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Created page with "'''156edo''' is the equal division of the octave into 156 parts of 7.6923 cents each. It tempers out 531441/524288 (pythagorean comma) and 1220703125/1207959552 (diton..."
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[[Category:Edo]]
[[Category:Edo]]
={{PAGENAME}}=
Welcome to {{PAGENAME}}
=={{PAGENAME}} = [[12edo]] × [[13edo]]==
Distinctively interesting choice for an edo, due to its divisibility by both 12 and 13. This means it can be used to play [[12edo]] music and [[13edo]] music at the same time, using the [[K/N|156/13 and 156/12]] vals respectively.
==7.692==
{{PAGENAME}} has a step size of {{#expr: 1200.0/156.0}} cents. Microtonal enthusiasts might notice it seems close to the [[225/224]] ratio, but it isn't in the patent val, because {{PAGENAME}} tempers out [[225/224]]. The edo step size closest to [[225/224]], taking into account the primes that compose it, is in [[171edo]]. You have to use the [[K*N|2*156]] val, sacrificing 3 for a new 9, to make this approximation come true. It is up to the microtonalist to decide whether this tradeoff is worth it.
==Selected just intervals by error==
The following table shows how [[15-odd-limit|some prominent just intervals]] are represented in 156edo (ordered by absolute error).
{| class="wikitable"
|-
| | '''Interval, complement'''
| | '''Error (abs., in [[cent]]s)'''
|-
| style="text-align:center;" | [[13/12]], [[24/13]]
| style="text-align:center;" | 0.111
|-
| style="text-align:center;" | [[6/5]], [[5/3]]
| style="text-align:center;" | 0.257
|-
| style="text-align:center;" | [[13/10]], [[20/13]]
| style="text-align:center;" | 0.368
|-
| style="text-align:center;" | [[8/7]], [[7/4]]
| style="text-align:center;" | 0.405
|-
| style="text-align:center;" | [[15/13]], [[26/15]]
| style="text-align:center;" | 1.587
|-
| style="text-align:center;" | [[5/4]], [[8/5]]
| style="text-align:center;" | 1.698
|-
| style="text-align:center;" | [[18/13]], [[13/9]]
| style="text-align:center;" | 1.844
|-
| style="text-align:center;" | [[4/3]], [[3/2]]
| style="text-align:center;" | 1.955
|-
| style="text-align:center;" | [[16/13]], [[13/8]]
| style="text-align:center;" | 2.066
|-
| style="text-align:center;" | [[7/5]], [[10/7]]
| style="text-align:center;" | 2.103
|-
| style="text-align:center;" | [[14/11]], [[11/7]]
| style="text-align:center;" | 2.123
|-
| style="text-align:center;" | [[10/9]], [[9/5]]
| style="text-align:center;" | 2.212
|-
| style="text-align:center;" | [[7/6]], [[12/7]]
| style="text-align:center;" | 2.36
|-
| style="text-align:center;" | [[14/13]], [[13/7]]
| style="text-align:center;" | 2.471
|-
| style="text-align:center;" | [[11/8]], [[16/11]]
| style="text-align:center;" | 2.528
|-
| style="text-align:center;" | [[16/15]], [[15/8]]
| style="text-align:center;" | 3.653
|-
| style="text-align:center;" | [[9/8]], [[16/9]]
| style="text-align:center;" | 3.91
|-
| style="text-align:center;" | [[15/14]], [[28/15]]
| style="text-align:center;" | 4.058
|-
