[2/1]]'''
| '''[[2/1]]'''
Line 1,598: Line 1,132:
| ''-33.381''
| ''-33.381''
| ''-40.598''
| ''-40.598''
|- style="background-color: #cccccc;"
| ''[[29/11]]''
| ''-33.797''
| ''-41.104''
|-
|-
| [[13/2]]
| [[13/2]]
Line 1,614: Line 1,144:
| ''+34.074''
| ''+34.074''
| ''+41.441''
| ''+41.441''
|-
| [[31/5]]
| -34.243
| -41.647
|-
| [[29/10]]
| -34.355
| -41.782
|-
| [[26/23]]
| +34.416
| +41.857
|-
| [[26/15]]
| +34.419
| +41.860
|- style="background-color: #cccccc;"
| ''[[29/12]]''
| ''+34.617''
| ''+42.101''
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[20/17]]''
| ''[[20/17]]''
| ''-34.689''
| ''-34.689''
| ''-42.189''
| ''-42.189''
|- style="background-color: #cccccc;"
| ''[[31/6]]''
| ''+34.729''
| ''+42.237''
|- style="background-color: #cccccc;"
| ''[[32/27]]''
| ''+34.757''
| ''+42.272''
|-
| [[27/7]]
| -34.792
| -42.314
|-
|-
| [[23/2]]
| [[23/2]]
Line 1,686: Line 1,184:
| +36.148
| +36.148
| +43.963
| +43.963
|-
| [[31/18]]
| -36.671
| -44.600
|-
|-
| [[21/17]]
| [[21/17]]
Line 1,718: Line 1,212:
| -38.262
| -38.262
| -46.534
| -46.534
|- style="background-color: #cccccc;"
| ''[[26/3]]''
| ''-38.532''
| ''-46.863''
|-
|-
| [[15/11]]
| [[15/11]]
Line 1,730: Line 1,220:
| +38.614
| +38.614
| +46.962
| +46.962
|- style="background-color: #cccccc;"
| ''[[31/25]]''
| ''+38.707''
| ''+47.076''
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[13/10]]''
| ''[[13/10]]''
Line 1,742: Line 1,228:
| +39.255
| +39.255
| +47.742
| +47.742
|- style="background-color: #cccccc;"
| ''[[29/16]]''
| ''+39.323''
| ''+47.825''
|- style="background-color: #cccccc;"
| ''[[31/8]]''
| ''+39.435''
| ''+47.961''
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[9/8]]''
| ''[[9/8]]''
Line 1,766: Line 1,244:
| ''+39.739''
| ''+39.739''
| ''+48.331''
| ''+48.331''
|- style="background-color: #cccccc;"
| ''[[32/11]]''
| ''-39.773''
| ''-48.372''
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[19/10]]''
| ''[[19/10]]''
Line 1,794: Line 1,268:
| ''+40.375''
| ''+40.375''
| ''+49.105''
| ''+49.105''
|- style="background-color: #cccccc;"
| ''[[27/5]]''
| ''+40.481''
| ''+49.233''
|-
|-
| [[19/11]]
| [[19/11]]
| +40.482
| +40.482
| +49.235
| +49.235
|-
| [[28/17]]
| +40.584
| +49.358
|-
| [[29/27]]
| +40.734
| +49.541
|- style="background-color: #cccccc;"
| ''[[26/21]]''
| ''-40.854''
| ''-49.687''
|}
|}


{| class="wikitable center-1 right-2 right-3 mw-collapsible mw-collapsed"
{| class="wikitable center-1 right-2 right-3 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | 32-integer-limit intervals in 45zpi (by patent val mapping)
|+ style="white-space: nowrap;" | 25-integer-limit intervals in 45zpi (by patent val mapping)
|-
|-
! Ratio
! Ratio
Line 1,838: Line 1,296:
| +0.800
| +0.800
| +0.973
| +0.973
|-
| [[29/5]]
| -1.008
| -1.226
|-
|-
| [[23/13]]
| [[23/13]]
Line 1,886: Line 1,340:
| -2.801
| -2.801
| -3.407
| -3.407
|-
| [[31/9]]
| -3.324
| -4.043
|-
| [[30/17]]
| +3.364
| +4.092
|-
| [[29/18]]
| -3.436
| -4.179
|-
|-
| [[23/7]]
| [[23/7]]
Line 1,914: Line 1,356:
| +4.008
| +4.008
| +4.875
| +4.875
|-
| [[26/17]]
| +4.436
| +5.395
