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Post AdCInJ6Ouy0kesQ0rQ by [email protected] |
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Post #AdBa3CtPHDnA5zY2r2 by [email protected] |
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Here's a number theory question that came up in thinking about music.I'… |
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Post #AdBgBmzdXV6c6JwCVk by [email protected] |
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@johncarlosbaez 3^n/5^m close to 1 ⇔ n log 3 close to m log 5 ⇔ n/m is a go… |
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Post #AdBgxqVXm7hKtwmFKi by [email protected] |
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@johncarlosbaez {1,3^1/5^0,3.00000000000000000000000000000},{2,3^1/5^1,0.600000… |
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Post #AdCHpoTDADJmZLidkm by [email protected] |
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@johncarlosbaez Are you asking for data? I can write this code and run it for a… |
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Post #AdCHpoX6viRAlRXkpc by [email protected] |
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@hallasurvivor - yes, I forgot to say that this was a plea for help. I think … |
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Post #AdCInJ1RDQ2cPU637o by [email protected] |
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@johncarlosbaez I try:(defun close-power-ratios (a b times) (loop :with closes… |
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Post #AdCInJ6Ouy0kesQ0rQ by [email protected] |
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@johncarlosbaez ⇒ which gives:CL-USER> (close-power-ratios 3 5 100)((0.08d… |
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Post #AdCInJAIgT88qyF7wG by [email protected] |
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@johncarlosbaez Maybe a more useful output format:(defun close-power-ratios (a … |
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Post #AdCInJECRyFX344F16 by [email protected] |
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@johncarlosbaez 3^3 / 5^2 = 27 / 25 = 1.083^19 / 5^13 = 1162261467 / 1220703125… |
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Post #AdCInJHkEn5LE3j4Xg by [email protected] |
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@Ardubal - thanks, that's great! 27/25 is known in music. Looking it up … |
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Post #AdCKEAEi5b0cvxfw9Y by [email protected] |
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@johncarlosbaez I don't think there are any reasonably small examples. I th… |
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Post #AdCKdk3Y34SDGcePwm by [email protected] |
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@gregeganSF - thanks! That's cool. 27/25 is known in music. Looking it … |
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Post #AdCLtJkNjV8mG4g1rs by [email protected] |
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@johncarlosbaez I've mused about "co-irrational" or "relativ… |
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Post #AdCLtJodTgXkTGfQUy by [email protected] |
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@demofox - musicians care a lot about rational and nearly rational numbers, whi… |
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Post #AdCM5gnPraJ1DazmaG by [email protected] |
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@dearlove - thanks! Yes, it looks like 3^63/5^43 is the first 'really goo… |
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Post #AdCPsiFvWXwdnXOnU8 by [email protected] |
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@johncarlosbaez @dearlove That's a good point about the *why* pairs of powe… |
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Post #AdCShYuUENKLUPkFfs by [email protected] |
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@edvin - thanks, that's really cool. The solution 5^157 ≈ 3^230 is indeed… |
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Post #AdCZcPCBcZbrakVobQ by [email protected] |
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I adapted the code to search for other close prime powers. I went through prime… |
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Post #AdCkrh2ke1lCmkaj0C by [email protected] |
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@johncarlosbaez This may not have been what you were looking for, but I remembe… |
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Post #AdF5USrfgIiVVJ5rY8 by [email protected] |
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@johncarlosbaez @edvin If my quick calculations are correct, just the 43/63 cas… |
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Post #AdFPUpkEc0BXY44JGq by [email protected] |
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@dearlove - heh! While I'd love to hear such a huge spectrum, I just meant… |