| style="text-align:center;" | [[11/10]], [[20/11]]
| style="text-align:center;" | 4.227
|-
| style="text-align:center;" | [[9/7]], [[14/9]]
| style="text-align:center;" | 4.315
|-
| style="text-align:center;" | [[12/11]], [[11/6]]
| style="text-align:center;" | 4.483
|-
| style="text-align:center;" | [[13/11]], [[22/13]]
| style="text-align:center;" | 4.594
|-
| style="text-align:center;" | [[15/11]], [[22/15]]
| style="text-align:center;" | 6.182
|-
| style="text-align:center;" | [[11/9]], [[18/11]]
| style="text-align:center;" | 6.438
|}
==Table of {{PAGENAME}} intervals==
{| class="wikitable"
|-
| | Step
| | Five limit
| | Seven limit
| | Eleven limit
| | Thirteen limit
|-
| | 1
| | 15625/15552
| | 1029/1024
| | 242/243
| | 144/143
|-
| | 2
| | 81/80
| | 81/80
| | 81/80
| | 78/77
|-
| | 3
| | 3125/3072
| | 245/243
| | 121/120
| | 65/64
|-
| | 4
| | 2048/2025
| | 50/49
| | 45/44
| | 45/44
|-
| | 5
| | 16875/16384
| | 49/48
| | 49/48
| | 49/48
|-
| | 6
| | 128/125
| | 36/35
| | 36/35
| | 36/35
|-
| | 7
| | 250/243
| | 250/243
| | 33/32
| | 33/32
|-
| | 8
| | 648/625
| | 648/625
| | 80/77
| | 27/26
|-
| | 9
| | 25/24
| | 25/24
| | 25/24
| | 25/24
|-
| | 10
| | 6561/6250
| | 256/245
| | 81/77
| | 81/77
|-
| | 11
| | 135/128
| | 21/20
| | 21/20
| | 21/20
|-
| | 12
| | 16384/15625
| | 729/686
| | 128/121
| | 96/91
|-
| | 13
| | 256/243
| | 200/189
| | 35/33
| | 35/33
|-
| | 14
| | 62500/59049
| | 343/324
| | 343/324
| | 143/135
|-
| | 15
| | 16/15
| | 15/14
| | 15/14
| | 15/14
|-
| | 16
| | 3125/2916
| | 343/320
| | 77/72
| | 77/72
|-
| | 17
| | 27/25
| | 27/25
| | 27/25
| | 14/13
|-
| | 18
| | 625/576
| | 175/162
| | 121/112
| | 13/12
|-
| | 19
| | 2187/2000
| | 160/147
| | 12/11
| | 12/11
|-
| | 20
| | 1125/1024
| | 35/32
| | 35/32
| | 35/32
|-
| | 21
| | 2048/1875
| | 54/49
| | 54/49
| | 54/49
|-
| | 22
| | 800/729
| | 441/400
| | 11/10
| | 11/10
|-
| | 23
| | 3456/3125
| | 972/875
| | 135/121
| | 72/65
|-
| | 24
| | 10/9
| | 10/9
| | 10/9
| | 10/9
|-
| | 25
| | 17496/15625
| | 384/343
| | 384/343
| | 143/128
|-
| | 26
| | 9/8
| | 9/8
| | 9/8
| | 9/8
|-
| | 27
| | 15625/13824
| | 1944/1715
| | 121/108
| | 91/81
|-
| | 28
| | 729/640
| | 500/441
| | 25/22
| | 25/22
|-
| | 29
| | 9375/8192
| | 245/216
| | 245/216
| | 91/80
|-
| | 30
| | 256/225
| | 8/7
| | 8/7
| | 8/7
|-
| | 31
| | 2500/2187
| | 147/128
| | 55/48
| | 55/48
|-
| | 32
| | 144/125
| | 81/70
| | 81/70
| | 15/13
|-
| | 33
| | 125/108
| | 125/108
| | 121/105
| | 52/45
|-
| | 34
| | 729/625
| | 400/343
| | 64/55
| | 64/55
|-
| | 35
| | 75/64
| | 7/6
| | 7/6
| | 7/6
|-
| | 36
| | 32768/28125
| | 288/245
| | 288/245
| | 168/143
|-
| | 37
| | 1215/1024
| | 147/125
| | 33/28
| | 13/11
|-
| | 38
| | 18432/15625
| | 1458/1225
| | 144/121
| | 108/91
|-
| | 39
| | 32/27
| | 25/21
| | 25/21
| | 25/21
|-
| | 40
| | 15625/13122
| | 343/288
| | 343/288
| | 143/120
|-
| | 41
| | 6/5
| | 6/5
| | 6/5
| | 6/5
|-
| | 42
| | 3125/2592
| | 875/729
| | 77/64
| | 65/54
|-
| | 43
| | 243/200
| | 243/200
| | 40/33
| | 40/33
|-
| | 44
| | 625/512
| | 98/81
| | 98/81
| | 39/32
|-
