143ed11: Difference between revisions

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Created page with "143 equal divisions of the 11th harmonic (abbreviated 143ed11), is the tuning system that divides the 11th harmonic into 143 equal parts of about 29.0302 ¢ each. Each step represents a frequency ratio of <math>11^{\frac{1}{143}}</math>, or the 143rd root of 11. == Theory == === Why 143ed11 matter === 143ed11 is extremely strong in the 5.7.8.9.11.13.17.23 subgroup. All ratios in the 5.7.8.9.11.13.17.23 subgroup and 25-integer-limit are approximated in 143ed11 with..."
 
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143 equal divisions of the 11th harmonic (abbreviated 143ed11), is the tuning system that divides the 11th harmonic into 143 equal parts of about 29.0302 ¢ each. Each step represents a frequency ratio of <math>11^{\frac{1}{143}}</math>, or the 143rd root of 11.
{{Infobox ET}}
 
{{ED intro}}
== Theory ==
== Theory ==


=== Why 143ed11 matter ===
143ed11 is extremely strong in the 8.9.5.7.11.13.17.23 subgroup. All ratios in the 8.9.5.7.11.13.17.23 subgroup and 25-integer-limit are approximated in 143ed11 with less than 2.5 ¢ error. According to the finite Euler product with sigma = 1, the maxima in the 8.9.5.7.11.13.17.23 subgroup is about 41.33601-ED2 (or 29.03038 ¢). The Tenney–Euclidean regular temperement in the 8.9.5.7.11.13.17.23 subgroup mapped with [⟨124 131 96 116 143 153 169 187]] gives 41.33650-ED2 (or 29.03004 ¢). The finite Euler product with sigma = 1/2 gives about the same result. 143ed11, with its size of about 41.33627-ED2 (or 29.03020 ¢), gives a simple, very near compromise between the different methods approaching 8.9.5.7.11.13.17.23 in this area.
 
143ed11 is extremely strong in the 5.7.8.9.11.13.17.23 subgroup.
 
All ratios in the 5.7.8.9.11.13.17.23 subgroup and 25-integer-limit are approximated in 143ed11 with less than 2.5 ¢ error.


According to the finite euler product with sigma = 1, the maxima in the 5.7.8.9.11.13.17.23 subgroup is about 41.33601-ED2 (or 29.03038 ¢).
It serves as a slightly stretched version of [[96ed5]].


The Tenney–Euclidean regular temperement in the 5.7.8.9.11.13.17.23 subgroup mapped with [⟨96 116 124 131 143 153 169 187]] gives 41.33650-ED2 (or 29.03005 ¢). The finite euler product with sigma = 1/2 gives about the same result.
=== Proposed name for tunings / temperaments in the ~29.03 ¢ area: Noctrino ===
'''Noctrino'''


143ed11, with its size of about 41.33627-ED2 (or 29.03020 ¢), gives a simple, very near compromise between the different methods approaching 5.7.8.9.11.13.17.23 in this area.
Etymology: No-octave no-tritave -> No-oct no-tri -> Noct trino -> Noctrino


== Intervals and approximation to JI ==
== Intervals and approximation to JI ==
 
{{Todo|inline=1|complete table|comment=Add the missing scale degrees.}}
{| class="wikitable sortable center-all right-2 left-3"
{| class="wikitable sortable center-all right-2 left-3"
|-
|-
! 143ed11<br>degree
! 143ed11<br>degree
! Cents
! Cents
! Ratios in the<br>5.7.8.9.11.13.17.23<br>subgroup
! Ratios in the<br>8.9.5.7.11.13.17.23<br>subgroup
! Error (abs, [[Cent|¢]])
! Error (abs, [[Cent|¢]])
! Error (rel, [[Relative cent|%]])
! Error (rel, [[Relative cent|%]])
Line 124: Line 121:
| 987.0
| 987.0
| [[23/13]]
| [[23/13]]
| -0.72
| -0.720
| -2.5
| -2.5
|-
|-
Line 172: Line 169:
| 1422.5
| 1422.5
| [[25/11]]
| [[25/11]]
| 1.17
| 1.170
| 4.0
| 4.0
|-
|-
Line 262: Line 259:
| 4151.3
| 4151.3
| [[11/1]]
| [[11/1]]
| 0.0
| 0.000
| 0.0
| 0.0
|-
|-
Line 286: Line 283:
| 5573.8
| 5573.8
| [[25/1]]
| [[25/1]]
| 1.17
| 1.170
| 4.0
| 4.0
|}
|}
Line 292: Line 289:
== Harmonics ==
== Harmonics ==