|-
|-
| [[17/2]]
| [[17/2]]
Line 1,934: Line 1,372:
| +5.908
| +5.908
| +7.186
| +7.186
|-
| [[29/7]]
| +5.942
| +7.227
|-
|-
| [[22/13]]
| [[22/13]]
Line 1,966: Line 1,400:
| -7.237
| -7.237
| -8.802
| -8.802
|-
| [[31/27]]
| +7.499
| +9.120
|-
| [[27/11]]
| +7.692
| +9.355
|-
| [[29/19]]
| +7.944
| +9.661
|-
|-
| [[21/13]]
| [[21/13]]
| -8.022
| -8.022
| -9.756
| -9.756
|-
| '''[[29/1]]'''
| '''+8.265'''
| '''+10.051'''
|-
|-
| [[21/1]]
| [[21/1]]
| -8.501
| -8.501
| -10.339
| -10.339
|-
| [[29/13]]
| +8.744
| +10.634
|-
|-
| [[21/19]]
| [[21/19]]
Line 2,022: Line 1,436:
| -9.751
| -9.751
| -11.860
| -11.860
|-
| [[29/23]]
| +9.813
| +11.934
|-
| [[29/15]]
| +9.815
| +11.937
|-
|-
| [[25/17]]
| [[25/17]]
| -9.887
| -9.887
| -12.025
| -12.025
|-
| [[29/25]]
| -10.280
| -12.503
|-
|-
| [[13/3]]
| [[13/3]]
Line 2,078: Line 1,480:
| +13.251
| +13.251
| +16.116
| +16.116
|-
| [[31/3]]
| -14.148
| -17.206
|-
|-
| [[17/10]]
| [[17/10]]
| -14.187
| -14.187
| -17.255
| -17.255
|-
| [[29/6]]
| -14.259
| -17.342
|-
| [[26/25]]
| +14.323
| +17.420
|-
|-
| [[25/2]]
| [[25/2]]
Line 2,102: Line 1,492:
| +14.831
| +14.831
| +18.038
| +18.038
|-
| [[29/22]]
| +15.079
| +18.340
|-
| [[31/11]]
| +15.191
| +18.475
|-
|-
| [[22/5]]
| [[22/5]]
Line 2,118: Line 1,500:
| +16.223
| +16.223
| +19.730
| +19.730
|-
| [[31/21]]
| -16.470
| -20.030
|-
|-
| [[18/17]]
| [[18/17]]
| -16.731
| -16.731
| -20.349
| -20.349
|-
| [[29/21]]
| +16.766
| +20.390
|-
|-
| [[25/14]]
| [[25/14]]
Line 2,138: Line 1,512:
| -17.773
| -17.773
| -21.616
| -21.616
|-
| [[31/22]]
| -18.156
| -22.081
|-
|-
| [[25/19]]
| [[25/19]]
Line 2,158: Line 1,528:
| +19.024
| +19.024
| +23.137
| +23.137
|-
| [[29/3]]
| +19.088
| +23.215
|-
|-
| [[17/5]]
| [[17/5]]
Line 2,178: Line 1,544:
| +20.098
| +20.098
| +24.443
| +24.443
|-
| [[29/17]]
| -20.167
| -24.528
|-
|-
| [[7/6]]
| [[7/6]]
Line 2,210: Line 1,572:
| -23.003
| -23.003
| -27.976
| -27.976
|-
| [[31/15]]
| -23.420
| -28.483
|-
| [[31/23]]
| -23.422
| -28.486
|-
| [[30/29]]
| +23.532
| +28.619
|-
| [[26/5]]
| +23.595
| +28.697
|-
|-
| [[9/7]]
| [[9/7]]
Line 2,238: Line 1,584:
| -24.074
| -24.074
| -29.279
| -29.279
|-
| [[31/13]]
| -24.492
| -29.787
|-
| [[29/26]]
| -24.603
| -29.923
|-
| '''[[31/1]]'''
| '''-24.971'''
| '''-30.369'''
|-
| [[29/2]]
| -25.082
| -30.505
|-
| [[31/19]]
| -25.291
| -30.759
|-
|-
| [[25/22]]
| [[25/22]]
| +25.360
| +25.360
| +30.843
| +30.843
|-
| [[27/22]]
| -25.655
| -31.201
|-
|-
| [[17/7]]
| [[17/7]]
Line 2,278: Line 1,600:
| +27.046
| +27.046
| +32.893
| +32.893
|-
| [[31/7]]
| -27.293
| -33.194
|-
| [[29/14]]
| -27.404
| -33.329
|-
|-
| [[17/12]]
| [[17/12]]
Line 2,310: Line 1,624:
| +29.368
| +29.368
| +35.718
| +35.718
|-
| [[30/7]]
| +29.474
| +35.846
|-
| [[29/9]]
| +29.911
| +36.378
|-
|-
| [[23/17]]
| [[23/17]]
Line 2,326: Line 1,632:
| +29.983
| +29.983
| +36.465
| +36.465
|-
| [[26/7]]
| +30.546
| +37.150
|-
|-
| [[9/5]]
| [[9/5]]
| -30.919
| -30.919
| -37.604
| -37.604
|-
| [[27/23]]
| -30.921
| -37.607
|-
|-
| [[7/2]]
| [[7/2]]
| -31.025
| -31.025
| -37.732
| -37.732
|-
| [[30/19]]
| +31.476
