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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 46: Line 30:


== Intervals ==
== Intervals ==
{| class="wikitable center-1 right-2 left-3 center-4 center-5"
{| class="wikitable center-1 right-2 left-3 center-4 center-5"
|+ 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 25-integer-limit ratios,<br>and are stylized as follows to indicate their accuracy:
| 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 %
* '''<u>Bold Underlined:</u>''' relative error < 8.333 %
* '''Bold:''' relative error < 16.667 %
* '''Bold:''' relative error < 16.667 %
Line 61: Line 46:
! Cents
! Cents
! Ratios
! Ratios
! Ups and Downs Notation
! Ups and downs notation
! Step
! Step
|-
|-
Line 72: 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 78: 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 84: 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 90: 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 96: 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 102: 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 108: 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 114: 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 120: 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 126: 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 132: 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 138: 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 144: 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 150: 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 156: 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 162: 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 168: 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 174: 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 180: 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 186: 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 192: 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 198: 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 210: 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 216: 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 222: 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 228: 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 234: 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 240: 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 246: 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 252: 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 258: 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 264: 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 276: 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 282: 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 288: 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 294: 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 300: 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 306: 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 318: 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 324: Line 309:
| 43
| 43
| 3535.594
| 3535.594
| '''[[23/3]]''', '''[[31/4]]'''
| '''[[23/3]]'''
| M7 +2 oct
| M7 +2 oct
| 215
| 215