{{Harmonics in equal|143|11|1|prec=1|columns=15}}
{{Harmonics in equal|143|11|1|prec=1|columns=12}}
{{Harmonics in equal|143|11|1|prec=1|columns=9|start=16}}
{{Harmonics in equal|143|11|1|prec=1|columns=12|start=13}}
 


== Commas of the 5.7.8.9.11.13.17.23 subgroup tempered out in 143ed11 ==
== Commas of the 8.9.5.7.11.13.17.23 subgroup tempered out in 143ed11 ==


Commas with numerator < 100000 :
Commas with numerator < 100000 include:


[[392/391]], [[441/440]], [[576/575]], [[729/728]], [[833/832]], [[847/845]], [[936/935]], [[1001/1000]], [[1089/1088]], [[1127/1125]], [[1225/1224]], [[1288/1287]], [[1377/1375]], [[1449/1445]], [[1496/1495]], [[1575/1573]], [[1771/1768]], [[1863/1859]], [[2024/2023]], [[2025/2023]], [[2025/2024]], [[2200/2197]], [[2205/2197]], [[2277/2275]], [[2401/2392]], [[2601/2600]], [[2695/2691]], [[2875/2873]], [[2880/2873]], [[3128/3125]], [[3136/3125]], [[3185/3179]], [[3520/3519]], [[3584/3575]], [[3773/3757]], [[4096/4095]], [[4232/4225]], [[4235/4232]], [[4459/4455]], [[4761/4760]], [[4928/4913]], [[5103/5083]], [[5544/5525]], [[5632/5625]], [[5635/5632]], [[5824/5819]], [[5831/5819]], [[5832/5819]], [[5832/5831]], [[6561/6545]], [[6655/6647]], [[6656/6647]], [[6656/6655]], [[6664/6655]], [[6877/6875]], [[6885/6877]], [[7371/7360]], [[7497/7475]], [[7616/7605]], [[7744/7735]], [[7889/7865]], [[8019/8000]], [[8281/8280]], [[9000/8993]], [[9009/8993]], [[9317/9315]], [[9801/9775]], [[9801/9800]], [[10304/10285]], [[10647/10625]], [[10648/10625]], [[10648/10647]], [[11016/10985]], [[11016/11011]], [[11583/11560]], [[11781/11776]], [[11979/11960]], [[12005/11968]], [[12005/11979]], [[12167/12155]], [[12168/12167]], [[12376/12375]], [[12397/12393]], [[13041/13000]], [[13013/13005]], [[13689/13685]], [[13720/13689]], [[13923/13915]], [[14175/14144]], [[14161/14157]], [[14399/14375]], [[14400/14399]], [[14641/14625]], [[14651/14641]], [[14875/14872]], [[14904/14875]], [[16807/16731]], [[16807/16767]], [[17595/17576]], [[17920/17901]], [[18515/18496]], [[18515/18513]], [[19136/19125]], [[19208/19125]], [[20480/20449]], [[20493/20480]], [[21609/21505]], [[21879/21875]], [[21952/21879]], [[22295/22264]], [[22680/22627]], [[23040/23023]], [[24219/24200]], [[24696/24565]], [[25047/25000]], [[25025/25024]], [[25088/25047]], [[25515/25432]], [[25921/25857]], [[25921/25920]], [[26411/26325]], [[27209/27200]], [[27225/27209]], [[27783/27625]], [[28611/28561]], [[28672/28561]], [[28672/28611]], [[30613/30600]], [[30625/30613]], [[31185/31096]], [[31752/31603]], [[31752/31625]], [[32768/32725]], [[32805/32768]], [[33327/33275]], [[33327/33280]], [[33957/33800]], [[33856/33813]], [[33880/33813]], [[33957/33856]], [[34391/34375]], [[34391/34385]], [[34496/34385]], [[34496/34425]], [[34983/34969]], [[35000/34969]], [[35000/34983]], [[35640/35581]], [[36179/36125]], [[36288/36125]], [[36288/36179]], [[39325/39304]], [[39375/39304]], [[39445/39304]], [[40131/40000]], [[40733/40625]], [[40817/40625]], [[40824/40625]], [[41400/41327]], [[41472/41327]], [[41503/41400]], [[41472/41405]], [[41503/41472]], [[42840/42757]], [[42875/42757]