| +38.281
|-
|-
| [[21/11]]
| [[21/11]]
| +31.661
| +31.661
| +38.506
| +38.506
|-
| [[30/1]]
| +31.796
| +38.671
|-
| [[27/13]]
| -31.990
| -38.907
|-
| [[30/13]]
| +32.275
| +39.253
|-
| [[27/1]]
| -32.469
| -39.489
|-
| [[26/19]]
| +32.547
| +39.584
|-
| [[27/19]]
| -32.790
| -39.879
|-
| [[26/1]]
| +32.868
| +39.974
|-
|-
| [[19/2]]
| [[19/2]]
| -33.026
| -33.026
| -40.167
| -40.167
|-
| [[31/29]]
| -33.235
| -40.421
|-
| [[30/23]]
| +33.344
| +40.554
|-
|-
| '''[[2/1]]'''
| '''[[2/1]]'''
Line 2,399: Line 1,657:
| -41.139
| -41.139
|-
|-
| [[31/5]]
| [[23/2]]
| -34.243
| -41.647
|-
| [[29/10]]
| -34.355
| -41.782
|-
| [[26/23]]
| +34.416
| +41.857
|-
| [[26/15]]
| +34.419
| +41.860
|-
| [[27/7]]
| -34.792
| -42.314
|-
| [[23/2]]
| -34.895
| -34.895
| -42.439
| -42.439
Line 2,442: Line 1,680:
| +36.148
| +36.148
| +43.963
| +43.963
|-
| [[31/18]]
| -36.671
| -44.600
|-
|-
| [[21/17]]
| [[21/17]]
Line 2,498: Line 1,732:
| +40.482
| +40.482
| +49.235
| +49.235
|-
| [[28/17]]
| +40.584
| +49.358
|-
| [[29/27]]
| +40.734
| +49.541
|- style="background-color: #cccccc;"
| ''[[26/21]]''
| ''+41.369''
| ''+50.313''
|- style="background-color: #cccccc;"
| ''[[27/5]]''
| ''-41.742''
| ''-50.767''
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[21/2]]''
| ''[[21/2]]''
Line 2,534: Line 1,752:
| ''-43.098''
| ''-43.098''
| ''-52.416''
| ''-52.416''
|- style="background-color: #cccccc;"
| ''[[31/25]]''
| ''-43.516''
| ''-52.924''
|- style="background-color: #cccccc;"
| ''[[26/3]]''
| ''+43.691''
| ''+53.137''
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[23/10]]''
| ''[[23/10]]''
Line 2,558: Line 1,768:
| ''+46.598''
| ''+46.598''
| ''+56.673''
| ''+56.673''
|- style="background-color: #cccccc;"
| ''[[31/6]]''
| ''-47.494''
| ''-57.763''
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[20/17]]''
| ''[[20/17]]''
| ''+47.534''
| ''+47.534''
| ''+57.811''
| ''+57.811''
|- style="background-color: #cccccc;"
| ''[[29/12]]''
| ''-47.606''
| ''-57.899''
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[25/4]]''
| ''[[25/4]]''
| ''-48.149''
| ''-48.149''
| ''-58.559''
| ''-58.559''
|- style="background-color: #cccccc;"
| ''[[29/11]]''
| ''+48.426''
| ''+58.896''
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[11/5]]''
| ''[[11/5]]''
Line 2,586: Line 1,784:
| ''+50.078''
| ''+50.078''
| ''+60.905''
| ''+60.905''
|- style="background-color: #cccccc;"
| ''[[28/25]]''
| ''+50.471''
| ''+61.383''
|- style="background-color: #cccccc;"
| ''[[27/25]]''
| ''-51.014''
| ''-62.044''
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[21/10]]''
| ''[[21/10]]''
Line 2,602: Line 1,792:
| ''+51.862''
| ''+51.862''
| ''+63.075''
| ''+63.075''
|- style="background-color: #cccccc;"
| ''[[31/17]]''
| ''-53.403''
| ''-64.948''
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[10/3]]''
| ''[[10/3]]''
Line 2,614: Line 1,800:
| ''+53.548''
| ''+53.548''
| ''+65.126''
| ''+65.126''
|- style="background-color: #cccccc;"
| ''[[26/9]]''
| ''+54.514''
| ''+66.300''
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[9/2]]''
| ''[[9/2]]''
