back to list

Abbreviation for vals

🔗Mike Battaglia <battaglia01@gmail.com>

1/19/2012 6:26:53 PM

There was recently a discussion about dropping the wart from the end
of a val to represent the patent val. For example, instead of 12p, it
was noted that just using 12 might be better, because of
self-consistency with the rest of the naming system, so that p doesn't
refer to "patent" and to alterations to the mapping 53/1 at the same
time. So now, 12p is no longer ambiguous between a patent val and a
53-limit altered val, it's only the latter.

This is a bit nicer, but it's left us with a different problem: the
number "12" is ambiguous with scalars. So we get stuff like this:

"Suppose, for example, we take the wedge product of the 7-limit patent
vals 612 and 441, W = 612∧441 = <<18 27 18 1 -22 -34||, which is the
wedgie for ennealimmal temperament, and is a 2-val."

It's easy enough for us to figure out what's going on here, because we
already know what's going on. It would have been equally easy for us
to figure out if we replaced 612 and 441 above with 612p and 441p. But
I think it's just a horrid notation that's begging for some
misinterpretations sooner or later. I wish we could have some way to
clearly specify that the number we're talking about is supposed to
represent a val or something like that.

If we were writing this by hand, we could just say that vals are
written in boldface, so that you know a bold *12* or a bold *12f* or
what not refers to that entity as a val. Or maybe we could put a hat
on it, the same way they do with covectors, to specify that the number
12 is supposed to be shorthand for a covector. Carl proposed using
Gene's "h12" notation system to specify that we're talking about
homomorphisms. I think a better variant of this is to put a specifier
in front of the number to show what the -limit- of the val is. You can
just say that A, B, C, D, E, F... represent the 2, 3, 5, 7, 11, 13
limits. So for example, here's a few common vals:

<7 11 16| = C7
<12 19 28| = C12
<12 19 28 34| = D12
<17 27 39 48 59 63| = F17
<17 27 40 48 59 63| = F17c
<12 19 28 33| = D12d
C7 ^ C12 = <<1 4 4||

I dunno about subgroups, but I definitely like it better than "12." Of
course, you can still say things like 12&19 for meantone in general,
but this is just when actually representing vals in mathematical
equations.

-Mike