We know that the wedge product of a regular temperament class works as a unique key that doesn't depend on the exact tuning or the equal temperament mappings...
As the next step on my search for an invariant quantity for temperaments, I'm looking at row echelon form. This is best described in the Oxford Dictionary of...
... Contorsion is like torsion but it involves sets of equal temperament mappings (or things like them) instead of unison vectors (or things like them). I...
The math is essentially completed, I am ready to make an outline and write my little book. This won't make any sense out of context, but it is pretty, so I ...
... symbols (- -, -o-, ---, -e-) depending on tritone count (always three without a circle and three with a circle) ... Transposing will cross various breaks,...
... The fact is I don't know how to do that! I looked at reduced echelon form because one reference said it was the same as Hermite normal form. But other...
(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...
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