(Has this newsgroup moved or something?) 1^2 + 2^2 + 3^2 ... 24^2 = 70^2 We know that 35 is about 50 cents flat. So, 4900, is about 100 cents flat. 4900,...
... cents ... 276, ... Not much to add, just that 6144/6125 is a comma here, which tempers out hemikleismic, and also that 300 is the 24th triangular number ...
... It is in fact, "Leech". Wikipedia's where to start, even though I read "Symmetry and the Monster" by Mark Ronan too. What's the "Leach" lattice? The...
Paul H. wrote... ... 70 is the only integer that's the sum of squares of... consecutive integers or....? ... It's not coming up. ... How do 12-ET represent the...
... 24 is the only integer, where Sigma{1,n} x^2 equals a perfect square, in this case 70 squared. n=24 of course. The trivial case is "1" (1^2=1^2) ... ...
... square, ... A dreamt a solution to this, but I forgot when I woke up. I don't know if I can justify throwing part of this in the denominator. However, I...
... generator" ... Well, M12 (and Steiner (5,6,12) is all about pentachords and hexachords (actually "pentads" and "hexads"). Well, complements of pentachords...
... Right. It's a Lattice! SPLAG is the best resource, just rather difficult. Especially with no MS or PhD :) Lattices and packings go together of course...
... Gene also can't figure out the relevsnce of all of this. In terms of simple groups, the Leech lattice is very closely associated to the Conway groups, but...
I have been reading with interest the various messages on this topic, particularly those of Gene Ward Smith and Paul Erlich. I'm a research assistant sponsored...
... Very interesting. Here is a problem of musical interest, whcih I think could also be relevant to applications in computing. Given a prime p, there can be...
... Do you think you could make a corrected, and perhaps extended, listing available? I would find a list of numerators in ascii format separated by commas...
... I will be providing a set of tables for primes up to 127 and beyond via Richard Brent's website sometime soon, with a choice of comma- delimited lists and...
... Yes, and as you add more primes, increasing the dimension, there are ever-increasing numbers of combinations that will form a basis, and mnany of these...
... Modulo some confusion about "larger" and "smaller" yes--of course, the largest ratios have the smallest height--ie, the smallest numerators. ... Results...
... of ... Darn. Nothing one can do with the Lorentzian lattice either? I was hoping that 0^ + 1^ ..24^2=70^2 had some relevance to 24-tET, or perhaps 12...
... the ... tuning? Actually, I'd like to trim this way down. Forget the LL, Conway groups, etc. How about a just a discussion of pyramidal numbers? We've...
... The pyramidal number function is pyr(n) = n(n+1)(2n+1)/6 and pyr(n)-1 = (n-1)(2n^2+5n+6). This isn't quite as well adapted as squares or triangles for...
... Right, so "Without dividing by 3" in my "pattern" Obtain (2n+1)(n+1)(n/2) for even (2n+1)(n)((n+1)/2) for odd This equals n^3 + (3/2)n^2 + (1/2)n Therefore...
... <phjelmstad@> ... producing ... Missed this post. Thanks, are there perhaps triangular pyramidal numbers, or squared pyramidal numbers, or squared...
Here are the complete lists for primes up to 31. Each group corresponds to a specific prime, P. It is a list of all the integers S having the property that...
... Square pyramidal numbers, of course, we know about. Both square and triangular pyramidal numbers give rise to an elliptic curve, which by Mordell's theorem...
... So ... We already knew pyr(1) and pyr(24) are the only square pyramidal numbers. It looks like pyr(1), pyr(5), pyr(6) and pyr(85) are the only triangular...
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