Line 336: 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 348: 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 354: 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 360: Line 345:
| 49
| 49
| 4028.933
| 4028.933
| [[31/3]]
|  
| M3 +3 oct
| M3 +3 oct
| 245
| 245
Line 366: 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 396: Line 381:
| 55
| 55
| 4522.272
| 4522.272
| [[27/2]]
|  
| M6 +3 oct
| M6 +3 oct
| 275
| 275
Line 402: 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 414: 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 477: 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
|}
|}


== Approximation to JI ==
== Approximation to JI ==
=== Interval mappings ===
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;" | Intervals by direct approximation (even if inconsistent)
|+ style="white-space: nowrap;" | 25-integer-limit intervals in 45zpi (by direct approximation)
|-
|-
! Ratio
! Ratio
Line 519: Line 478:
|-
|-
| [[23/15]]
| [[23/15]]
| -0.002
| +0.002
| -0.003
| +0.003
|-
| ''[[32/7]]''
| ''+0.034''
| ''+0.042''
|-
|-
| '''[[19/1]]'''
| '''[[19/1]]'''
| '''-0.321'''
| '''+0.321'''
| '''-0.390'''
| '''+0.390'''
|-
|-
| '''[[13/1]]'''
| '''[[13/1]]'''
| '''+0.479'''
| '''-0.479'''
| '''+0.583'''
| '''-0.583'''
|-
|- style="background-color: #cccccc;"
| ''[[11/10]]''
| ''[[11/10]]''
| ''+0.558''
| ''-0.558''
| ''+0.679''
| ''-0.679''
|-
|- style="background-color: #cccccc;"
| ''[[25/8]]''
| ''[[25/8]]''
| ''-0.728''
| ''+0.728''
| ''-0.885''
| ''+0.885''
|-
|-
| [[19/13]]
| [[19/13]]
| -0.800
| +0.800
| -0.973
| +0.973
|-
| [[29/5]]
| +1.008
| +1.226
|-
|-
| [[23/13]]
| [[23/13]]
| +1.069
| -1.069
| +1.300
| -1.300
|-
|-
| [[15/13]]
| [[15/13]]
| +1.072
| -1.072
| +1.303
| -1.303
|-
| ''[[29/24]]''
| ''-1.270''
| ''-1.545''
|-
| ''[[31/12]]''
| ''-1.382''
| ''-1.681''
|-
| ''[[27/16]]''
| ''+1.411''
| ''+1.716''
|-
|-
| '''[[23/1]]'''
| '''[[23/1]]'''
| '''+1.548'''
| '''-1.548'''
| '''+1.883'''
| '''-1.883'''
|-
|-
| [[15/1]]
| [[15/1]]
| +1.551
| -1.551
| +1.886
| -1.886
|-
|-
| [[22/21]]
| [[22/21]]
| -1.686
| +1.686
| -2.051
| +2.051
|-
|-
| [[23/19]]
| [[23/19]]
| +1.869
| -1.869
| +2.273
| -2.273
|-
|-
| [[19/15]]
| [[19/15]]
| -1.871
| +1.871
| -2.276
| +2.276
|-
| ''[[32/19]]''
| ''-1.967''
| ''-2.393''
|-
|-
| [[19/7]]
| [[19/7]]
| +2.002
| -2.002
| +2.434
| -2.434
|-
|- style="background-color: #cccccc;"
| ''[[21/20]]''
| ''[[21/20]]''
| ''+2.244''
| ''-2.244''
| ''+2.729''
| ''-2.729''
|-
|- style="background-color: #cccccc;"
| ''[[24/5]]''
| ''[[24/5]]''
| ''+2.278''
| ''-2.278''
| ''+2.771''
| ''-2.771''
|-
| ''[[32/1]]''
| ''-2.288''
| ''-2.783''
|-
|-
| '''[[7/1]]'''
| '''[[7/1]]'''
| '''-2.322'''
| '''+2.322'''
| '''-2.824'''
| '''+2.824'''
|-
| ''[[28/3]]''
| ''+2.384''
| ''+2.900''
|-
|-
| [[18/5]]
| [[18/5]]
| -2.428
| +2.428
| -2.953
| +2.953
|-
| ''[[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
|-
| ''[[32/23]]''
| ''-3.836''
| ''-4.666''
|-
| ''[[32/15]]''
| ''-3.839''
| ''-4.669''
|-
|-
| [[23/7]]
| [[23/7]]
| +3.870
| -3.870
| +4.707
| -4.707
|-
|-
| [[15/7]]
| [[15/7]]
| +3.873
| -3.873
| +4.710
| -4.710
|-
|-
| [[25/6]]
| [[25/6]]
| +3.979
| -3.979
| +4.839
| -4.839
|-
|-
| [[22/3]]
