A LATTICE IS A LETTUCE LEAF.....

Greetings:

You are probably wondering what I refer to when I compare your
beloved lattices to lettuce. I know that you believe that lattices
show certain relationships which are, I suppose, impossible to
imagine in the mind. This allows a lattice to represent a certain
harmonic structure, or at least, its possibilities or paths. The
problem is what direction should one ratio go? How do you determine
what ratios are placed where? Do you use a subjective scale of
interval "importance" to determine where your ratios are configured
in your lattices?
I really do not see the benefit of these things in the first
place. They seem like theoretical jargon which is only able to
display complexity. What is the use of having
these "multidimensional" lattices when it is impossible to look at it
and see everything going on? If you believe that these lattices
represent harmonic structures accurately, you are wrong. These
ratios can be configured in any possible path or direction either in
1, 2, or 3 dimensional space. I do not believe you have created one
in supposed "7-dimensional" space. What exactly does the "seventh
dimension" look like, and how would you know what it looks like when
you live in a 3D world yourself?
I see nothing wrong with real theory in general. Theory based
primarily on objectivity is the best where certain ratios are
represented symbolically. That is fine. I only see lattices as
colorful symbolic representations based on subjectivity. Every one
of them looks alike since they are all 2 or limited 3
dimensional "representations." Lattices are nice geometrical patterns
of complexity, but nothing more really. Just as you can take a
figure from a chemistry lab and use it as one of your harmonic
lattices, it proves that a geometric figure bares no resemblance to a
tonal structure. Have you even seen what a tonal structure looks
like? No. So does this make your lattices accurate? No. They are
assumptions basically. They are assumptions which assume that a
certain "orderly" yet "complex" geometrical figure is able to
accurately represent a certain pitch class. This is simply untrue.

Sincerely,
PageWizard

--- In tuning@y..., "PageWizard, Magician of the Caverns"
<PageWizard17@a...> wrote:
> Greetings:
>
> You are probably wondering what I refer to when I compare your
> beloved lattices to lettuce. I know that you believe that lattices
> show certain relationships which are, I suppose, impossible to
> imagine in the mind. This allows a lattice to represent a certain
> harmonic structure, or at least, its possibilities or paths. The
> problem is what direction should one ratio go?

That's not a problem, it's simply a choice.

> I really do not see the benefit of these things in the first
> place. They seem like theoretical jargon

Just because one has never been useful to you doesn't mean one has
never been useful to anyone else, nor that one won't be useful to you
in the future. Plenty of people on this list have found lattices
useful in various endeavors. Don't be so quick to dismiss entire
fields of study with which you may have little familiarity.

> which is only able to
> display complexity. What is the use of having
> these "multidimensional" lattices when it is impossible to look at
it
> and see everything going on?

Why is it impossible? You may be referring to a particular lattice or
set of lattices that looked like "lettuce" to you, but there are
plenty of others.

> I do not believe you have created one
> in supposed "7-dimensional" space. What exactly does the "seventh
> dimension" look like, and how would you know what it looks like
when
> you live in a 3D world yourself?

These are issues of data visualization and have been explored a great
deal by mathematicians and visual artists outside the field of
tuning. I humbly suggest that studying these matters, and striving
for good solutions, is a far more productive approach that dismissing
it all out of hand a priori.

> I see nothing wrong with real theory in general. Theory based
> primarily on objectivity is the best where certain ratios are
> represented symbolically. That is fine. I only see lattices as
> colorful symbolic representations based on subjectivity. Every one
> of them looks alike since they are all 2 or limited 3
> dimensional "representations."

If every one of them looked alike, they would be pretty useless,
wouldn't they? Please.

> Lattices are nice geometrical patterns
> of complexity, but nothing more really.

Evidently you've never used one to compose music or to design an
instrument or anything else. I'll take a lattice over a list of
ratios any day of the week. The arithmetic involved in trying to
relate each ratio to every other in a large list is daunting, and a
lattice eliminates the necessity of doing any of this arithmetic by
portraying all the consonant relationships between pitches at a
glance.

> Just as you can take a
> figure from a chemistry lab and use it as one of your harmonic
> lattices, it proves that a geometric figure bares no resemblance to
a
> tonal structure.

That sentence doesn't make sense to me.