], [[42875/42849]], [[43659/43520]], [[44275/44217]], [[45056/44965]], [[45927/45760]], [[46529/46475]], [[46648/46475]], [[46656/46475]], [[46656/46529]], [[46592/46575]], [[46648/46575]], [[46656/46585]], [[47320/47311]], [[47385/47311]], [[47432/47385]], [[49000/48841]], [[49005/48841]], [[49049/48875]], [[49049/48960]], [[50575/50531]], [[50625/50531]], [[50688/50531]], [[50688/50575]], [[51597/51425]], [[52488/52325]], [[53248/53125]], [[53361/53125]], [[53235/53176]], [[53361/53176]], [[53361/53248]], [[54080/54043]], [[55223/54925]], [[55223/55000]], [[55125/55016]], [[55223/55080]], [[56000/55913]], [[57024/56875]], [[57967/57800]], [[59049/58880]], [[60025/59823]], [[60025/59904]], [[60928/60835]], [[60984/60835]], [[61952/61893]], [[61965/61952]], [[62951/62920]], [[64000/63869]], [[64009/63869]], [[64152/63869]], [[64009/64000]], [[64141/64000]], [[65219/65000]], [[65219/65025]], [[66248/66125]], [[66339/66125]], [[67392/67375]], [[69632/69575]], [[71001/70720]], [[72128/71825]], [[72171/71825]], [[72072/71875]], [[72171/71875]], [[72171/71944]], [[72171/72128]], [[73125/73117]], [[73304/73125]], [[75712/75625]], [[75803/75625]], [[75816/75625]], [[75735/75712]], [[78336/78125]], [[78408/78125]], [[83655/83521]], [[83720/83521]], [[83835/83521]], [[83853/83521]], [[84035/83521]], [[83835/83776]], [[85169/85000]], [[85293/85000]], [[85184/85169]], [[85293/85169]], [[85293/85184]], [[86625/86411]], [[86751/86515]], [[86625/86528]], [[86751/86528]], [[86779/86528]], [[88209/87880]], [[88088/87975]], [[89600/89401]], [[91125/91091]], [[92664/92575]], [[94208/93925]], [[94325/94208]], [[95823/95744]], [[95832/95795]], [[97461/97336]], [[97405/97344]], [[98923/98865]], [[99127/98865]], [[99176/98865]], [[99225/98923]], [[99127/99000]]
[[392/391]], [[441/440]], [[576/575]], [[729/728]], [[833/832]], [[847/845]], [[936/935]], [[1001/1000]], [[1089/1088]], [[1127/1125]], [[1225/1224]], [[1288/1287]], [[1377/1375]], [[1449/1445]], [[1496/1495]], [[1575/1573]], [[1771/1768]], [[1863/1859]], [[2024/2023]], [[2025/2023]], [[2025/2024]], [[2200/2197]], [[2205/2197]], [[2277/2275]], [[2401/2392]], [[2601/2600]], [[2695/2691]], [[2875/2873]], [[2880/2873]], [[3128/3125]], [[3136/3125]], [[3185/3179]], [[3520/3519]], [[3584/3575]], [[3773/3757]], [[4096/4095]], [[4232/4225]], [[4235/4232]], [[4459/4455]], [[4761/4760]], [[4928/4913]], [[5103/5083]], [[5544/5525]], [[5632/5625]], [[5635/5632]], [[5824/5819]], [[5831/5819]], [[5832/5819]], [[5832/5831]], [[6561/6545]], [[6655/6647]], [[6656/6647]], [[6656/6655]], [[6664/6655]], [[6877/6875]], [[6885/6877]], [[7371/7360]], [[7497/7475]], [[7616/7605]], [[7744/7735]], [[7889/7865]], [[8019/8000]], [[8281/8280]], [[9000/8993]], [[9009/8993]], [[9317/9315]], [[9801/9775]], [[9801/9800]], [[10304/10285]], [[10647/10625]], [[10648/10625]], [[10648/10647]], [[11016/10985]], [[11016/11011]], [[11583/11560]], [[11781/11776]], [[11979/11960]], [[12005/11968]], [[12005/11979]], [[12167/12155]], [[12168/12167]], [[12376/12375]], [[12397/12393]], [[13041/13000]], [[13013/13005]], [[13689/13685]], [[13720/13689]], [[13923/13915]], [[14175/14144]], [[14161/14157]], [[14399/14375]], [[14400/14399]], [[14641/14625]], [[14651/14641]], [[14875/14872]], [[14904/14875]], [[16807/16731]], [[16807/16767]], [[17595/17576]], [[17920/17901]], [[18515/18496]], [[18515/18513]], [[19136/19125]], [[19208/19125]], [[20480/20449]], [[20493/20480]], [[21609/21505]], [[21879/21875]], [[21952/21879]], [[22295/22264]], [[22680/22627]], [[23040/23023]], [[24219/24200]], [[24696/24565]], [[25047/25000]], [[25025/25024]], [[25088/25047]], [[25515/25432]], [[25921/25857]], [[25921/25920]], [[26411/26325]], [[27209/27200]], [[27225/27209]], [[27783/27625]], [[28611/28561]], [[28672/28561]], [[28672/28611]], [[30613/30600]], [[30625/30613]], [[31185/31096]], [[31752/31603]], [[31752/31625]], [[32768/32725]], [[32805/32768]], [[33327/33275]], [[33327/33280]], [[33957/33800]], [[33856/33813]], [[33880/33813]], [[33957/33856]], [[34391/34375]], [[34391/34385]], [[34496/34385]], [[34496/34425]], [[34983/34969]], [[35000/34969]], [[35000/34983]], [[35640/35581]], [[36179/36125]], [[36288/36125]], [[36288/36179]], [[39325/39304]], [[39375/39304]], [[39445/39304]], [[40131/40000]], [[40733/40625]], [[40817/40625]], [[40824/40625]], [[41400/41327]], [[41472/41327]], [[41503/41400]], [[41472/41405]], [[41503/41472]], [[42840/42757]], [[42875/42757]], [[42875/42849]], [[43659/43520]], [[44275/44217]], [[45056/44965]], [[45927/45760]], [[46529/46475]], [[46648/46475]], [[46656/46475]], [[46656/46529]], [[46592/46575]], [[46648/46575]], [[46656/46585]], [[47320/47311]], [[47385/47311]], [[47432/47385]], [[49000/48841]], [[49005/48841]], [[49049/48875]], [[49049/48960]], [[50575/50531]], [[50625/50531]], [[50688/50531]], [[50688/50575]], [[51597/51425]], [[52488/52325]], [[53248/53125]], [[53361/53125]], [[53235/53176]], [[53361/53176]], [[53361/53248]], [[54080/54043]], [[55223/54925]], [[55223/55000]], [[55125/55016]], [[55223/55080]], [[56000/55913]], [[57024/56875]], [[57967/57800]], [[59049/58880]], [[60025/59823]], [[60025/59904]], [[60928/60835]], [[60984/60835]], [[61952/61893]], [[61965/61952]], [[62951/62920]], [[64000/63869]], [[64009/63869]], [[64152/63869]], [[64009/64000]], [[64141/64000]], [[65219/65000]], [[65219/65025]], [[66248/66125]], [[66339/66125]], [[67392/67375]], [[69632/69575]], [[71001/70720]], [[72128/71825]], [[72171/71825]], [[72072/71875]], [[72171/71875]], [[72171/71944]], [[72171/72128]], [[73125/73117]], [[73304/73125]], [[75712/75625]], [[75803/75625]], [[75816/75625]], [[75735/75712]], [[78336/78125]], [[78408/78125]], [[83655/83521]], [[83720/83521]], [[83835/83521]], [[83853/83521]], [[84035/83521]], [[83835/83776]], [[85169/85000]], [[85293/85000]], [[85184/85169]], [[85293/85169]], [[85293/85184]], [[86625/86411]], [[86751/86515]], [[86625/86528]], [[86751/86528]], [[86779/86528]], [[88209/87880]], [[88088/87975]], [[89600/89401]], [[91125/91091]], [[92664/92575]], [[94208/93925]], [[94325/94208]], [[95823/95744]], [[95832/95795]], [[97461/97336]], [[97405/97344]], [[98923/98865]], [[99127/98865]], [[99176/98865]], [[99225/98923]], [[99127/99000]]