| [[22/3]]
| -4.008
| +4.008
| -4.875
| +4.875
|-
|- style="background-color: #cccccc;"
| [[26/17]]
| -4.436
| -5.395
|-
| ''[[20/3]]''
| ''[[20/3]]''
| ''-4.566''
| ''+4.566''
| ''-5.553''
| ''+5.553''
|-
|- style="background-color: #cccccc;"
| ''[[24/7]]''
| ''[[24/7]]''
| ''-4.672''
| ''+4.672''
| ''-5.682''
| ''+5.682''
|-
|- style="background-color: #cccccc;"
| ''[[4/3]]''
| ''[[4/3]]''
| ''+4.706''
| ''-4.706''
| ''+5.724''
| ''-5.724''
|-
|- style="background-color: #cccccc;"
| ''[[23/20]]''
| ''[[23/20]]''
| ''-4.709''
| ''+4.709''
| ''-5.727''
| ''+5.727''
|-
|-
| [[17/2]]
| [[17/2]]
| +4.915
| -4.915
| +5.977
| -5.977
|-
|-
| [[22/15]]
| [[22/15]]
| +5.264
| -5.264
| +6.402
| -6.402
|-
|-
| [[23/22]]
| [[23/22]]
| -5.267
| +5.267
| -6.405
| +6.405
|-
|- style="background-color: #cccccc;"
| ''[[20/13]]''
| ''[[20/13]]''
| ''+5.778''
| ''-5.778''
| ''+7.027''
| ''-7.027''
|-
|-
| [[17/6]]
| [[17/6]]
| -5.908
| +5.908
| -7.186
| +7.186
|-
|- style="background-color: #cccccc;"
| [[29/7]]
| -5.942
| -7.227
|-
| ''[[32/29]]''
| ''+5.977''
| ''+7.269''
|-
| ''[[31/16]]''
| ''-6.088''
| ''-7.404''
|-
| ''[[9/4]]''
| ''[[9/4]]''
| ''+6.117''
| ''-6.117''
| ''+7.439''
| ''-7.439''
|-
|- style="background-color: #cccccc;"
| ''[[20/1]]''
| ''[[20/1]]''
| ''+6.257''
| ''-6.257''
| ''+7.610''
| ''-7.610''
|-
|-
| [[22/13]]
| [[22/13]]
| +6.336
| -6.336
| +7.706
| -7.706
|-
|- style="background-color: #cccccc;"
| ''[[14/11]]''
| ''[[14/11]]''
| ''+6.392''
| ''-6.392''
| ''+7.774''
| ''-7.774''
|-
|- style="background-color: #cccccc;"
| ''[[20/19]]''
| ''[[20/19]]''
| ''+6.578''
| ''-6.578''
| ''+8.000''
| ''-8.000''
|-
|- style="background-color: #cccccc;"
| ''[[24/19]]''
| ''[[24/19]]''
| ''-6.674''
| ''+6.674''
| ''-8.116''
| ''+8.116''
|-
|-
| [[22/1]]
| [[22/1]]
| +6.815
| -6.815
| +8.288
| -8.288
|-
|-
| [[25/18]]
| [[25/18]]
| -6.844
| +6.844
| -8.324
| +8.324
|-
|-
| [[7/5]]
| [[7/5]]
| +6.950
| -6.950
| +8.453
| -8.453
|-
|-
| [[23/21]]
| [[23/21]]
| -6.953
| +6.953
| -8.456
| +8.456
|-
|- style="background-color: #cccccc;"
| ''[[32/5]]''
| ''+6.984''
| ''+8.495''
|-
| ''[[24/1]]''
| ''[[24/1]]''
| ''-6.994''
| ''+6.994''
| ''-8.506''
| ''+8.506''
|-
|- style="background-color: #cccccc;"
| ''[[21/4]]''
| ''[[21/4]]''
| ''-7.028''
| ''+7.028''
| ''-8.548''
| ''+8.548''
|-
| ''[[27/10]]''
| ''-7.134''
| ''-8.677''
|-
|-
| [[22/19]]
| [[22/19]]
| +7.136
| -7.136
| +8.678
| -8.678
|-
|-
| [[17/14]]
| [[17/14]]
| +7.237
| -7.237
| +8.802
| -8.802
|-
|- style="background-color: #cccccc;"
| ''[[24/13]]''
| ''[[24/13]]''
| ''-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'''
|-
| ''[[28/9]]''
| ''-8.439''
| ''-10.264''
|-
|-
| [[21/1]]
| [[21/1]]
| +8.501
| -8.501
| +10.339
| -10.339
|-
|- style="background-color: #cccccc;"
| ''[[24/23]]''
| ''[[24/23]]''
| ''-8.542''
| ''+8.542''
| ''-10.389''
| ''+10.389''
|-
|- style="background-color: #cccccc;"
| ''[[8/5]]''
| ''[[8/5]]''
| ''-8.545''
| ''+8.545''
| ''-10.392''
| ''+10.392''
|-
|- style="background-color: #cccccc;"
| ''[[20/7]]''
| ''[[20/7]]''
| ''+8.579''
| ''-8.579''
| ''+10.434''
| ''-10.434''
|-
|- style="background-color: #cccccc;"
| ''[[11/2]]''
| ''[[11/2]]''
| ''-8.714''
