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LLL reduction of pairs of 7-limit commas

🔗genewardsmith@juno.com

11/17/2001 11:25:44 PM

Paul gave a list previously which was a little more inclusive:

25/24, 28/27, 36/35, 49/48, 50/49, 64/63, 81/80, 126/125, 245/243,
225/224, 1029/1024, 1728/1715, 2401/2400, 3136/3125, 4375/4374,
6144/6125

I did an LLL reduction on all the 16 choose 2 = 120 pairs of elements
from this list, and obtained the following 94 reduced LLL-reduced
pairs:

[36/35, 50/49]
[126/125, 1029/1024]
[25/24, 48/49]
[49/48, 126/125]
[64/63, 4375/4374]
[81/80, 875/864]
[225/224, 4375/4374]
[64/63, 686/675]
[28/27, 3024/3125]
[28/27, 25/24]
[3136/3125, 1029/1024]
[126/125, 245/243]
[126/125, 81/80]
[126/125, 64/63]
[25/24, 49/45]
[49/48, 392/375]
[2401/2400, 3136/3125]
[126/125, 1715/1728]
[1728/1715, 3136/3125]
[225/224, 49/48]
[28/27, 126/125]
[225/224, 1029/1024]
[225/224, 1728/1715]
[225/224, 245/243]
[225/224, 81/80]
[225/224, 64/63]
[50/49, 128/125]
[25/24, 392/405]
[4375/4374, 6144/6125]
[4375/4374, 3136/3125]
[24/25, 49/48]
[21/20, 27/28]
[64/63, 50/49]
[36/35, 200/189]
[25/24, 64/63]
[126/125, 1024/1029]
[81/80, 50/49]
[81/80, 49/48]
[15/14, 36/35]
[4375/4374, 2401/2400]
[1728/1715, 4000/3969]
[50/49, 4375/4374]
[27/28, 49/48]
[245/243, 2048/2025]
[64/63, 243/245]
[245/243, 3136/3125]
[25/24, 360/343]
[28/27, 625/672]
[36/35, 1323/1280]
[4375/4374, 1029/1024]
[36/35, 225/224]
[28/27, 3087/3200]
[36/35, 128/135]
[28/27, 48/49]
[21/20, 24/25]
[36/35, 49/50]
[50/49, 525/512]
[36/35, 16/15]
[81/80, 3136/3125]
[36/35, 63/64]
[21/20, 35/36]
[25/24, 81/80]
[81/80, 1728/1715]
[81/80, 6144/6125]
[25/24, 27/28]
[28/27, 6144/6125]
[49/48, 3136/3125]
[50/49, 6144/6125]
[81/80, 1715/1728]
[25/24, 3087/3200]
[36/35, 64/63]
[49/48, 80/81]
[28/27, 49/48]
[64/63, 245/243]
[245/243, 3969/4000]
[49/48, 5000/5103]
[25/24, 224/243]
[25/24, 2401/2400]
[64/63, 3136/3125]
[81/80, 2401/2400]
[64/63, 864/875]
[6144/6125, 2401/2400]
[20/21, 36/35]
[36/35, 1029/1000]
[25/24, 49/48]
[36/35, 5488/5625]
[28/27, 1029/1024]
[245/243, 1029/1024]
[126/125, 1728/1715]
[28/27, 50/49]
[28/27, 256/245]
[50/49, 245/243]
[50/49, 864/875]
[25/24, 160/147]

Some of these have a big difference between the large and small
commas, and some introduce commas not on the orginal list.