Latest revision as of 14:34, 29 April 2026

← 142ed11 143ed11 144ed11 →
Prime factorization 11 × 13
Step size 29.0302 ¢ 
Octave 41\143ed11 (1190.24 ¢)
Twelfth 66\143ed11 (1915.99 ¢) (→ 6\13ed11)
Consistency limit 2
Distinct consistency limit 2

143 equal divisions of the 11th harmonic (abbreviated 143ed11) is a nonoctave tuning system that divides the interval of 11/1 into 143 equal parts of about 29 ¢ each. Each step represents a frequency ratio of 111/143, or the 143rd root of 11.

Theory

143ed11 is extremely strong in the 8.9.5.7.11.13.17.23 subgroup. All ratios in the 8.9.5.7.11.13.17.23 subgroup and 25-integer-limit are approximated in 143ed11 with less than 2.5 ¢ error. According to the finite Euler product with sigma = 1, the maxima in the 8.9.5.7.11.13.17.23 subgroup is about 41.33601-ED2 (or 29.03038 ¢). The Tenney–Euclidean regular temperement in the 8.9.5.7.11.13.17.23 subgroup mapped with [⟨124 131 96 116 143 153 169 187]] gives 41.33650-ED2 (or 29.03004 ¢). The finite Euler product with sigma = 1/2 gives about the same result. 143ed11, with its size of about 41.33627-ED2 (or 29.03020 ¢), gives a simple, very near compromise between the different methods approaching 8.9.5.7.11.13.17.23 in this area.

It serves as a slightly stretched version of 96ed5.

Proposed name for tunings / temperaments in the ~29.03 ¢ area: Noctrino

Noctrino

Etymology: No-octave no-tritave -> No-oct no-tri -> Noct trino -> Noctrino

Intervals and approximation to JI

Todo: complete table

Add the missing scale degrees.