Line 2,634: Line 1,816:
| ''-56.350''
| ''-56.350''
| ''-68.532''
| ''-68.532''
|- style="background-color: #cccccc;"
| ''[[31/30]]''
| ''-56.767''
| ''-69.040''
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[14/9]]''
| ''[[14/9]]''
Line 2,650: Line 1,828:
| ''-57.421''
| ''-57.421''
| ''-69.836''
| ''-69.836''
|- style="background-color: #cccccc;"
| ''[[31/26]]''
| ''-57.839''
| ''-70.343''
|- style="background-color: #cccccc;"
| ''[[31/2]]''
| ''-58.318''
| ''-70.926''
|- style="background-color: #cccccc;"
| ''[[29/4]]''
| ''-58.429''
| ''-71.062''
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[25/11]]''
| ''[[25/11]]''
| ''+58.707''
| ''+58.707''
| ''+71.399''
| ''+71.399''
|- style="background-color: #cccccc;"
| ''[[28/5]]''
| ''+59.743''
| ''+72.660''
|- style="background-color: #cccccc;"
| ''[[31/14]]''
| ''-60.640''
| ''-73.750''
|- style="background-color: #cccccc;"
| ''[[29/28]]''
| ''-60.751''
| ''-73.886''
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[24/17]]''
| ''[[24/17]]''
| ''+60.785''
| ''+60.785''
| ''+73.927''
| ''+73.927''
|- style="background-color: #cccccc;"
| ''[[27/17]]''
| ''-60.901''
| ''-74.069''
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[11/6]]''
| ''[[11/6]]''
Line 2,698: Line 1,848:
| ''-64.372''
| ''-64.372''
| ''-78.289''
| ''-78.289''
|- style="background-color: #cccccc;"
| ''[[27/26]]''
| ''-65.337''
| ''-79.463''
|- style="background-color: #cccccc;"
| ''[[27/2]]''
| ''-65.816''
| ''-80.046''
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[19/4]]''
| ''[[19/4]]''
Line 2,719: Line 1,861:
| ''-81.696''
| ''-81.696''
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[31/10]]''
| ''[[23/4]]''
| ''-67.590''
| ''-82.203''
|- style="background-color: #cccccc;"
| ''[[29/20]]''
| ''-67.702''
| ''-82.339''
|- style="background-color: #cccccc;"
| ''[[27/14]]''
| ''-68.138''
| ''-82.870''
|- style="background-color: #cccccc;"
| ''[[23/4]]''
| ''-68.242''
| ''-68.242''
| ''-82.996''
| ''-82.996''
Line 2,742: Line 1,872:
| ''+68.594''
| ''+68.594''
| ''+83.424''
| ''+83.424''
|- style="background-color: #cccccc;"
| ''[[28/19]]''
| ''+68.695''
| ''+83.547''
|- style="background-color: #cccccc;"
| ''[[28/1]]''
| ''+69.016''
| ''+83.937''
|- style="background-color: #cccccc;"
| ''[[28/13]]''
| ''+69.495''
| ''+84.520''
|- style="background-color: #cccccc;"
| ''[[28/23]]''
| ''+70.564''
| ''+85.820''
|- style="background-color: #cccccc;"
| ''[[28/15]]''
| ''+70.567''
| ''+85.823''
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[25/24]]''
| ''[[25/24]]''
Line 2,770: Line 1,880:
| ''-71.609''
| ''-71.609''
| ''-87.091''
| ''-87.091''
|- style="background-color: #cccccc;"
| ''[[30/11]]''
| ''+71.958''
| ''+87.515''
|- style="background-color: #cccccc;"
| ''[[26/11]]''
| ''+73.030''
| ''+88.819''
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[11/2]]''
| ''[[11/2]]''
Line 2,786: Line 1,888:
| ''+73.644''
| ''+73.644''
| ''+89.566''
| ''+89.566''
|- style="background-color: #cccccc;"
| ''[[27/10]]''
| ''-75.089''
| ''-91.323''
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[21/4]]''