| ''+8.714''
| ''-10.599''
| ''+10.599''
|-
| [[29/13]]
| -8.744
| -10.634
|-
|-
| [[21/19]]
| [[21/19]]
| +8.822
| -8.822
| +10.729
| -10.729
|-
|-
| [[19/5]]
| [[19/5]]
| +8.952
| -8.952
| +10.887
| -10.887
|-
|- style="background-color: #cccccc;"
| ''[[16/11]]''
| ''[[16/11]]''
| ''-9.103''
| ''+9.103''
| ''-11.071''
| ''+11.071''
|-
|-
| [[22/7]]
| [[22/7]]
| +9.137
| -9.137
| +11.113
| -11.113
|-
| ''[[26/11]]''
| ''+9.194''
| ''+11.181''
|-
|-
| '''[[5/1]]'''
| '''[[5/1]]'''
| '''-9.272'''
| '''+9.272'''
| '''-11.277'''
| '''+11.277'''
|-
|-
| [[23/3]]
| [[23/3]]
| -9.275
| +9.275
| -11.280
| +11.280
|-
|-
| [[18/7]]
| [[18/7]]
| -9.378
| +9.378
| -11.406
| +11.406
|-
|- style="background-color: #cccccc;"
| ''[[16/9]]''
| ''[[16/9]]''
| ''+9.413''
| ''-9.413''
| ''+11.448''
| ''-11.448''
|-
| ''[[31/4]]''
| ''+9.441''
| ''+11.483''
|-
| ''[[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
|-
| ''[[30/11]]''
| ''+10.265''
| ''+12.485''
|-
| [[29/25]]
| +10.280
| +12.503
|-
|-
| [[13/3]]
| [[13/3]]
| -10.344
| +10.344
| -12.581
| +12.581
|-
|- style="background-color: #cccccc;"
| ''[[17/8]]''
| ''[[17/8]]''
| ''-10.615''
| ''+10.615''
| ''-12.909''
| ''+12.909''
|-
| ''[[32/21]]''
| ''-10.789''
| ''-13.122''
|-
|-
| [[23/5]]
| [[23/5]]
| +10.821
| -10.821
| +13.160
| -13.160
|-
|-
| '''[[3/1]]'''
| '''[[3/1]]'''
| '''+10.823'''
| '''-10.823'''
| '''+13.163'''
| '''-13.163'''
|-
|-
| [[19/3]]
| [[19/3]]
| -11.144
| +11.144
| -13.553
| +13.553
|-
|-
| [[19/18]]
| [[19/18]]
| +11.380
| -11.380
| +13.840
| -13.840
|-
|- style="background-color: #cccccc;"
| ''[[25/24]]''
| ''[[25/24]]''
| ''-11.551''
| ''+11.551''
| ''-14.048''
| ''+14.048''
|-
| ''[[28/15]]''
| ''+11.657''
| ''+14.177''
|-
| ''[[28/23]]''
| ''+11.659''
| ''+14.180''
|-
|-
| [[18/1]]
| [[18/1]]
| -11.701
| +11.701
| -14.230
| +14.230
|-
| ''[[31/28]]''
| ''+11.763''
| ''+14.307''
|-
|-
| [[18/13]]
| [[18/13]]
| -12.180
| +12.180
| -14.813
| +14.813
|-
| ''[[28/13]]''
| ''+12.728''
| ''+15.480''
|-
| ''[[32/3]]''
| ''-13.111''
| ''-15.946''
|-
|-
| [[7/3]]
| [[7/3]]
| -13.145
| +13.145
| -15.987
| +15.987
|-
| ''[[28/1]]''
| ''+13.207''
| ''+16.063''
|-
|-
| [[23/18]]
| [[23/18]]
| +13.249
| -13.249
| +16.113
| -16.113
|-
|-
| [[6/5]]
| [[6/5]]
| -13.251
| +13.251
| -16.116
| +16.116
|-
|- style="background-color: #cccccc;"
| ''[[28/19]]''
| ''+13.528''
| ''+16.453''
|-
| ''[[17/11]]''
| ''[[17/11]]''
| ''+13.629''
| ''-13.629''
| ''+16.576''
| ''-16.576''
|-
|- style="background-color: #cccccc;"
| ''[[12/11]]''
| ''[[12/11]]''
| ''-13.809''
| ''+13.809''
| ''-16.795''
| ''+16.795''
|-
|- style="background-color: #cccccc;"
| ''[[15/4]]''
| ''[[15/4]]''
| ''-13.979''
| ''+13.979''
| ''-17.001''
| ''+17.001''
|-
|- style="background-color: #cccccc;"
| ''[[23/4]]''
| ''[[23/4]]''
| ''-13.981''
| ''+13.981''
| ''-17.004''
| ''+17.004''
|-
| ''[[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
|-
| ''[[29/20]]''
| ''-14.522''
| ''-17.661''
|-
| ''[[31/10]]''
| ''-14.633''
| ''-17.797''
|-
|-
| [[25/2]]
| [[25/2]]
| +14.802
| -14.802
| +18.002
| -18.002
|-
|-
| [[22/9]]
| [[22/9]]
| -14.831
| +14.831
| -18.038
| +18.038
|-
|- style="background-color: #cccccc;"