143ed11
degree 		Cents Ratios in the
8.9.5.7.11.13.17.23
subgroup 		Error (abs, ¢) Error (rel, %)
5 145.2 25/23 0.798 2.7
7 203.2 9/8 -0.699 -2.4
8 232.2 8/7 1.067 3.7
10 290.3 13/11 1.092 3.8
12 348.4 11/9 0.954 3.3
15 435.5 9/7 0.369 1.3
16 464.5 17/13 0.055 0.2
18 522.5 23/17 -0.775 -2.7
19 551.6 11/8 0.256 0.9
20 580.6 7/5 -1.908 -6.6
22 638.7 13/9 2.047 7.1
23 667.7 25/17 0.022 0.1
26 754.8 17/11 1.148 4.0
27 783.8 11/7 1.323 4.6
28 812.8 8/5 -0.841 -2.9
29 841.9 13/8 1.348 4.6
34 987.0 23/13 -0.720 -2.5
35 1016.1 9/5 -1.539 -5.3
37 1074.1 13/7 2.415 8.3
38 1103.1 17/9 2.102 7.2
39 1132.2 25/13 0.078 0.3
44 1277.3 23/11 0.372 1.3
45 1306.4 17/8 1.403 4.8
47 1364.4 11/5 -0.585 -2.0
49 1422.5 25/11 1.170 4.0
53 1538.6 17/7 2.471 8.5
56 1625.7 23/9 1.327 4.6
57 1654.7 13/5 0.507 1.7
61 1770.8 25/9 2.124 7.3
63 1828.9 23/8 0.628 2.2
68 1974.1 25/8 1.426 4.9
71 2061.1 23/7 1.695 5.8
73 2119.2 17/5 0.563 1.9
76 2206.3 25/7 2.493 8.6
91 2641.7 23/5 -0.213 -0.7
96 2786.9 5/1 0.585 2.0
116 3367.5 7/1 -1.323 -4.6
124 3599.7 8/1 -0.256 -0.9
131 3803.0 9/1 -0.954 -3.3
143 4151.3 11/1 0.000 0.0
153 4441.6 13/1 1.092 3.8
169 4906.1 17/1 1.148 4.0
187 5428.6 23/1 0.372 1.3
192 5573.8 25/1 1.170 4.0

Harmonics

Approximation of harmonics in 143ed11
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) -9.8 +14.0 +9.5 +0.6 +4.3 -1.3 -0.3 -1.0 -9.2 +0.0 -5.5 +1.1
Relative (%) -33.6 +48.4 +32.7 +2.0 +14.7 -4.6 -0.9 -3.3 -31.6 +0.0 -18.9 +3.8
Steps
(reduced) 		41
(41) 		66
(66) 		83
(83) 		96
(96) 		107
(107) 		116
(116) 		124
(124) 		131
(131) 		137
(137) 		143
(0) 		148
(5) 		153
(10)
Approximation of harmonics in 143ed11
Harmonic 14 15 16 17 18 19 20 21 22 23 24 25
Error Absolute (¢) -11.1 -14.4 -10.0 +1.1 -10.7 +11.8 +10.1 +12.7 -9.8 +0.4 +13.8 +1.2
Relative (%) -38.2 -49.6 -34.5 +4.0 -36.9 +40.7 +34.8 +43.8 -33.6 +1.3 +47.5 +4.0
Steps
(reduced) 		157
(14) 		161
(18) 		165
(22) 		169
(26) 		172
(29) 		176
(33) 		179
(36) 		182
(39) 		184
(41) 		187
(44) 		190
(47) 		192
(49)

Commas of the 8.9.5.7.11.13.17.23 subgroup tempered out in 143ed11

Commas with numerator < 100000 include:

392/391, 441/440, 576/575, 729/728, 833/832, 847/845, 936/935, 1001/1000, 1089/1088, 1127/1125, 1225/1224, 1288/1287, 1377/1375, 1449/1445, 1496/1495, 1575/1573, 1771/1768, 1863/1859, 2024/2023, 2025/2023, 2025/2024, 2200/2197, 2205/2197, 2277/2275, 2401/2392, 2601/2600, 2695/2691, 2875/2873, 2880/2873, 3128/3125, 3136/3125, 3185/3179, 3520/3519, 3584/3575, 3773/3757, 4096/4095, 4232/4225, 4235/4232, 4459/4455, 4761/4760, 4928/4913, 5103/5083, 5544/5525, 5632/5625, 5635/5632, 5824/5819, 5831/5819, 5832/5819, 5832/5831, 6561/6545, 6655/6647, 6656/6647, 6656/6655, 6664/6655, 6877/6875, 6885/6877, 7371/7360, 7497/7475, 7616/7605, 7744/7735, 7889/7865, 8019/8000, 8281/8280, 9000/8993, 9009/8993, 9317/9315, 9801/9775, 9801/9800, 10304/10285, 10647/10625, 10648/10625, 10648/10647, 11016/10985, 11016/11011, 11583/11560, 11781/11776, 11979/11960, 12005/11968, 12005/11979, 12167/12155, 12168/12167, 12376/12375, 12397/12393, 13041/13000, 13013/13005, 13689/13685, 13720/13689, 13923/13915, 14175/14144, 14161/14157, 14399/14375, 14400/14399, 14641/14625, 14651/14641, 14875/14872, 14904/14875, 16807/16731, 16807/16767, 17595/17576, 17920/17901, 18515/18496, 18515/18513, 19136/19125, 19208/19125, 20480/20449, 20493/20480, 21609/21505, 21879/21875, 21952/21879, 22295/22264, 22680/22627, 23040/23023, 24219/24200, 24696/24565, 25047/25000, 25025/25024, 25088/25047, 25515/25432, 25921/25857, 25921/25920, 26411/26325, 27209/27200, 27225/27209, 27783/27625, 28611/28561, 28672/28561, 28672/28611, 30613/30600, 30625/30613, 31185/31096, 31752/31603, 31752/31625, 32768/32725, 32805/32768, 33327/33275, 33327/33280, 33957/33800, 33856/33813, 33880/33813, 33957/33856, 34391/34375, 34391/34385, 34496/34385, 34496/34425, 34983/34969, 35000/34969, 35000/34983, 35640/35581, 36179/36125, 36288/36125, 36288/36179, 39325/39304, 39375/39304, 39445/39304, 40131/40000, 40733/40625, 40817/40625, 40824/40625, 41400/41327, 41472/41327, 41503/41400, 41472/41405, 41503/41472, 42840/42757, 42875/42757, 42875/42849, 43659/43520, 44275/44217, 45056/44965, 45927/45760, 46529/46475, 46648/46475, 46656/46475, 46656/46529, 46592/46575, 46648/46575, 46656/46585, 47320/47311, 47385/47311, 47432/47385, 49000/48841, 49005/48841, 49049/48875, 49049/48960, 50575/50531, 50625/50531, 50688/50531, 50688/50575, 51597/51425, 52488/52325, 53248/53125, 53361/53125, 53235/53176, 53361/53176, 53361/53248, 54080/54043, 55223/54925, 55223/55000, 55125/55016, 55223/55080, 56000/55913, 57024/56875, 57967/57800, 59049/58880, 60025/59823, 60025/59904, 60928/60835, 60984/60835, 61952/61893, 61965/61952, 62951/62920, 64000/63869, 64009/63869, 64152/63869, 64009/64000, 64141/64000, 65219/65000, 65219/65025, 66248/66125, 66339/66125, 67392/67375, 69632/69575, 71001/70720, 72128/71825, 72171/71825, 72072/71875, 72171/71875, 72171/71944, 72171/72128, 73125/73117, 73304/73125, 75712/75625, 75803/75625, 75816/75625, 75735/75712, 78336/78125, 78408/78125, 83655/83521, 83720/83521, 83835/83521, 83853/83521, 84035/83521, 83835/83776, 85169/85000, 85293/85000, 85184/85169, 85293/85169, 85293/85184, 86625/86411, 86751/86515, 86625/86528, 86751/86528, 86779/86528, 88209/87880, 88088/87975, 89600/89401, 91125/91091, 92664/92575, 94208/93925, 94325/94208, 95823/95744, 95832/95795, 97461/97336, 97405/97344, 98923/98865, 99127/98865, 99176/98865, 99225/98923, 99127/99000

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