| ''[[21/4]]''
Line 2,818: Line 1,916:
| ''+77.517''
| ''+77.517''
| ''+94.276''
| ''+94.276''
|- style="background-color: #cccccc;"
| ''[[28/3]]''
| ''+79.839''
| ''+97.100''
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[24/5]]''
| ''[[24/5]]''
| ''+79.945''
| ''+79.945''
| ''+97.229''
| ''+97.229''
|- style="background-color: #cccccc;"
| ''[[31/12]]''
| ''-80.841''
| ''-98.319''
|- style="background-color: #cccccc;"
| ''[[29/24]]''
| ''-80.953''
| ''-98.455''
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[25/8]]''
| ''[[25/8]]''
Line 2,870: Line 1,956:
| ''+89.696''
| ''+89.696''
| ''+109.089''
| ''+109.089''
|- style="background-color: #cccccc;"
| ''[[28/9]]''
| ''+90.662''
| ''+110.264''
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[24/23]]''
| ''[[24/23]]''
Line 2,882: Line 1,964:
| ''+90.768''
| ''+90.768''
| ''+110.392''
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|- style="background-color: #cccccc;"
| ''[[31/4]]''
| ''-91.664''
| ''-111.483''
|- style="background-color: #cccccc;"
| ''[[29/8]]''
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| ''-111.618''
|- style="background-color: #cccccc;"
| ''[[31/28]]''
| ''-93.987''
| ''-114.307''
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[12/11]]''
| ''[[12/11]]''
Line 2,906: Line 1,976:
| ''+97.718''
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| ''+118.845''
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|- style="background-color: #cccccc;"
| ''[[27/4]]''
| ''-99.163''
| ''-120.603''
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[19/8]]''
| ''[[19/8]]''
Line 2,922: Line 1,988:
| ''-100.520''
| ''-100.520''
| ''-122.252''
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|- style="background-color: #cccccc;"
| ''[[31/20]]''
| ''-100.937''
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|- style="background-color: #cccccc;"
| ''[[28/27]]''
| ''+101.485''
| ''+123.427''
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[23/8]]''
| ''[[23/8]]''
Line 2,946: Line 2,004:
| ''-106.855''
| ''-106.855''
| ''-129.958''
| ''-129.958''
|- style="background-color: #cccccc;"
| ''[[27/20]]''
| ''-108.436''
| ''-131.880''
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[21/8]]''
| ''[[21/8]]''
| ''-108.542''
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| ''-132.009''
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|- style="background-color: #cccccc;"
| ''[[28/11]]''
| ''+109.178''
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|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[8/3]]''
| ''[[8/3]]''
| ''+110.864''
| ''+110.864''
| ''+134.833''
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|- style="background-color: #cccccc;"
| ''[[31/24]]''
| ''-114.188''
| ''-138.876''
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[25/16]]''
| ''[[25/16]]''
Line 2,982: Line 2,028:
| ''+124.115''
| ''+124.115''
| ''+150.949''
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|- style="background-color: #cccccc;"
| ''[[31/8]]''
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| ''-152.039''