| ''[[13/4]]''
| ''[[13/4]]''
| ''-15.050''
| ''+15.050''
| ''-18.304''
| ''+18.304''
|-
|- style="background-color: #cccccc;"
| [[29/22]]
| -15.079
| -18.340
|-
| [[31/11]]
| -15.191
| -18.475
|-
| ''[[20/9]]''
| ''[[20/9]]''
| ''-15.389''
| ''+15.389''
| ''-18.717''
| ''+18.717''
|-
|- style="background-color: #cccccc;"
| ''[[8/7]]''
| ''[[8/7]]''
| ''-15.495''
| ''+15.495''
| ''-18.845''
| ''+18.845''
|-
|- style="background-color: #cccccc;"
| ''[[4/1]]''
| ''[[4/1]]''
| ''+15.529''
| ''-15.529''
| ''+18.887''
| ''-18.887''
|-
|- style="background-color: #cccccc;"
| ''[[19/4]]''
| ''[[19/4]]''
| ''-15.850''
| ''+15.850''
| ''-19.277''
| ''+19.277''
|-
|-
| [[22/5]]
| [[22/5]]
| +16.087
| -16.087
| +19.566
| -19.566
|-
|-
| [[25/7]]
| [[25/7]]
| -16.223
| +16.223
| -19.730
| +19.730
|-
| ''[[32/25]]''
| ''+16.257''
| ''+19.772''
|-
| ''[[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
|-
| ''[[27/26]]''
| ''-16.886''
| ''-20.537''
|-
| ''[[27/4]]''
| ''+16.940''
| ''+20.603''
|-
|-
| [[25/14]]
| [[25/14]]
| +17.124
| -17.124
| +20.826
| -20.826
|-
|- style="background-color: #cccccc;"
| ''[[19/8]]''
| ''[[19/8]]''
| ''+17.497''
| ''-17.497''
| ''+21.280''
| ''-21.280''
|-
|-
| [[21/5]]
| [[21/5]]
| +17.773
| -17.773
| +21.616
| -21.616
|-
|- style="background-color: #cccccc;"
| ''[[8/1]]''
| ''[[8/1]]''
| ''-17.817''
| ''+17.817''
| ''-21.670''
| ''+21.670''
|-
|- style="background-color: #cccccc;"
| ''[[7/4]]''
| ''[[7/4]]''
| ''-17.852''
| ''+17.852''
| ''-21.711''
| ''+21.711''
|-
|- style="background-color: #cccccc;"
| ''[[10/9]]''
| ''[[10/9]]''
| ''+17.957''
| ''-17.957''
| ''+21.840''
| ''-21.840''
|-
| [[31/22]]
| +18.156
| +22.081
|-
|-
| [[25/19]]
| [[25/19]]
| -18.224
| +18.224
| -22.164
| +22.164
|-
|- style="background-color: #cccccc;"
| ''[[13/8]]''
| ''[[13/8]]''
| ''+18.296''
| ''-18.296''
| ''+22.252''
| ''-22.252''
|-
|-
| [[11/9]]
| [[11/9]]
| +18.515
| -18.515
| +22.519
| -22.519
|-
|-
| [[25/1]]
| [[25/1]]
| -18.545
| +18.545
| -22.554
| +22.554
|-
| ''[[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''
|-
| ''[[23/8]]''
| ''[[23/8]]''
| ''+19.366''
| ''-19.366''
| ''+23.553''
| ''-23.553''
|-
|- style="background-color: #cccccc;"
| ''[[15/8]]''
| ''[[15/8]]''
| ''+19.368''
| ''-19.368''
| ''+23.556''
| ''-23.556''
|-
|- style="background-color: #cccccc;"
| ''[[11/6]]''
| ''[[11/6]]''
| ''-19.538''
| ''+19.538''
| ''-23.762''
| ''+23.762''
|-
|-
| [[25/23]]
| [[25/23]]
| -20.093
| +20.093
| -24.437
| +24.437
|-
|-
| [[5/3]]
| [[5/3]]
| -20.096
| +20.096
| -24.440
| +24.440
|-
|-
| [[23/9]]
| [[23/9]]
| -20.098
| +20.098
| -24.443
| +24.443
|-
| [[29/17]]
| +20.167
| +24.528
|-
|-
| [[7/6]]
| [[7/6]]
| +20.202
| -20.202
| +24.569
| -24.569
|-
|- style="background-color: #cccccc;"
| ''[[16/3]]''
| ''[[16/3]]''
| ''+20.236''
| ''-20.236''
| ''+24.611''
| ''-24.611''
|-
|-
| [[13/9]]
| [[13/9]]
| -21.167
| +21.167
| -25.744
| +25.744
|-
|- style="background-color: #cccccc;"
| ''[[27/17]]''
| ''-21.322''
| ''-25.931''
|-
| ''[[24/17]]''
| ''[[24/17]]''
| ''+21.438''
| ''-21.438''
| ''+26.073''
| ''-26.073''
|-
| ''[[29/28]]''
| ''-21.472''
| ''-26.114''
|-
| ''[[31/14]]''
| ''-21.583''
| ''-26.250''
|-
|-
