Yet another revised list

This started from the commas

49/48, 50/49, 64/63, 81/80, 2048/2025, 245/243, 126/125, 4000/3969,
1728/1715, 1029/1024, 225/224, 3136/3125, 5120/5103, 6144/6125,
2401/2400, 4375/4374

I obtained the following 72 reduced pairs; the number following the
pair is the ratio between the largest and the smallest comma. I think
some bound needs to be placed on this, as the [4375/4374, 50/49]
system is obviously a little absurd.

[1728/1715, 2048/2025] 1.495580025
[225/224, 49/48] 4.629021956
[245/243, 50/49] 2.464716366
[5103/5000, 49/48] 1.011210863
[2401/2400, 3136/3125] 8.434916361
[49/48, 28/27] 1.763768279
[5120/5103, 1728/1715] 2.270583084
[64/63, 50/49] 1.282845376
[4000/3969, 245/243] 1.053543673
[3136/3125, 245/243] 2.332723121
[126/125, 49/48] 2.587706812
[3645/3584, 50/49] 1.197064798
[6144/6125, 81/80] 4.010835974
[245/243, 64/63] 1.921288732
[225/224, 1728/1715] 1.695329007
[126/125, 245/243] 1.028688881
[126/125, 81/80] 1.559018011
[2401/2400, 2048/2025] 27.11124152
[4375/4374, 6144/6125] 13.54885592
[1029/1024, 686/675] 3.318654575
[3136/3125, 49/48] 5.868055561
[225/224, 4000/3969] 1.746649139
[81/80, 128/125] 1.909155841
[4375/4374, 225/224] 19.48552996
[1728/1715, 81/80] 1.645020488
[64/63, 686/675] 1.026452250
[1029/1024, 245/243] 1.682792874
[4375/4374, 2401/2400] 1.822327650
[50/49, 525/512] 1.241102862
[875/864, 50/49] 1.596910924
[4000/3969, 2048/2025] 1.451636818
[2048/2025, 50/49] 1.788798893
[4375/4374, 3136/3125] 15.37118131
[3136/3125, 64/63] 4.481834648
[4375/4374, 2048/2025] 49.40556506
[225/224, 64/63] 3.535500094
[225/224, 1029/1024] 1.093522071
[2401/2400, 5120/5103] 7.983665859
[2401/2400, 81/80] 29.82023498
[2401/2400, 6144/6125] 7.434917601
[1029/1024, 126/125] 1.635861828
[875/864, 64/63] 1.244819488
[49/48, 2240/2187] 1.161297413
[4375/4374, 64/63] 68.89109299
[81/80, 50/49] 1.626297004
[81/80, 875/864] 1.018401828
[3136/3125, 1029/1024] 1.386221179
[245/243, 2048/2025] 1.377861075
[6144/6125, 5120/5103] 1.073806905
[4375/4374, 50/49] 88.37662008
[126/125, 64/63] 1.976408356
[49/48, 250/243] 1.377325721
[49/48, 25/24] 1.979796637
[225/224, 245/243] 1.840171149
[1728/1715, 126/125] 1.055164518
[6144/6125, 4000/3969] 2.511974761
[49/48, 6272/6075] 1.547739961
[3136/3125, 81/80] 3.535332623
[49/48, 392/375] 2.150210807
[4375/4374, 1029/1024] 21.30785708
[64/63, 36/35] 1.788813730
[4000/3969, 875/864] 1.626068363
[225/224, 81/80] 2.788850951
[50/49, 128/125] 1.173928155
[81/80, 49/48] 1.659831249
[1728/1715, 4000/3969] 1.030271488
[126/125, 2048/2025] 1.417390368
[36/35, 21/20] 1.731936266
[50/49, 36/35] 1.394411021
[3136/3125, 1728/1715] 2.149111606
[6144/6125, 50/49] 6.522810530
[5120/5103, 3136/3125] 1.056521717

--- In tuning-math@y..., genewardsmith@j... wrote:

> [2401/2400, 81/80] 29.82023498

To get an in idea of what these extreme systems might be like, I took
a look at this one. It is the 31&45 system, and has 3 5.79 cents
flat, 5 1.66 cents flat, and 7 2.46 cents flat. The map to generators
I got from LLL reduction of 31 and 45 is

[2 -1]
[2 1]
[0 8]
[3 3]

The first column generator is 19.99605624/31 and the second is
8.992112464/31, and it seems these might best be thought of as a
generator system for the 31-et.