| | 45
| | 4096/3375
| | 60/49
| | 27/22
| | 27/22
|-
| | 46
| | 8000/6561
| | 49/40
| | 11/9
| | 11/9
|-
| | 47
| | 768/625
| | 216/175
| | 150/121
| | 16/13
|-
| | 48
| | 100/81
| | 100/81
| | 99/80
| | 26/21
|-
| | 49
| | 3888/3125
| | 1280/1029
| | 96/77
| | 81/65
|-
| | 50
| | 5/4
| | 5/4
| | 5/4
| | 5/4
|-
| | 51
| | 19683/15625
| | 432/343
| | 432/343
| | 169/135
|-
| | 52
| | 81/64
| | 63/50
| | 44/35
| | 44/35
|-
| | 53
| | 15625/12288
| | 1225/972
| | 121/96
| | 91/72
|-
| | 54
| | 512/405
| | 80/63
| | 14/11
| | 14/11
|-
| | 55
| | 25000/19683
| | 245/192
| | 245/192
| | 143/112
|-
| | 56
| | 32/25
| | 9/7
| | 9/7
| | 9/7
|-
| | 57
| | 625/486
| | 625/486
| | 77/60
| | 77/60
|-
| | 58
| | 162/125
| | 162/125
| | 100/77
| | 84/65
|-
| | 59
| | 125/96
| | 35/27
| | 35/27
| | 13/10
|-
| | 60
| | 6561/5000
| | 64/49
| | 64/49
| | 64/49
|-
| | 61
| | 675/512
| | 21/16
| | 21/16
| | 21/16
|-
| | 62
| | 4096/3125
| | 324/245
| | 160/121
| | 120/91
|-
| | 63
| | 320/243
| | 250/189
| | 33/25
| | 33/25
|-
| | 64
| | 20736/15625
| | 1715/1296
| | 162/121
| | 143/108
|-
| | 65
| | 4/3
| | 4/3
| | 4/3
| | 4/3
|-
| | 66
| | 15625/11664
| | 343/256
| | 343/256
| | 169/126
|-
| | 67
| | 27/20
| | 27/20
| | 27/20
| | 27/20
|-
| | 68
| | 3125/2304
| | 875/648
| | 121/90
| | 65/48
|-
| | 69
| | 2187/1600
| | 200/147
| | 15/11
| | 15/11
|-
| | 70
| | 5625/4096
| | 49/36
| | 49/36
| | 49/36
|-
| | 71
| | 512/375
| | 48/35
| | 48/35
| | 48/35
|-
| | 72
| | 1000/729
| | 343/250
| | 11/8
| | 11/8
|-
| | 73
| | 864/625
| | 243/175
| | 168/121
| | 18/13
|-
| | 74
| | 25/18
| | 25/18
| | 25/18
| | 25/18
|-
| | 75
| | 4374/3125
| | 480/343
| | 108/77
| | 108/77
|-
| | 76
| | 45/32
| | 7/5
| | 7/5
| | 7/5
|-
| | 77
| | 65536/46875
| | 486/343
| | 486/343
| | 128/91
|-
| | 78
| | 729/512
| | 567/400
| | 99/70
| | 55/39
|-
| | 79
| | 46875/32768
| | 343/243
| | 343/243
| | 91/64
|-
| | 80
| | 64/45
| | 10/7
| | 10/7
| | 10/7
|-
| | 81
| | 3125/2187
| | 343/240
| | 77/54
| | 77/54
|-
| | 82
| | 36/25
| | 36/25
| | 36/25
| | 36/25
|-
| | 83
| | 625/432
| | 350/243
| | 121/84
| | 13/9
|-
| | 84
| | 729/500
| | 500/343
| | 16/11
| | 16/11
|-
| | 85
| | 375/256
| | 35/24
| | 35/24
| | 35/24
|-
| | 86
| | 8192/5625
| | 72/49
| | 72/49
| | 72/49
|-
| | 87
| | 3200/2187
| | 147/100
| | 22/15
| | 22/15
|-
| | 88
| | 4608/3125
| | 729/490
| | 180/121
| | 96/65
|-
| | 89
| | 40/27
| | 40/27
| | 40/27
| | 40/27
|-
| | 90
| | 23328/15625
| | 512/343
| | 512/343
| | 143/96
|-
| | 91
| | 3/2
| | 3/2
| | 3/2
| | 3/2
|-
| | 92
| | 15625/10368
| | 2401/1600
| | 121/81
| | 121/81
|-
| | 93
| | 243/160
| | 189/125
| | 50/33
| | 50/33
|-
| | 94
| | 3125/2048
| | 245/162
| | 121/80
| | 91/60
|-
| | 95
| | 1024/675
| | 32/21
| | 32/21
| | 32/21
|-
| | 96
| | 10000/6561
| | 49/32
| | 49/32
| | 49/32
|-
| | 97
| | 192/125
| | 54/35
| | 54/35
| | 20/13
|-
| | 98
| | 125/81
| | 125/81
| | 77/50
| | 65/42
|-
| | 99
| | 972/625
| | 972/625
| | 120/77
| | 81/52
|-
| | 100
| | 25/16
| | 14/9
| | 14/9
| | 14/9
|-
| | 101
| | 19683/12500
| | 384/245