| [[9/1]]
| [[9/1]]
| +21.646
| -21.646
| +26.326
| -26.326
|-
|-
| [[19/9]]
| [[19/9]]
| -21.967
| +21.967
| -26.716
| +26.716
|-
|-
| [[19/6]]
| [[19/6]]
| +22.203
| -22.203
| +27.003
| -27.003
|-
| ''[[28/5]]''
| ''+22.480''
| ''+27.340''
|-
|-
| [[6/1]]
| [[6/1]]
| -22.524
| +22.524
| -27.393
| +27.393
|-
|- style="background-color: #cccccc;"
| ''[[21/16]]''
| ''[[21/16]]''
| ''-22.558''
| ''+22.558''
| ''-27.435''
| ''+27.435''
|-
|- style="background-color: #cccccc;"
| ''[[17/16]]''
| ''[[17/16]]''
| ''+22.732''
| ''-22.732''
| ''+27.647''
| ''-27.647''
|-
|-
| [[13/6]]
| [[13/6]]
| +23.003
| -23.003
| +27.976
| -27.976
|- style="background-color: #cccccc;"
| ''[[25/11]]''
| ''-23.516''
| ''-28.601''
|-
|-
| [[31/15]]
| [[9/7]]
| +23.420
| -23.968
| +28.483
| -29.151
|-
| [[23/6]]
| -24.072
| -29.276
|-
| [[5/2]]
| -24.074
| -29.279
|- style="background-color: #cccccc;"
| ''[[11/8]]''
| ''+24.244''
| ''+29.486''
|- style="background-color: #cccccc;"
| ''[[11/4]]''
| ''-24.632''
| ''-29.958''
|- style="background-color: #cccccc;"
| ''[[5/4]]''
| ''+24.802''
| ''+30.164''
|- style="background-color: #cccccc;"
| ''[[23/12]]''
| ''+24.804''
| ''+30.167''
|- style="background-color: #cccccc;"
| ''[[14/9]]''
| ''-24.908''
| ''-30.293''
|-
| [[25/22]]
| +25.360
| +30.843
|- style="background-color: #cccccc;"
| ''[[13/12]]''
| ''+25.874''
| ''+31.468''
|-
| [[17/7]]
| +26.110
| +31.755
|- style="background-color: #cccccc;"
| ''[[21/8]]''
| ''-26.318''
| ''-32.009''
|- style="background-color: #cccccc;"
| ''[[12/1]]''
| ''-26.353''
| ''-32.050''
|-
| [[14/5]]
| +26.397
| +32.104
|- style="background-color: #cccccc;"
| ''[[19/12]]''
| ''+26.673''
| ''+32.440''
|-
| [[25/21]]
| +27.046
| +32.893
|- style="background-color: #cccccc;"
| ''[[9/2]]''
| ''+27.230''
| ''+33.117''
|-
| [[17/12]]
| -27.439
| -33.371
|-
| [[19/17]]
| -28.111
| -34.189
|-
|-
| [[31/23]]
| '''[[17/1]]'''
| +23.422
| '''+28.432'''
| +28.486
| '''+34.579'''
|- style="background-color: #cccccc;"
| ''[[8/3]]''
| ''+28.641''
| ''+34.833''
|- style="background-color: #cccccc;"
| ''[[12/7]]''
| ''-28.675''
| ''-34.874''
|- style="background-color: #cccccc;"
| ''[[10/3]]''
| ''-28.781''
| ''-35.003''
|-
|-
| ''[[25/11]]''
| [[17/13]]
| ''+23.516''
| +28.911
| ''+28.601''
| +35.162
|-
| [[11/3]]
| -29.339
| -35.682
|-
|-
| [[30/29]]
| [[25/3]]
| -23.532
| +29.368
| -28.619
| +35.718
|- style="background-color: #cccccc;"
| ''[[16/15]]''
| ''-29.508''
| ''-35.888''
|- style="background-color: #cccccc;"
| ''[[23/16]]''
| ''+29.511''
| ''+35.891''
|-
|-
| [[26/5]]
| [[23/17]]
| -23.595
| -29.980
| -28.697
| -36.462
|-
|-
| ''[[29/4]]''
| [[17/15]]
| ''-23.794''
| +29.983
| ''-28.938''
| +36.465
|- style="background-color: #cccccc;"
| ''[[18/11]]''
| ''-30.361''
| ''-36.925''
|- style="background-color: #cccccc;"
| ''[[16/13]]''
| ''-30.580''
| ''-37.191''
|-
|-
| ''[[31/2]]''
| [[9/5]]
| ''-23.906''
| -30.919
| ''-29.074''
| -37.604
|-
|-
| ''[[32/9]]''
| [[7/2]]
| ''-23.934''
| -31.025
| ''-29.109''
| -37.732
|- style="background-color: #cccccc;"
| ''[[16/1]]''
| ''-31.059''
| ''-37.774''
|- style="background-color: #cccccc;"
| ''[[21/10]]''
| ''+31.103''
| ''+37.827''