|- style="background-color: #cccccc;"
| ''[[29/16]]''
| ''-125.123''
| ''-152.175''
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[24/11]]''
| ''[[24/11]]''
Line 2,998: Line 2,036:
| ''+131.065''
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| ''+159.402''
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|- style="background-color: #cccccc;"
| ''[[27/8]]''
| ''-132.510''
| ''-161.159''
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[19/16]]''
| ''[[19/16]]''
Line 3,022: Line 2,056:
| ''+134.938''
| ''+134.938''
| ''+164.112''
| ''+164.112''
|- style="background-color: #cccccc;"
| ''[[32/17]]''
| ''+138.302''
| ''+168.204''
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[11/8]]''
| ''[[11/8]]''
Line 3,038: Line 2,068:
| ''+144.211''
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| ''+175.389''
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|- style="background-color: #cccccc;"
| ''[[32/25]]''
| ''+148.189''
| ''+180.228''
|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[16/9]]''
| ''[[16/9]]''
| ''+155.034''
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|- style="background-color: #cccccc;"
| ''[[32/5]]''
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|- style="background-color: #cccccc;"
| ''[[31/16]]''
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|- style="background-color: #cccccc;"
| ''[[32/29]]''
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|- style="background-color: #cccccc;"
| ''[[32/7]]''
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|- style="background-color: #cccccc;"
| ''[[27/16]]''
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|- style="background-color: #cccccc;"
| ''[[32/19]]''
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|- style="background-color: #cccccc;"
| ''[[32/1]]''
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|- style="background-color: #cccccc;"
| ''[[32/13]]''
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|- style="background-color: #cccccc;"
| ''[[32/23]]''
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|- style="background-color: #cccccc;"
| ''[[32/15]]''
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|- style="background-color: #cccccc;"
|- style="background-color: #cccccc;"
| ''[[16/11]]''
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|- style="background-color: #cccccc;"
| ''[[32/21]]''
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|- style="background-color: #cccccc;"
| ''[[32/3]]''
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|- style="background-color: #cccccc;"
| ''[[32/9]]''
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|- style="background-color: #cccccc;"
| ''[[32/31]]''
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|- style="background-color: #cccccc;"
| ''[[32/27]]''
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|- style="background-color: #cccccc;"
| ''[[32/11]]''
| ''+206.896''
| ''+251.628''
|}
|}


{{Stub}}
{{Stub}}


[[Category:Zeta peak indexes]]
[[Category:Zeta peak indexes]]
Retrieved from "https://en.xen.wiki/w/45zpi"