| | 243/154
| | 169/108
|-
| | 102
| | 405/256
| | 63/40
| | 11/7
| | 11/7
|-
| | 103
| | 24576/15625
| | 1944/1225
| | 192/121
| | 144/91
|-
| | 104
| | 128/81
| | 100/63
| | 35/22
| | 35/22
|-
| | 105
| | 31250/19683
| | 343/216
| | 343/216
| | 143/90
|-
| | 106
| | 8/5
| | 8/5
| | 8/5
| | 8/5
|-
| | 107
| | 3125/1944
| | 1029/640
| | 77/48
| | 77/48
|-
| | 108
| | 81/50
| | 81/50
| | 81/50
| | 21/13
|-
| | 109
| | 625/384
| | 175/108
| | 121/75
| | 13/8
|-
| | 110
| | 6561/4000
| | 80/49
| | 18/11
| | 18/11
|-
| | 111
| | 3375/2048
| | 49/30
| | 44/27
| | 44/27
|-
| | 112
| | 1024/625
| | 81/49
| | 81/49
| | 64/39
|-
| | 113
| | 400/243
| | 400/243
| | 33/20
| | 33/20
|-
| | 114
| | 5184/3125
| | 1458/875
| | 128/77
| | 108/65
|-
| | 115
| | 5/3
| | 5/3
| | 5/3
| | 5/3
|-
| | 116
| | 26244/15625
| | 576/343
| | 539/324
| | 240/143
|-
| | 117
| | 27/16
| | 27/16
| | 27/16
| | 27/16
|-
| | 118
| | 15625/9216
| | 1225/729
| | 121/72
| | 91/54
|-
| | 119
| | 2048/1215
| | 250/147
| | 56/33
| | 22/13
|-
| | 120
| | 28125/16384
| | 245/144
| | 245/144
| | 143/84
|-
| | 121
| | 128/75
| | 12/7
| | 12/7
| | 12/7
|-
| | 122
| | 1250/729
| | 343/200
| | 55/32
| | 55/32
|-
| | 123
| | 216/125
| | 216/125
| | 210/121
| | 45/26
|-
| | 124
| | 125/72
| | 125/72
| | 121/70
| | 26/15
|-
| | 125
| | 2187/1250
| | 256/147
| | 96/55
| | 96/55
|-
| | 126
| | 225/128
| | 7/4
| | 7/4
| | 7/4
|-
| | 127
| | 16384/9375
| | 432/245
| | 432/245
| | 160/91
|-
| | 128
| | 1280/729
| | 441/250
| | 44/25
| | 39/22
|-
| | 129
| | 27648/15625
| | 1715/972
| | 216/121
| | 143/81
|-
| | 130
| | 16/9
| | 16/9
| | 16/9
| | 16/9
|-
| | 131
| | 15625/8748
| | 343/192
| | 343/192
| | 143/80
|-
| | 132
| | 9/5
| | 9/5
| | 9/5
| | 9/5
|-
| | 133
| | 3125/1728
| | 875/486
| | 231/128
| | 65/36
|-
| | 134
| | 729/400
| | 625/343
| | 20/11
| | 20/11
|-
| | 135
| | 1875/1024
| | 49/27
| | 49/27
| | 49/27
|-
| | 136
| | 2048/1125
| | 64/35
| | 64/35
| | 64/35
|-
| | 137
| | 4000/2187
| | 147/80
| | 11/6
| | 11/6
|-
| | 138
| | 1152/625
| | 324/175
| | 224/121
| | 24/13
|-
| | 139
| | 50/27
| | 50/27
| | 50/27
| | 13/7
|-
| | 140
| | 5832/3125
| | 640/343
| | 144/77
| | 144/77
|-
| | 141
| | 15/8
| | 15/8
| | 15/8
| | 15/8
|-
| | 142
| | 59049/31250
| | 648/343
| | 539/288
| | 169/90
|-
| | 143
| | 243/128
| | 189/100
| | 66/35
| | 49/26
|-
| | 144
| | 15625/8192
| | 1225/648
| | 121/64
| | 91/48
|-
| | 145
| | 256/135
| | 40/21
| | 21/11
| | 21/11
|-
| | 146
| | 12500/6561
| | 245/128
| | 154/81
| | 143/75
|-
| | 147
| | 48/25
| | 27/14
| | 27/14
| | 25/13
|-
| | 148
| | 625/324
| | 625/324
| | 77/40
| | 52/27
|-
| | 149
| | 243/125
| | 243/125
| | 64/33
| | 64/33
|-
| | 150
| | 125/64
| | 35/18
| | 35/18
| | 35/18
|-
| | 151
| | 19683/10000
| | 96/49
| | 96/49
| | 96/49
|-
| | 152
| | 2025/1024
| | 49/25
| | 49/25
| | 49/25
|-
| | 153
| | 6144/3125
| | 486/245
| | 240/121
| | 128/65
|-
| | 154
| | 160/81
| | 125/63
| | 99/50
| | 77/39
|-
| | 155
| | 31104/15625
| | 1715/864
| | 243/121
| | 143/72
|-
| | 156
| | 2/1
| | 2/1
| | 2/1
| | 2/1
|}

