If D(q) is the symmetrical lattice distance of interval class q from the origin, then a logflat badness measure related to this lattice is cents(q)*D(q). Using...
... I searched for "symmetrical lattice" and found several messages of me asking you to define it, but no answer. Is it merely A3 or Z3, or does it depend on...
... By a {5,7,9,11}-symmetrical lattice I mean that these form a symmetrical simplex, and a corresponding A4 lattice. Since I've left 3 off, we get the same...
hi Gene, ... Gene, the stuff you post here has always been nearly incomprehensible to me, but now, in failing to keep up with what you've been writing about...
... This isn't a lattice, and mathematicians would call it D4+. The mathematicians names for the basic lattices are taken from the classification of simple Lie...
... Let's suppose |* a b c d> represents an 11-limit pitch class. Then we can measure the symmetrical size of it by ... If u and v are two such pitch class...
If we take the 11-limit diamond, sort it by size, and look at the interval differences, we get 121/120, 100/99, 99/98, 81/80, 64/63, 56/55, 55/54, 50/49,...
... The 22&58 should really be 54 steps, since it has two periods to an octave. The correct formula in general is 2G+P, where P is the number of periods to an...
... Rank two means two generators, and therefore linear; but Paul tells us we can't say that anymore, which is fine by me. ... A scale with steps of sizes...
I was counting orwell as working simply because of roundoff error from the TOP tuning. In fact, it is not consistent with the diamond, which we can easily...
... You mean it isn't unique? That's been the problem all along! 58 is the smallest constant structure (MOS/periodicity block) that uniquely represents the...
... Sorry, no. I was all excited by the idea we could go as low as 35, but orwell will not take us there. That's been the problem all along! 58 is the ... It...
Suppose we put a seminorm on the 7-limit pitch classes by setting ... This is a seminorm, since it sets ||2401/2400|| = 0. It is a norm, however, on 2401/2400...
... I feel like 'canonical detemperings' have come before, but I can't remember particular attempts -- can you? Is it that the commas of the TM-reduced basis...
... Sure; I've done it lots of times around here, using either Tenney hight reduction, or reduction with respect to either the Tenney norm or the symmetrical...
... Glad I wasn't imagining it. But what's the difference between Tenney height reduction and Tenney norm reduction? ... Oh, you're enforcing some particular...
This 7-limit 2401/2400 lattice can be approached via Joe's favorite fractional monzos, and from that I think he could figure out how to do planar 7-limit...
... There isn't any. Number theorists call things like the Tenney norm a "height". Maybe I should quit saying that word. ... I am not a Fokker expert, but if...
i've been playing around on a 19-edo keyboard at the Sonic Arts Gallery, with a version of the diminished scale in 19. it alternates steps of 3 degrees of 19...
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