|- style="background-color: #cccccc;"
| ''[[19/16]]''
| ''+31.379''
| ''+38.164''
|-
|-
| [[9/7]]
| [[21/11]]
| +23.968
| +31.661
| +29.151
| +38.506
|- style="background-color: #cccccc;"
| ''[[17/9]]''
| ''-32.145''
| ''-39.095''
|- style="background-color: #cccccc;"
| ''[[25/16]]''
| ''-32.619''
| ''-39.672''
|- style="background-color: #cccccc;"
| ''[[11/5]]''
| ''+32.789''
| ''+39.878''
|-
| [[19/2]]
| -33.026
| -40.167
|-
| '''[[2/1]]'''
| '''+33.347'''
| '''+40.557'''
|- style="background-color: #cccccc;"
| ''[[16/7]]''
| ''-33.381''
| ''-40.598''
|-
| [[13/2]]
| -33.826
| -41.139
|- style="background-color: #cccccc;"
| ''[[20/11]]''
| ''+33.905''
| ''+41.235''
|- style="background-color: #cccccc;"
| ''[[25/4]]''
| ''+34.074''
| ''+41.441''
|- style="background-color: #cccccc;"
| ''[[20/17]]''
| ''-34.689''
| ''-42.189''
|-
|-
| [[23/6]]
| [[23/2]]
| +24.072
| -34.895
| +29.276
| -42.439
|-
|-
| [[5/2]]
| [[15/2]]
| +24.074
| -34.898
| +29.279
| -42.442
|- style="background-color: #cccccc;"
| ''[[24/11]]''
| ''-35.067''
| ''-42.649''
|-
|-
| ''[[11/8]]''
| [[22/17]]
| ''-24.244''
| -35.247
| ''-29.486''
| -42.867
|-
|-
| ''[[31/26]]''
| [[19/14]]
| ''-24.385''
| -35.348
| ''-29.657''
| -42.991
|- style="background-color: #cccccc;"
| ''[[12/5]]''
| ''-35.625''
| ''-43.327''
|-
|-
| [[31/13]]
| [[14/1]]
| +24.492
| +35.669
| +29.787
| +43.381
|- style="background-color: #cccccc;"
| ''[[14/3]]''
| ''-35.731''
| ''-43.456''
|-
|-
| [[29/26]]
| [[14/13]]
| +24.603
| +36.148
| +29.923
| +43.963
|-
|-
| ''[[11/4]]''
| [[21/17]]
| ''+24.632''
| -36.933
| ''+29.958''
| -44.918
|-
|-
| ''[[5/4]]''
| [[23/14]]
| ''-24.802''
| -37.217
| ''-30.164''
| -45.264
|-
|-
| ''[[23/12]]''
| [[15/14]]
| ''-24.804''
| -37.220
| ''-30.167''
| -45.267
|-
|-
| ''[[14/9]]''
| [[25/12]]
| ''+24.908''
| -37.326
| ''+30.293''
| -45.395
|- style="background-color: #cccccc;"
| ''[[3/2]]''
| ''+38.053''
| ''+46.280''
|- style="background-color: #cccccc;"
| ''[[23/10]]''
| ''+38.056''
| ''+46.283''
|-
|-
| '''[[31/1]]'''
| [[17/4]]
| '''+24.971'''
| -38.262
| '''+30.369'''
| -46.534
|-
|-
| [[29/2]]
| [[15/11]]
| +25.082
| +38.611
| +30.505
| +46.959
|-
|-
| [[31/19]]
| [[23/11]]
| +25.291
| +38.614
| +30.759
| +46.962
|- style="background-color: #cccccc;"
| ''[[13/10]]''
| ''+39.125''
| ''+47.584''
|-
|-
| [[25/22]]
| [[17/3]]
| -25.360
| +39.255
| -30.843
| +47.742
|- style="background-color: #cccccc;"
| ''[[9/8]]''
| ''-39.464''
| ''-47.996''
|- style="background-color: #cccccc;"
| ''[[10/1]]''
| ''-39.604''
| ''-48.166''
|-
|-
| ''[[31/30]]''
| [[13/11]]
| ''-25.456''
| +39.683
| ''-30.960''
| +48.262
|- style="background-color: #cccccc;"
| ''[[11/7]]''
| ''+39.739''
| ''+48.331''
|- style="background-color: #cccccc;"
| ''[[19/10]]''
| ''+39.924''
| ''+48.556''
|-
|-
| [[27/22]]
| '''[[11/1]]'''
| +25.655
| '''-40.162'''
| +31.201
| '''-48.845'''
|-
|-
| ''[[13/12]]''
| [[25/9]]
| ''-25.874''
| +40.191
| ''-31.468''
| +48.881
|-
|-
| [[17/7]]
| [[10/7]]
| -26.110
| +40.297
| -31.755
| +49.010
|- style="background-color: #cccccc;"
| ''[[16/5]]''
| ''-40.331''
| ''-49.051''
|- style="background-color: #cccccc;"
| ''[[21/2]]''
| ''+40.375''
| ''+49.105''
|-
|-
| ''[[32/17]]''