Revision as of 15:43, 17 July 2020

156edo is the equal division of the octave into 156 parts of 7.6923 cents each. It tempers out 531441/524288 (pythagorean comma) and 1220703125/1207959552 (ditonic comma) in the 5-limit, as well as 1224440064/1220703125 (parakleisma); 225/224, 250047/250000, and 589824/588245 in the 7-limit. Using the patent val, it tempers out 441/440, 1375/1372, 4375/4356, and 65536/65219 in the 11-limit; 351/350, 364/363, 625/624, 1625/1617, and 13122/13013 in the 13-limit. Using the 156e val, it tempers out 385/384, 540/539, 1331/1323, and 78408/78125 in the 11-limit; 351/350, 625/624, 847/845, and 1001/1000 in the 13-limit.

156edo

Welcome to 156edo

156edo = 12edo × 13edo

Distinctively interesting choice for an edo, due to its divisibility by both 12 and 13. This means it can be used to play 12edo music and 13edo music at the same time, using the 156/13 and 156/12 vals respectively.

7.692

156edo has a step size of 7.6923076923077 cents. Microtonal enthusiasts might notice it seems close to the 225/224 ratio, but it isn't in the patent val, because 156edo tempers out 225/224. The edo step size closest to 225/224, taking into account the primes that compose it, is in 171edo. You have to use the 2*156 val, sacrificing 3 for a new 9, to make this approximation come true. It is up to the microtonalist to decide whether this tradeoff is worth it.

Selected just intervals by error

The following table shows how some prominent just intervals are represented in 156edo (ordered by absolute error).

