Table of 94edo intervals: Difference between revisions

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He's correct. Should be 245/216
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Assuming 23-limit patent val <94 149 218 264 325 348 384 399 425|.  
Assuming [[23-limit]] [[patent val]] <94 149 218 264 325 348 384 399 425|, here is a table of intervals as approximated by [[94edo]] steps.
 
{| class="wikitable"
{| class="wikitable"
|-
|-
!| Step
! Step
!| Cents
! Cents
!| 5 limit
! 5 limit
!| 7 limit
! 7 limit
!| 11 limit
! 11 limit
!| 13 limit
! 13 limit
!17 limit
! 17 limit
!19 limit
! 19 limit
!23 limit
! 23 limit
|-
|-
| | 1
| 1
|12.766
| 12.766
| | 3125/3072
| 3125/3072
| | 245/243
| 245/243
| colspan="2" | 99/98
| colspan="2" | 99/98
| colspan="3" |85/84
| colspan="3" | 85/84
|-
|-
| | 2
| 2
|25.532
| 25.532
| | 81/80
| 81/80
| colspan="6" | 50/49
| colspan="6" | 50/49
|-
|-
| | 3
| 3
|38.298
| 38.298
| | 250/243
| 250/243
| | 49/48
| 49/48
| | 45/44
| 45/44
| colspan="4" | 40/39
| colspan="4" | 40/39
|-
|-
| | 4
| 4
|51.064
| 51.064
| | 128/125
| 128/125
| | 36/35
| 36/35
| colspan="5" | 33/32
| colspan="5" | 33/32
|-
|-
| | 5
| 5
|63.830
| 63.830
| colspan="7" | 25/24
| colspan="7" | 25/24
|-
|-
| | 6
| 6
|76.596
| 76.596
| | 648/625
| 648/625
| | 256/245
| 256/245
| colspan="5" | 22/21
| colspan="5" | 22/21
|-
|-
| | 7
| 7
|89.362
| 89.362
| | 135/128
| 135/128
| colspan="4" | 21/20
| colspan="4" | 21/20
| colspan="2" |19/18
| colspan="2" | 19/18
|-
|-
| | 8
| 8
|102.128
| 102.128
| | 3125/2916
| 3125/2916
| | 343/324
| 343/324
| colspan="2" | 35/33
| colspan="2" | 35/33
| colspan="3" |17/16
| colspan="3" | 17/16
|-
|-
| | 9
| 9
|114.894
| 114.894
| | 16/15
| 16/15
| colspan="6" | 15/14
| colspan="6" | 15/14
|-
|-
| | 10
| 10
|127.660
| 127.660
| | 625/576
| 625/576
| | 175/162
| 175/162
| | 121/112
| 121/112
| colspan="4" | 14/13
| colspan="4" | 14/13
|-
|-
| | 11
| 11
|140.426
| 140.426
| colspan="3" | 27/25
| colspan="3" | 27/25
| colspan="4" | 13/12
| colspan="4" | 13/12
|-
|-
| | 12
| 12
|153.191
| 153.191
| | 800/729
| 800/729
| | 35/32
| 35/32
| colspan="5" | 12/11
| colspan="5" | 12/11
|-
|-
| | 13
| 13
|165.957
| 165.957
| | 2048/1875
| 2048/1875
| | 54/49
| 54/49
| colspan="5" | 11/10
| colspan="5" | 11/10
|-
|-
| | 14
| 14
|178.723
| 178.723
| colspan="7" | 10/9
| colspan="7" | 10/9
|-
|-
| | 15
| 15
|191.489
| 191.489
| | 3456/3125
| 3456/3125
| | 384/343
| 384/343
| | 49/44
| 49/44
| colspan="2" | 39/35
| colspan="2" | 39/35
| colspan="2" |19/17
| colspan="2" | 19/17
|-
|-
| | 16
| 16
|204.255
| 204.255
| colspan="7" | 9/8
| colspan="7" | 9/8
|-
|-
| | 17
| 17
|217.021
| 217.021
| | 2500/2187
| 2500/2187