| [[19/11]]
| ''+26.144''
| +40.482
| ''+31.796''
| +49.235
|}
 
{| class="wikitable center-1 right-2 right-3 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | 25-integer-limit intervals in 45zpi (by patent val mapping)
|-
|-
| ''[[27/20]]''
! Ratio
| ''+26.213''
! Error (abs, [[Cent|¢]])
| ''+31.880''
! Error (rel, [[Relative cent|%]])
|-
|-
| ''[[21/8]]''
| [[23/15]]
| ''+26.318''
| +0.002
| ''+32.009''
| +0.003
|-
|-
| ''[[12/1]]''
| '''[[19/1]]'''
| ''+26.353''
| '''+0.321'''
| ''+32.050''
| '''+0.390'''
|-
|-
| [[14/5]]
| '''[[13/1]]'''
| -26.397
| '''-0.479'''
| -32.104
| '''-0.583'''
|-
|-
| ''[[19/12]]''
| [[19/13]]
| ''-26.673''
| +0.800
| ''-32.440''
| +0.973
|-
|-
| ''[[28/11]]''
| [[23/13]]
| ''-26.955''
| -1.069
| ''-32.782''
| -1.300
|-
|-
| [[25/21]]
| [[15/13]]
| -27.046
| -1.072
| -32.893
| -1.303
|-
|-
| ''[[9/2]]''
| '''[[23/1]]'''
| ''-27.230''
| '''-1.548'''
| ''-33.117''
| '''-1.883'''
|-
|-
| ''[[32/31]]''
| [[15/1]]
| ''-27.259''
| -1.551
| ''-33.152''
| -1.886
|-
|-
| [[31/7]]
| [[22/21]]
| +27.293
| +1.686
| +33.194
| +2.051
|-
|-
| [[29/14]]
| [[23/19]]
| +27.404
| -1.869
| +33.329
| -2.273
|-
|-
| [[17/12]]
| [[19/15]]
| +27.439
| +1.871
| +33.371
| +2.276
|-
| [[19/7]]
| -2.002
| -2.434
|-
| '''[[7/1]]'''
| '''+2.322'''
| '''+2.824'''
|-
|-
| ''[[26/9]]''
| [[18/5]]
| ''+27.709''
| +2.428
| ''+33.700''
| +2.953
|-
|-
| [[19/17]]
| [[13/7]]
| +28.111
| -2.801
| +34.189
| -3.407
|-
|-
| '''[[17/1]]'''
| [[23/7]]
| '''-28.432'''
| -3.870
| '''-34.579'''
| -4.707
|-
|-
| ''[[8/3]]''
| [[15/7]]
| ''-28.641''
| -3.873
| ''-34.833''
| -4.710
|-
|-
| ''[[12/7]]''
| [[25/6]]
| ''+28.675''
| -3.979
| ''+34.874''
| -4.839
|-
|-
| ''[[10/3]]''
| [[22/3]]
| ''+28.781''
| +4.008
| ''+35.003''
| +4.875
|-
|-
| ''[[31/17]]''
| [[17/2]]
| ''-28.820''
| -4.915
| ''-35.052''
| -5.977
|-
|-
| [[17/13]]
| [[22/15]]
| -28.911
| -5.264
| -35.162
| -6.402
|-
|-
| [[11/3]]
| [[23/22]]
| +29.339
| +5.267
| +35.682
| +6.405
|-
|-
| [[25/3]]
| [[17/6]]
| -29.368
| +5.908
| -35.718
| +7.186
|-
|-
| [[30/7]]
| [[22/13]]
| -29.474
| -6.336
| -35.846
| -7.706
|-
|-
| ''[[16/15]]''
| [[22/1]]
| ''+29.508''
| -6.815
| ''+35.888''
| -8.288
|-
|-
| ''[[23/16]]''
| [[25/18]]
| ''-29.511''
| +6.844
| ''-35.891''
| +8.324
|-
|-
| [[29/9]]
| [[7/5]]
| -29.911
| -6.950
| -36.378
| -8.453
|-
|-
| [[23/17]]
| [[23/21]]
| +29.980
| +6.953
| +36.462
| +8.456
|-
|-
| [[17/15]]
| [[22/19]]
| -29.983
| -7.136
| -36.465
| -8.678
|-
|-
| ''[[18/11]]''
| [[17/14]]
| ''+30.361''
| -7.237
| ''+36.925''
| -8.802
|-
|-
| [[26/7]]
| [[21/13]]
| -30.546
| -8.022
| -37.150
| -9.756
|-
|-
| ''[[16/13]]''
| [[21/1]]
| ''+30.580''
| -8.501
| ''+37.191''
| -10.339
|-
|-
| [[9/5]]
| [[21/19]]
| +30.919
| -8.822
| +37.604
| -10.729
|-
|-
| [[27/23]]
| [[19/5]]
| +30.921
| -8.952
| +37.607
| -10.887
|-
|-
| [[7/2]]
| [[22/7]]
| +31.025
| -9.137
| +37.732
| -11.113
|-
|-
| ''[[16/1]]''
| '''[[5/1]]'''
| ''+31.059''
| '''+9.272'''
| ''+37.774''
| '''+11.277'''
|-
|-
| ''[[21/10]]''
| [[23/3]]
| ''-31.103''
| +9.275
| ''-37.827''
| +11.280
|-
|-
| ''[[27/25]]''
| [[18/7]]
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Retrieved from "https://en.xen.wiki/w/45zpi"