Interval, complement Error (abs., in cents)
13/12, 24/13 0.111
6/5, 5/3 0.257
13/10, 20/13 0.368
8/7, 7/4 0.405
15/13, 26/15 1.587
5/4, 8/5 1.698
18/13, 13/9 1.844
4/3, 3/2 1.955
16/13, 13/8 2.066
7/5, 10/7 2.103
14/11, 11/7 2.123
10/9, 9/5 2.212
7/6, 12/7 2.36
14/13, 13/7 2.471
11/8, 16/11 2.528
16/15, 15/8 3.653
9/8, 16/9 3.91
15/14, 28/15 4.058
11/10, 20/11 4.227
9/7, 14/9 4.315
12/11, 11/6 4.483
13/11, 22/13 4.594
15/11, 22/15 6.182
11/9, 18/11 6.438

Table of 156edo intervals

Step Five limit Seven limit Eleven limit Thirteen limit
1 15625/15552 1029/1024 242/243 144/143
2 81/80 81/80 81/80 78/77
3 3125/3072 245/243 121/120 65/64
4 2048/2025 50/49 45/44 45/44
5 16875/16384 49/48 49/48 49/48
6 128/125 36/35 36/35 36/35
7 250/243 250/243 33/32 33/32
8 648/625 648/625 80/77 27/26
9 25/24 25/24 25/24 25/24
10 6561/6250 256/245 81/77 81/77
11 135/128 21/20 21/20 21/20
12 16384/15625 729/686 128/121 96/91
13 256/243 200/189 35/33 35/33
14 62500/59049 343/324 343/324 143/135
15 16/15 15/14 15/14 15/14
16 3125/2916 343/320 77/72 77/72
17 27/25 27/25 27/25 14/13
18 625/576 175/162 121/112 13/12
19 2187/2000 160/147 12/11 12/11
20 1125/1024 35/32 35/32 35/32
21 2048/1875 54/49 54/49 54/49
22 800/729 441/400 11/10 11/10
23 3456/3125 972/875 135/121 72/65
24 10/9 10/9 10/9 10/9
25 17496/15625 384/343 384/343 143/128
26 9/8 9/8 9/8 9/8
27 15625/13824 1944/1715 121/108 91/81
28 729/640 500/441 25/22 25/22
29 9375/8192 245/216 245/216 91/80
30 256/225 8/7 8/7 8/7
31 2500/2187 147/128 55/48 55/48
32 144/125 81/70 81/70 15/13
33 125/108 125/108 121/105 52/45
34 729/625 400/343 64/55 64/55
35 75/64 7/6 7/6 7/6
36 32768/28125 288/245 288/245 168/143
37 1215/1024 147/125 33/28 13/11
38 18432/15625 1458/1225 144/121 108/91
39 32/27 25/21 25/21 25/21
40 15625/13122 343/288 343/288 143/120
41 6/5 6/5 6/5 6/5
42 3125/2592 875/729 77/64 65/54
43 243/200 243/200 40/33 40/33
44 625/512 98/81 98/81 39/32
45 4096/3375 60/49 27/22 27/22
46 8000/6561 49/40 11/9 11/9
47 768/625 216/175 150/121 16/13
48 100/81 100/81 99/80 26/21
49 3888/3125 1280/1029 96/77 81/65
50 5/4 5/4 5/4 5/4
51 19683/15625 432/343 432/343 169/135
52 81/64 63/50 44/35 44/35
53 15625/12288 1225/972 121/96 91/72
54 512/405 80/63 14/11 14/11
55 25000/19683 245/192 245/192 143/112
56 32/25 9/7 9/7 9/7
57 625/486 625/486 77/60 77/60
58 162/125 162/125 100/77 84/65
59 125/96 35/27 35/27 13/10
60 6561/5000 64/49 64/49 64/49
61 675/512 21/16 21/16 21/16
62 4096/3125 324/245 160/121 120/91
63 320/243 250/189 33/25 33/25
64 20736/15625 1715/1296 162/121 143/108
65 4/3 4/3 4/3 4/3
66 15625/11664 343/256 343/256 169/126
67 27/20 27/20 27/20 27/20
68 3125/2304 875/648 121/90 65/48
69 2187/1600 200/147 15/11 15/11
70 5625/4096 49/36 49/36 49/36
71 512/375 48/35 48/35 48/35