| | 245/216
| 245/216
| colspan="2" |25/22
| colspan="2" | 25/22
| colspan="3" |17/15
| colspan="3" | 17/15
|-
|-
| | 18
| 18
|229.787
| 229.787
| | 256/225
| 256/225
| colspan="6" | 8/7
| colspan="6" | 8/7
|-
|-
| | 19
| 19
|242.553
| 242.553
| colspan="2"| 125/108
| colspan="2" | 125/108
| | 63/55
| 63/55
| colspan="4" | 15/13
| colspan="4" | 15/13
|-
|-
| | 20
| 20
|255.319
| 255.319
| | 144/125
| 144/125
| colspan="2" | 81/70
| colspan="2" | 81/70
| | 52/45
| 52/45
|51/44
| 51/44
| colspan="2" |22/19
| colspan="2" | 22/19
|-
|-
| | 21
| 21
|268.085
| 268.085
| | 75/64
| 75/64
| colspan="6" | 7/6
| colspan="6" | 7/6
|-
|-
| | 22
| 22
|280.851
| 280.851
| | 729/625
| 729/625
| | 288/245
| 288/245
| colspan="2" | 33/28
| colspan="2" | 33/28
| colspan="3" |20/17
| colspan="3" | 20/17
|-
|-
| | 23
| 23
|293.617
| 293.617
| | 32/27
| 32/27
| colspan="2" | 25/21
| colspan="2" | 25/21
| colspan="4" | 13/11
| colspan="4" | 13/11
|-
|-
| | 24
| 24
|306.383
| 306.383
| | 3125/2592
| 3125/2592
| | 343/288
| 343/288
| colspan="2" | 105/88
| colspan="2" | 105/88
|81/68
| 81/68
|68/57
| 68/57
|55/46
| 55/46
|-
|-
| | 25
| 25
|319.149
| 319.149
| colspan="7" | 6/5
| colspan="7" | 6/5
|-
|-
| | 26
| 26
|331.915
| 331.915
| | 625/512
| 625/512
| | 98/81
| 98/81
| colspan="2" | 40/33
| colspan="2" | 40/33
| colspan="3" |17/14
| colspan="3" | 17/14
|-
|-
| | 27
| 27
|344.681
| 344.681
| | 243/200
| 243/200
| | 60/49
| 60/49
| colspan="5" | 11/9
| colspan="5" | 11/9
|-
|-
| | 28
| 28
|357.447
| 357.447
| | 100/81
| 100/81
| | 49/40
| 49/40
| | 27/22
| 27/22
| colspan="4" | 16/13
| colspan="4" | 16/13
|-
|-
| | 29
| 29
|370.213
| 370.213
| | 768/625
| 768/625
| | 216/175
| 216/175
| | 99/80
| 99/80
| | 26/21
| 26/21
| colspan="3" |21/17
| colspan="3" | 21/17
|-
|-
| | 30
| 30
|382.979
| 382.979
| colspan="7" | 5/4
| colspan="7" | 5/4
|-
|-
| | 31
| 31
|395.745
| 395.745
| | 3888/3125
| 3888/3125
| | 432/343
| 432/343
| colspan="2" | 44/35
| colspan="2" | 44/35
| colspan="3" |34/27
| colspan="3" | 34/27
|-
|-
| | 32
| 32
|408.511
| 408.511
| | 81/64
| 81/64
| colspan="2" | 63/50
| colspan="2" | 63/50
| colspan="2" | 33/26
| colspan="2" | 33/26
| colspan="2" |19/15
| colspan="2" | 19/15
|-
|-
| | 33
| 33
|421.277
| 421.277
| | 625/486
| 625/486
| | 245/192
| 245/192
| colspan="5" | 14/11
| colspan="5" | 14/11
|-
|-
| | 34
| 34
|434.043
| 434.043
| | 32/25
| 32/25
| colspan="6" | 9/7
| colspan="6" | 9/7
|-
|-
| | 35
| 35
|446.809
| 446.809
| | 125/96
| 125/96
| colspan="3" | 35/27
| colspan="3" | 35/27
| colspan="3" |22/17
| colspan="3" | 22/17
|-
|-
| | 36
| 36
|459.574
| 459.574
| | 162/125
| 162/125
| | 64/49
| 64/49
| | 55/42
| 55/42
| colspan="4" | 13/10
