Comma pairs

I searched among 7-limit intervals less than 50 cents in size and within a radius of 10 of 1 in the symmetric 7-limit lattice (so that the first invariant is <= 100) and came up with a list of matching pairs. Particularly noteworthy, I think, are the following, all within 6 of the unison:

4375/4374 829440/823543 35 56 4180
589824/588245 28672/28125 33 -60 4744
33075/32768 8748/8575 33 84 4456
110592/109375 5103/5000 31 -72 6228
2048/2025 15876/15625 28 0 2304
16875/16807 300125/294912 27 -120 6676
2430/2401 84035/82944 23 -40 2164
2430/2401 51200/50421 23 -40 2164
2430/2401 31104/30625 23 -40 2164
2430/2401 9604/9375 23 -40 2164
3136/3125 3125/3087 19 0 900
3136/3125 250/243 19 0 900
3125/3087 250/243 19 0 900
4000/3969 5625/5488 19 -72 2772
1029/1024 81/80 13 0 144
2401/2400 525/512 11 8 148
1728/1715 875/864 10 -9 180
1728/1715 1029/1000 10 -9 180
875/864 1029/1000 10 -9 180
126/125 64/63 7 0 36
49/48 36/35 3 0 4

The complete cycle of 2430/2401 is noteworthy, as are the
{1728/1715, 875/864, 1029/1000} and {3136/3125, 3125/3087, 250/243} sets. The 2401/2400 and 525/512 matchup seems worth investigating, and of course 49/48 and 36/35 is a no-brainer.

Here is the complete list:

250047/250000 256000/250047 45 -324 29160
4375/4374 829440/823543 35 56 4180
2401/2400 525/512 11 8 148
52734375/52706752 2579890176/2573571875 82 -945 164196
52734375/52706752 1313046875/1289945088 82 -945 164196
420175/419904 5898240/5764801 47 80 8356
420175/419904 390625/381024 47 80 8356
2460375/2458624 3623878656/3603000625 85 -864 150480
2460375/2458624 15752961/15625000 85 -864 150480
2460375/2458624 679477248/669921875 85 -864 150480
703125/702464 843750/823543 49 -252 25992
48828125/48771072 67528125/67108864 83 440 69844
48828125/48771072 34034175/33554432 83 440 69844
13841287201/13824000000 14155776000/13841287201 99 648 107892
65625/65536 2240/2187 38 35 2524
95703125/95551488 1019215872/1008840175 73 -540 96264
95703125/95551488 17578125/17210368 73 -540 96264
134217728/133984375 725594112/720600125 97 0 69696
134217728/133984375 177147/175616 97 0 69696
134217728/133984375 5764801/5668704 97 0 69696
2100875/2097152 1071875/1048576 49 0 14400
9191328125/9172942848 257298363/256000000 85 -1764 299880
283115520/282475249 15116544/14706125 73 180 37224
2579890176/2573571875 1313046875/1289945088 82 -945 164196
3276800000/3268642167 41006250/40353607 93 -1440 270544
3276800000/3268642167 3268642167/3200000000 93 -1440 270544
589824/588245 28672/28125 33 -60 4744
26873856/26796875 144120025/143327232 63 -336 44836
26873856/26796875 321489/312500 63 -336 44836
4096000/4084101 273375/268912 54 -525 58300
4096000/4084101 2151296/2109375 54 -525 58300
5120/5103 117649/116640 37 -36 2664
5120/5103 3645/3584 37 -36 2664
3136/3125 3125/3087 19 0 900
3136/3125 250/243 19 0 900
40500000/40353607 458752/455625 67 -216 51444
49009212/48828125 367653125/362797056 91 0 108900
49009212/48828125 1977326743/1944000000 91 0 108900
49009212/48828125 48828125/47775744 91 0 108900
49009212/48828125 268435456/262609375 91 0 108900
10976/10935 83349/81920 42 -105 12916
118098/117649 9834496/9765625 76 0 57600
118098/117649 9765625/9529569 76 0 57600
235298/234375 15625/15309 45 -84 9160
235298/234375 786432/765625 45 -84 9160
16875/16807 300125/294912 27 -120 6676
823543/820125 66706983/65536000 69 -672 94672
823543/820125 1404928/1366875 69 -672 94672
823543/820125 160000000/155649627 69 -672 94672
19683/19600 157464/153125 57 180 17896
282475249/281250000 413343/409600 93 -180 41224
282475249/281250000 847425747/838860800 93 -180 41224
321489/320000 37748736/37515625 60 -384 52480
321489/320000 75497472/73530625 60 -384 52480
1029/1024 81/80 13 0 144
1500625/1492992 50625/50176 36 -192 14848
158203125/157351936 161414428/158203125 97 -1296 251424
144120025/143327232 321489/312500 63 -336 44836
3623878656/3603000625 15752961/15625000 85 -864 150480
3623878656/3603000625 679477248/669921875 85 -864 150480
2109375/2097152 282475249/279936000 79 0 44100
2109375/2097152 286654464/282475249 79 0 44100
37748736/37515625 75497472/73530625 60 -384 52480
67528125/67108864 34034175/33554432 83 440 69844
2097152/2083725 9765625/9680832 69 300 37000
2097152/2083725 4194304/4134375 69 300 37000
393216/390625 4194304/4117715 57 0 3136
393216/390625 839808/823543 57 0 3136
725594112/720600125 177147/175616 97 0 69696
725594112/720600125 5764801/5668704 97 0 69696
9834496/9765625 9765625/9529569 76 0 57600
34420736/34171875 18345885696/18015003125 87 -1680 292996
7558272/7503125 1063125/1048576 71 200 44500
3200000/3176523 5359375/5308416 43 -360 31284
1728/1715 875/864 10 -9 180
1728/1715 1029/1000 10 -9 180
78732/78125 40353607/40000000 67 0 15876
78732/78125 20588575/20155392 67 0 15876
4000/3969 5625/5488 19 -72 2772
126/125 64/63 7 0 36
1250000/1240029 200120949/195312500 98 -385 158404
15752961/15625000 679477248/669921875 85 -864 150480
1071875/1062882 2125764/2100875 97 720 114336
117649/116640 3645/3584 37 -36 2664
177147/175616 5764801/5668704 97 0 69696
9765625/9680832 4194304/4134375 69 300 37000
40353607/40000000 20588575/20155392 67 0 15876
282475249/279936000 286654464/282475249 79 0 44100
413343/409600 847425747/838860800 93 -180 41224
390625/387072 214375/209952 45 96 10960
33075/32768 8748/8575 33 84 4456
1058841/1048576 6561/6400 52 0 9216
1058841/1048576 401408/390625 52 0 9216
514714375/509607936 191102976/187578125 63 -840 106324
1019215872/1008840175 17578125/17210368 73 -540 96264
52428800/51883209 19140625/18874368 68 -256 34816
10616832/10504375 153664/151875 41 -400 32800
65536/64827 78125/76832 37 0 7056
110592/109375 5103/5000 31 -72 6228
2048/2025 15876/15625 28 0 2304
5832000/5764801 3176523/3125000 55 -144 23940
5832000/5764801 28824005/28311552 55 -144 23940
2500000/2470629 234375/229376 50 -49 4900
2500000/2470629 559872/546875 50 -49 4900
9882516/9765625 3828125/3779136 77 140 25096
9882516/9765625 9765625/9633792 77 140 25096
9882516/9765625 535815/524288 77 140 25096
2430/2401 84035/82944 23 -40 2164
2430/2401 51200/50421 23 -40 2164
2430/2401 31104/30625 23 -40 2164
2430/2401 9604/9375 23 -40 2164
11529602/11390625 16000000/15752961 76 -1152 177408
3125/3087 250/243 19 0 900
20253807/20000000 262144000/257298363 97 -1260 268776
20253807/20000000 7529536/7381125 97 -1260 268776
875/864 1029/1000 10 -9 180
3828125/3779136 9765625/9633792 77 140 25096
3828125/3779136 535815/524288 77 140 25096
84035/82944 51200/50421 23 -40 2164
84035/82944 31104/30625 23 -40 2164
84035/82944 9604/9375 23 -40 2164
51883209/51200000 53747712/52521875 59 -400 55300
367653125/362797056 1977326743/1944000000 91 0 108900
367653125/362797056 48828125/47775744 91 0 108900
367653125/362797056 268435456/262609375 91 0 108900
11390625/11239424 1838265625/1811939328 81 -972 169128
9765625/9633792 535815/524288 77 140 25096
49545216/48828125 48828125/48009024 90 231 60820
40960000/40353607 20000/19683 61 0 32400
40960000/40353607 1990656/1953125 61 0 32400
40960000/40353607 19683/19208 61 0 32400
2985984/2941225 765625/746496 40 -144 11520
51200/50421 31104/30625 23 -40 2164
51200/50421 9604/9375 23 -40 2164
31104/30625 9604/9375 23 -40 2164
20000/19683 1990656/1953125 61 0 32400
20000/19683 19683/19208 61 0 32400
41006250/40353607 3268642167/3200000000 93 -1440 270544
5859375/5764801 13671875/13436928 75 -144 26500
5859375/5764801 327680/321489 75 -144 26500
5859375/5764801 100352/98415 75 -144 26500
3176523/3125000 28824005/28311552 55 -144 23940
273375/268912 2151296/2109375 54 -525 58300
1977326743/1944000000 48828125/47775744 91 0 108900
1977326743/1944000000 268435456/262609375 91 0 108900
13671875/13436928 327680/321489 75 -144 26500
13671875/13436928 100352/98415 75 -144 26500
66706983/65536000 1404928/1366875 69 -672 94672
66706983/65536000 160000000/155649627 69 -672 94672
4194304/4117715 839808/823543 57 0 3136
262144000/257298363 7529536/7381125 97 -1260 268776
1990656/1953125 19683/19208 61 0 32400
327680/321489 100352/98415 75 -144 26500
120000/117649 12005/11664 27 24 1204
15625/15309 786432/765625 45 -84 9160
49/48 36/35 3 0 4
234375/229376 559872/546875 50 -49 4900
48828125/47775744 268435456/262609375 91 0 108900
4689453125/4586471424 257298363/250000000 91 -1512 281268
5159780352/5044200875 40353607/39366000 90 -729 131220
89915392/87890625 7247757312/7061881225 97 -540 111816
89915392/87890625 52734375/51380224 97 -540 111816
5898240/5764801 390625/381024 47 80 8356
5904900/5764801 7061881225/6879707136 92 -640 138496
6561/6400 401408/390625 52 0 9216
40353607/39321600 131072/127575 61 108 15048
7247757312/7061881225 52734375/51380224 97 -540 111816
1404928/1366875 160000000/155649627 69 -672 94672