Re: [tuning] mccartney lattice

re:
http://www.ixpres.com/interval/dict/eqtemp.htm

> From: paulerlich <paul@stretch-music.com>
> To: <tuning@yahoogroups.com>
> Sent: Monday, March 11, 2002 8:07 PM
> Subject: [tuning] mccartney lattice (was: Re: "wolf" pack, rat pack
[Isacoff])
>
>
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
> >
> > so then, what *would* you say the colors on my lattices
> > are showing? it's *something* having to do with the
> > relationship of EDOs to JI, but what?
>
> here's a proposal.
>
> let's leave the general idea of the colors intact --
> they can be useful for showing how the consonances as
> a whole deviate from ji (as you showed me with the
> curious "lines" in your cylindrical meantone lattices).
> like marc (if i've understood him correctly), though,
> i wouldn't wrap the colors around mod anything -- they
> should just smoothly get redder, or greener, or whatever
> as you go further out.

not sure exactly what you mean by that. can you explain
further? the colors or grey-shades i used are related
directly to the amount of error of an EDO pitch from
its implied JI pitch.

> i'd also prefer it if *absolute error*, rather than
> *relative error*. this will show immediately which of
> the consonant intervals bear the brunt of the error,
> and in what proportions.

ok, in the diagrams you send me (see below) that's fine.
but i'm keeping my color-mapping too ... i'll be putting
these lattices on a separate page of diagrams.

> planes to incorporate the 7- and 11-identities should,
> at the very least, run in planes _perpendicular_ to the
> 3-5 plane. otherwise, the angles of the bands of color
> continue to merely present the error vector in the 3-5 plane.

yes, well, i'd like very much to make multidimensional
lattices using these ideas, but this 3 * 5 * x method
was the quickest way to do it when i had the inspiration.

feel free to incorporate multidimensionality in your own
diagrams; i'll put them in the definitions.

> can we agree that the *numbers* in the table should be
> 'mccartney style'; that is, very simply, the actual et notes
> as they occur in their own harmonic lattice, rather than
> where they sit with respect to the parallel ji lattice
> (as rarely would such a parallel be musically relevant).

i've actually made a few of these myself already, about
a month ago when i made the diagrams which appear on the
page. i used color-coding on them too: a unique color for
each degree of the EDO. obviously, as the cardinality
of the EDO gets larger this becomes more difficult, because
one has to keep all the different colors separate, and
the quantization of the finite color spectrum must necessarily
make each color resemble its adjacent neighbors more and
more closely as the cardinality increases. perhaps i'll
upload the few i made when i have a chance.

> if you wish, i will write a program to implement all these
> ideas in matlab, run it for all the ets on your page, and
> give you the results, to replace the tables you have
> up currently. in addition, the colors will change smoothly
> rather than in a blocky fashion, and the grid will be hexagonal,
> not rectangular.
>
> do you accept my proposal?

sure, paul! if you're able to do all the grunt work and
simply email me the graphics, i can incorporate them into
the several pages into which this one will ultimately be split.

but i won't simply "replace" my diagrams ... i'll *supplement*
them with yours, or perhaps even make yours the "main" ones
and mine the "supplemenatary" ones. but i'm convinced that
there's some usefulness to the ones i made, and plan to
keep them online.

thanks for being willing to get involved so deeply
in this, paul.

-monz

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