| colspan="4" | 13/10
|-
|-
| | 37
| 37
|472.340
| 472.340
| | 320/243
| 320/243
| colspan="6" | 21/16
| colspan="6" | 21/16
|-
|-
| | 38
| 38
|485.106
| 485.106
| | 4096/3125
| 4096/3125
| | 324/245
| 324/245
| colspan="5" | 33/25
| colspan="5" | 33/25
|-
|-
| | 39
| 39
|497.872
| 497.872
| colspan="7" | 4/3
| colspan="7" | 4/3
|-
|-
| | 40
| 40
|510.638
| 510.638
| | 3125/2304
| 3125/2304
| | 343/256
| 343/256
| | 66/49
| 66/49
| colspan="4" | 35/26
| colspan="4" | 35/26
|-
|-
| | 41
| 41
|523.404
| 523.404
| colspan="5" | 27/20
| colspan="5" | 27/20
| colspan="2" |19/14
| colspan="2" | 19/14
|-
|-
| | 42
| 42
|536.170
| 536.170
| | 1000/729
| 1000/729
| | 49/36
| 49/36
| colspan="5" | 15/11
| colspan="5" | 15/11
|-
|-
| | 43
| 43
|548.936
| 548.936
| | 512/375
| 512/375
| | 48/35
| 48/35
| colspan="5" | 11/8
| colspan="5" | 11/8
|-
|-
| | 44
| 44
|561.702
| 561.702
| | 25/18
| 25/18
| colspan="2" | 25/18
| colspan="2" | 25/18
| colspan="4" | 18/13
| colspan="4" | 18/13
|-
|-
| | 45
| 45
|574.468
| 574.468
| | 864/625
| 864/625
| | 243/175
| 243/175
| | 88/63
| 88/63
| colspan="3" | 39/28
| colspan="3" | 39/28
|32/23
| 32/23
|-
|-
| | 46
| 46
|587.234
| 587.234
| | 45/32
| 45/32
| colspan="6" | 7/5
| colspan="6" | 7/5
|-
|-
| | 47
| 47
|600.000
| 600.000
| | 3125/2187
| 3125/2187
| | 343/243
| 343/243
| colspan="2" | 99/70
| colspan="2" | 99/70
| colspan="3" |17/12
| colspan="3" | 17/12
|-
|-
| | 48
| 48
|612.766
| 612.766
| | 64/45
| 64/45
| colspan="6" | 10/7
| colspan="6" | 10/7
|-
|-
| | 49
| 49
|625.532
| 625.532
| | 625/432
| 625/432
| | 343/240
| 343/240
| | 63/44
| 63/44
| colspan="3" | 56/39
| colspan="3" | 56/39
|23/16
| 23/16
|-
|-
| | 50
| 50
|638.298
| 638.298
| | 36/25
| 36/25
| colspan="2" | 36/25
| colspan="2" | 36/25
| colspan="4" | 13/9
| colspan="4" | 13/9
|-
|-
| | 51
| 51
|651.064
| 651.064
| | 375/256
| 375/256
| | 35/24
| 35/24
| colspan="5" | 16/11
| colspan="5" | 16/11
|-
|-
| | 52
| 52
|663.830
| 663.830
| | 729/500
| 729/500
| | 72/49
| 72/49
| colspan="5" | 22/15
| colspan="5" | 22/15
|-
|-
| | 53
| 53
|676.596
| 676.596
| colspan="5" | 40/27
| colspan="5" | 40/27
| colspan="2" |28/19
| colspan="2" | 28/19
|-
|-
| | 54
| 54
|689.362
| 689.362
| | 4608/3125
| 4608/3125
| | 512/343
| 512/343
| colspan="5" | 49/33
| colspan="5" | 49/33
|-
|-
| | 55
| 55
|702.128
| 702.128
| colspan="7" | 3/2
| colspan="7" | 3/2
|-
|-
| | 56
| 56
|714.894
| 714.894
| | 3125/2048
| 3125/2048
| | 245/162
| 245/162
| colspan="5" | 50/33
| colspan="5" | 50/33
|-
|-
| | 57
| 57
|727.660
| 727.660
| | 243/160
| 243/160
| colspan="6" | 32/21
| colspan="6" | 32/21
|-
|-
| | 58
| 58
|740.426
| 740.426
| | 125/81
| 125/81
| colspan="2" | 49/32