72 1000/729 343/250 11/8 11/8
73 864/625 243/175 168/121 18/13
74 25/18 25/18 25/18 25/18
75 4374/3125 480/343 108/77 108/77
76 45/32 7/5 7/5 7/5
77 65536/46875 486/343 486/343 128/91
78 729/512 567/400 99/70 55/39
79 46875/32768 343/243 343/243 91/64
80 64/45 10/7 10/7 10/7
81 3125/2187 343/240 77/54 77/54
82 36/25 36/25 36/25 36/25
83 625/432 350/243 121/84 13/9
84 729/500 500/343 16/11 16/11
85 375/256 35/24 35/24 35/24
86 8192/5625 72/49 72/49 72/49
87 3200/2187 147/100 22/15 22/15
88 4608/3125 729/490 180/121 96/65
89 40/27 40/27 40/27 40/27
90 23328/15625 512/343 512/343 143/96
91 3/2 3/2 3/2 3/2
92 15625/10368 2401/1600 121/81 121/81
93 243/160 189/125 50/33 50/33
94 3125/2048 245/162 121/80 91/60
95 1024/675 32/21 32/21 32/21
96 10000/6561 49/32 49/32 49/32
97 192/125 54/35 54/35 20/13
98 125/81 125/81 77/50 65/42
99 972/625 972/625 120/77 81/52
100 25/16 14/9 14/9 14/9
101 19683/12500 384/245 243/154 169/108
102 405/256 63/40 11/7 11/7
103 24576/15625 1944/1225 192/121 144/91
104 128/81 100/63 35/22 35/22
105 31250/19683 343/216 343/216 143/90
106 8/5 8/5 8/5 8/5
107 3125/1944 1029/640 77/48 77/48
108 81/50 81/50 81/50 21/13
109 625/384 175/108 121/75 13/8
110 6561/4000 80/49 18/11 18/11
111 3375/2048 49/30 44/27 44/27
112 1024/625 81/49 81/49 64/39
113 400/243 400/243 33/20 33/20
114 5184/3125 1458/875 128/77 108/65
115 5/3 5/3 5/3 5/3
116 26244/15625 576/343 539/324 240/143
117 27/16 27/16 27/16 27/16
118 15625/9216 1225/729 121/72 91/54
119 2048/1215 250/147 56/33 22/13
120 28125/16384 245/144 245/144 143/84
121 128/75 12/7 12/7 12/7
122 1250/729 343/200 55/32 55/32
123 216/125 216/125 210/121 45/26
124 125/72 125/72 121/70 26/15
125 2187/1250 256/147 96/55 96/55
126 225/128 7/4 7/4 7/4
127 16384/9375 432/245 432/245 160/91
128 1280/729 441/250 44/25 39/22
129 27648/15625 1715/972 216/121 143/81
130 16/9 16/9 16/9 16/9
131 15625/8748 343/192 343/192 143/80
132 9/5 9/5 9/5 9/5
133 3125/1728 875/486 231/128 65/36
134 729/400 625/343 20/11 20/11
135 1875/1024 49/27 49/27 49/27
136 2048/1125 64/35 64/35 64/35
137 4000/2187 147/80 11/6 11/6
138 1152/625 324/175 224/121 24/13
139 50/27 50/27 50/27 13/7
140 5832/3125 640/343 144/77 144/77
141 15/8 15/8 15/8 15/8
142 59049/31250 648/343 539/288 169/90
143 243/128 189/100 66/35 49/26
144 15625/8192 1225/648 121/64 91/48
145 256/135 40/21 21/11 21/11
146 12500/6561 245/128 154/81 143/75
147 48/25 27/14 27/14 25/13
148 625/324 625/324 77/40 52/27
149 243/125 243/125 64/33 64/33
150 125/64 35/18 35/18 35/18
151 19683/10000 96/49 96/49 96/49
152 2025/1024 49/25 49/25 49/25
153 6144/3125 486/245 240/121 128/65
154 160/81 125/63 99/50 77/39
155 31104/15625 1715/864 243/121 143/72
156 2/1 2/1 2/1 2/1
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