Robert T. Kelley

Was anybody aware of this

http://garnet.acns.fsu.edu/~rtk1218/ReconcilingTonalConflicts.pdf

?

-C.

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@...> wrote:
>
> Was anybody aware of this
>
> http://garnet.acns.fsu.edu/~rtk1218/ReconcilingTonalConflicts.pdf

No, but I see he's figured out that

[<12 19 28|, <7 11 16|, <3 5 7|]

gives a unimodular matrix and hence a way of representing the 5-limit.
This is what I proposed calling a "notation" a few years back; maybe a
better name could be found.

He also figures out you can invert it to

[|3 -1 2>, |7 0 -3>, |-4 4 -1>]

but I don't see that he notices these are [25/24, 128/125, 81/80],
which is fairly basic when doing this stuff.

Then he goes on to make the whole thing seem much harder than it
actually is, something I've been accused of, of course. I note he's
also been arguing with Agmon about whether tuning is relevant to these
mappings, which has a familiar ring to it.

Gene Ward Smith wrote:
> --- In tuning-math@yahoogroups.com, Carl Lumma <ekin@...> wrote:
> >>Was anybody aware of this
>>
>>http://garnet.acns.fsu.edu/~rtk1218/ReconcilingTonalConflicts.pdf
> > > No, but I see he's figured out that
> > [<12 19 28|, <7 11 16|, <3 5 7|]
> > gives a unimodular matrix and hence a way of representing the 5-limit.
> This is what I proposed calling a "notation" a few years back; maybe a
> better name could be found.
> > He also figures out you can invert it to
> > [|3 -1 2>, |7 0 -3>, |-4 4 -1>]
> > but I don't see that he notices these are [25/24, 128/125, 81/80],
> which is fairly basic when doing this stuff.

He cites Karp, who does some of this. I can't remember exactly what. He also cites Monzo, and generally uses terms in a way we're comfortable with, so he may have read more than he lets on.

> Then he goes on to make the whole thing seem much harder than it
> actually is, something I've been accused of, of course. I note he's
> also been arguing with Agmon about whether tuning is relevant to these
> mappings, which has a familiar ring to it.

Yes, it starts out looking promising, and then he goes through a load of theorems that I couldn't follow. Some of it's about octave equivalence, and maybe he wants some other invariant transforms. But because of the the passive-voice, pseudo-objective academic style, he never says why he's doing it, so I can't see what the point is. Perhaps there is one.

He doesn't say he's argued with Agmon, only that Agmon's paper doesn't consider tuning. And may be right to avoid it.

Graham

--- In tuning-math@yahoogroups.com, Graham Breed <gbreed@...> wrote:

> > He also figures out you can invert it to
> >
> > [|3 -1 2>, |7 0 -3>, |-4 4 -1>]
> >
> > but I don't see that he notices these are [25/24, 128/125, 81/80],
> > which is fairly basic when doing this stuff.
>
> He cites Karp, who does some of this.

I read some more, and he is aware that the three monzos above are
25/24, 128/125 and 81/80, in fact.

> Yes, it starts out looking promising, and then he goes through a
load of
> theorems that I couldn't follow.

I emailed him about that, and it turns out that all the weird
complexity results from an attempt to make things simpler. He was
worried that musicians would not understand equivalence classes, and
would not like a class representative which reduced to something other
than the octave. So, all of that complicated and painful looking stuff
is actually irrelevant and can be ignored.

Some of it's about octave equivalence,
> and maybe he wants some other invariant transforms. But because of the
> the passive-voice, pseudo-objective academic style, he never says why
> he's doing it, so I can't see what the point is. Perhaps there is one.

Now that I know the point has nothing to do with those weird formulas
involving the floor function I'm going to try again and see if his
thesis gets me somewhere.

> He doesn't say he's argued with Agmon, only that Agmon's paper doesn't
> consider tuning. And may be right to avoid it.

Well, he thinks, correctly in my view, that there are implicit tuning
implications in the whole 12+7 business, which means in "diatonic set
theory". And gosh, who would have thunk? It's a theory which arose in
a context involving tuning.