| colspan="2" | 49/32
| colspan="4" | 20/13
| colspan="4" | 20/13
|-
|-
| | 59
| 59
|753.191
| 753.191
| | 192/125
| 192/125
| colspan="3" | 54/35
| colspan="3" | 54/35
| colspan="3" |17/11
| colspan="3" | 17/11
|-
|-
| | 60
| 60
|765.957
| 765.957
| | 25/16
| 25/16
| colspan="6" | 14/9
| colspan="6" | 14/9
|-
|-
| | 61
| 61
|778.723
| 778.723
| | 972/625
| 972/625
| | 384/245
| 384/245
| colspan="5" | 11/7
| colspan="5" | 11/7
|-
|-
| | 62
| 62
|791.489
| 791.489
| | 128/81
| 128/81
| colspan="2" | 63/40
| colspan="2" | 63/40
| colspan="2" | 52/33
| colspan="2" | 52/33
| colspan="2" |19/12
| colspan="2" | 19/12
|-
|-
| | 63
| 63
|804.255
| 804.255
| | 3125/1944
| 3125/1944
| | 343/216
| 343/216
| colspan="2" | 35/22
| colspan="2" | 35/22
| colspan="3" |27/17
| colspan="3" | 27/17
|-
|-
| | 64
| 64
|817.021
| 817.021
| colspan="7" | 8/5
| colspan="7" | 8/5
|-
|-
| | 65
| 65
|829.787
| 829.787
| | 625/384
| 625/384
| | 175/108
| 175/108
| | 121/75
| 121/75
| colspan="4" | 21/13
| colspan="4" | 21/13
|-
|-
| | 66
| 66
|842.553
| 842.553
| | 81/50
| 81/50
| | 80/49
| 80/49
| | 44/27
| 44/27
| colspan="4" | 13/8
| colspan="4" | 13/8
|-
|-
| | 67
| 67
|855.319
| 855.319
| | 400/243
| 400/243
| | 49/30
| 49/30
| colspan="5" | 18/11
| colspan="5" | 18/11
|-
|-
| | 68
| 68
|868.085
| 868.085
| | 1024/625
| 1024/625
| | 81/49
| 81/49
| colspan="2" | 33/20
| colspan="2" | 33/20
| colspan="3" |28/17
| colspan="3" | 28/17
|-
|-
| | 69
| 69
|880.851
| 880.851
| colspan="7" | 5/3
| colspan="7" | 5/3
|-
|-
| | 70
| 70
|893.617
| 893.617
| | 5184/3125
| 5184/3125
| | 576/343
| 576/343
| | 121/72
| 121/72
| colspan="2" | 117/70
| colspan="2" | 117/70
| colspan="2" |57/34
| colspan="2" | 57/34
|-
|-
| | 71
| 71
|906.383
| 906.383
| colspan="3" | 27/16
| colspan="3" | 27/16
| colspan="4" | 22/13
| colspan="4" | 22/13
|-
|-
| | 72
| 72
|919.149
| 919.149
| | 1250/729
| 1250/729
| | 245/144
| 245/144
| | 56/33
| 56/33
| | 56/33
| 56/33
| colspan="3" |17/10
| colspan="3" | 17/10
|-
|-
| | 73
| 73
|931.915
| 931.915
| | 128/75
| 128/75
| colspan="6" | 12/7
| colspan="6" | 12/7
|-
|-
| | 74
| 74
|944.681
| 944.681
| colspan="2" | 125/72
| colspan="2" | 125/72
| | 121/70
| 121/70
| colspan="2" | 45/26
| colspan="2" | 45/26
| colspan="2" |19/11
| colspan="2" | 19/11
|-
|-
| | 75
| 75
|957.447
| 957.447
|  colspan="2"| 216/125
|  colspan="2"| 216/125
| | 110/63
| 110/63
| colspan="4" | 26/15
| colspan="4" | 26/15
|-
|-
| | 76
| 76
|970.213
| 970.213
| | 225/128
| 225/128
| colspan="6" | 7/4
| colspan="6" | 7/4
|-
|-
| | 77
| 77
|982.979
| 982.979
| | 2187/1250
| 2187/1250
| | 432/245
| 432/245
| colspan="2" | 44/25
| colspan="2" | 44/25
| colspan="2" |30/17
| colspan="2" | 30/17
|23/13
| 23/13
|-
|-
| | 78
| 78
|995.745
| 995.745
| colspan="7" | 16/9
| colspan="7" | 16/9
|-
|-
| | 79
| 79
|1008.511
| 1008.511
| | 3125/1728
| 3125/1728
|343/192
| 343/192
| colspan="3" |88/49
| colspan="3" | 88/49
| colspan="2" |34/19
| colspan="2" | 34/19
|-
|-
| | 80
| 80
|1021.277
| 1021.277
| colspan="7" | 9/5
| colspan="7" | 9/5
|-
|-
| | 81
| 81
|1034.043
| 1034.043
| | 1875/1024
| 1875/1024
| | 49/27
| 49/27
| colspan="5" | 20/11
| colspan="5" | 20/11
|-
|-
| | 82
| 82
|1046.809
| 1046.809
| | 729/400
| 729/400
| | 64/35
| 64/35
| colspan="5" | 11/6
| colspan="5" | 11/6
|-
|-
| | 83
| 83
|1059.574
| 1059.574
| colspan="3" | 50/27
| colspan="3" | 50/27
| colspan="4" | 24/13
| colspan="4" | 24/13
|-
|-
| | 84
| 84
|1072.340
| 1072.340
| | 1152/625
| 1152/625
| | 324/175
| 324/175
| | 224/121
| 224/121
| colspan="4" | 13/7
| colspan="4" | 13/7
|-
|-
| | 85
| 85
|1085.106
| 1085.106
| colspan="7" | 15/8
| colspan="7" | 15/8
|-
|-
| | 86
| 86
|1097.872
| 1097.872
| | 5832/3125
| 5832/3125
| | 648/343
| 648/343
| | 66/35
| 66/35
| | 49/26
| 49/26
| colspan="3" |17/9
| colspan="3" | 17/9
|-
|-
| | 87
| 87
|1110.638
| 1110.638
| | 243/128
| 243/128
| colspan="4" | 40/21
| colspan="4" | 40/21
| colspan="2" |19/10
| colspan="2" | 19/10
|-
|-
| | 88
| 88
|1123.404
| 1123.404
| | 625/324
| 625/324
| | 245/128
| 245/128
| colspan="5" | 21/11
| colspan="5" | 21/11
|-
|-
| | 89
| 89
|1136.170
| 1136.170
| | 48/25
| 48/25
| colspan="6" | 27/14
| colspan="6" | 27/14
|-
|-
| | 90
| 90
|1148.936
| 1148.936
| | 125/64
| 125/64
| colspan="3" | 35/18
| colspan="3" | 35/18
| colspan="3" |33/17
| colspan="3" | 33/17
|-
|-
| | 91
| 91
|1161.702
| 1161.702
| | 243/125
| 243/125
| | 96/49
| 96/49
| | 55/28
| 55/28
| colspan="4" | 39/20
| colspan="4" | 39/20
|-
|-
| | 92
| 92
|1174.468
| 1174.468
| | 160/81
| 160/81
| colspan="6" | 49/25
| colspan="6" | 49/25
|-
|-
| | 93
| 93
|1187.234
| 1187.234
| | 6144/3125
| 6144/3125
| | 486/245
| 486/245
| colspan="4" | 99/50
| colspan="4" | 99/50
|91/46
| 91/46
|-
|-
| | 94
| 94
|1200.000
| 1200.000
| colspan="7" | 2/1
| colspan="7" | 2/1
|}
|}


[[Category:interval collection]]
[[Category:Interval collection]]
[[Category:11-limit]]
[[Category:13-limit]]
[[Category:94edo]]
[[Category:94edo]]
[[Category:5-limit]]
[[Category:5-limit]]
[[Category:7-limit]]
[[Category:7-limit]]
[[Category:11-limit]]
[[Category:13-limit]]
[[Category:Todo:expand]]
[[Category:Todo:clarify]] <!-- what are the criteria for a given interval to appear in this table -->

Revision as of 20:39, 25 October 2020

Assuming 23-limit patent val <94 149 218 264 325 348 384 399 425|, here is a table of intervals as approximated by 94edo steps.

Step Cents 5 limit 7 limit 11 limit 13 limit 17 limit 19 limit 23 limit
1 12.766 3125/3072 245/243 99/98 85/84
2 25.532 81/80 50/49
3 38.298 250/243 49/48 45/44 40/39
4 51.064 128/125 36/35 33/32
5 63.830 25/24
6 76.596 648/625 256/245 22/21
7 89.362 135/128 21/20 19/18
8 102.128 3125/2916 343/324 35/33 17/16
9 114.894 16/15 15/14
10 127.660 625/576 175/162 121/112 14/13
11 140.426 27/25 13/12
12 153.191 800/729 35/32 12/11
13 165.957 2048/1875 54/49 11/10
14 178.723 10/9
15 191.489 3456/3125 384/343 49/44 39/35 19/17
16 204.255 9/8
17 217.021 2500/2187 245/216 25/22 17/15
18 229.787 256/225 8/7
19 242.553 125/108 63/55 15/13
20 255.319 144/125 81/70 52/45 51/44 22/19
21 268.085 75/64 7/6
22 280.851 729/625 288/245 33/28 20/17
23 293.617 32/27 25/21 13/11
24 306.383 3125/2592 343/288 105/88 81/68 68/57 55/46
25 319.149 6/5
26 331.915 625/512 98/81 40/33 17/14
27 344.681 243/200 60/49 11/9
28 357.447 100/81 49/40 27/22 16/13
29 370.213 768/625 216/175 99/80 26/21 21/17
30 382.979 5/4
31 395.745 3888/3125 432/343 44/35 34/27
32 408.511 81/64 63/50 33/26 19/15
33 421.277 625/486 245/192 14/11
34 434.043 32/25 9/7
35 446.809 125/96 35/27 22/17
36 459.574 162/125 64/49 55/42 13/10
37 472.340 320/243 21/16
38 485.106 4096/3125 324/245 33/25
39 497.872 4/3
40 510.638 3125/2304 343/256 66/49 35/26
41 523.404 27/20 19/14
42 536.170 1000/729 49/36 15/11
43 548.936 512/375 48/35 11/8
44 561.702 25/18 25/18 18/13
45 574.468 864/625 243/175 88/63 39/28 32/23
46 587.234 45/32 7/5
47 600.000 3125/2187 343/243 99/70 17/12
48 612.766 64/45 10/7
49 625.532 625/432 343/240 63/44 56/39 23/16
50 638.298 36/25 36/25 13/9
51 651.064 375/256 35/24 16/11
52 663.830 729/500 72/49 22/15
53 676.596 40/27 28/19
54 689.362 4608/3125 512/343 49/33
55 702.128 3/2
56 714.894 3125/2048 245/162 50/33
57 727.660 243/160 32/21
58 740.426 125/81 49/32 20/13
59 753.191 192/125 54/35 17/11
60 765.957 25/16 14/9
61 778.723 972/625 384/245 11/7
62 791.489 128/81 63/40 52/33 19/12
63 804.255 3125/1944 343/216 35/22 27/17
64 817.021 8/5
65 829.787 625/384 175/108 121/75 21/13
66 842.553 81/50 80/49 44/27 13/8
67 855.319 400/243 49/30 18/11
68 868.085 1024/625 81/49 33/20 28/17
69 880.851 5/3
70 893.617 5184/3125 576/343 121/72 117/70 57/34
71 906.383 27/16 22/13
72 919.149 1250/729 245/144 56/33 56/33 17/10
73 931.915 128/75 12/7
74 944.681 125/72 121/70 45/26 19/11
75 957.447 216/125 110/63 26/15
76 970.213 225/128 7/4
77 982.979 2187/1250 432/245 44/25 30/17 23/13
78 995.745 16/9
79 1008.511 3125/1728 343/192 88/49 34/19
80 1021.277 9/5
81 1034.043 1875/1024 49/27 20/11
82 1046.809 729/400 64/35 11/6
83 1059.574 50/27 24/13
84 1072.340 1152/625 324/175 224/121 13/7
85 1085.106 15/8
86 1097.872 5832/3125 648/343 66/35 49/26 17/9
87 1110.638 243/128 40/21 19/10
88 1123.404 625/324 245/128 21/11
89 1136.170 48/25 27/14
90 1148.936 125/64 35/18 33/17
91 1161.702 243/125 96/49 55/28 39/20
92 1174.468 160/81 49/25
93 1187.234 6144/3125 486/245 99/50 91/46
94 1200.000 2/1
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