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lattice angles

🔗monz@juno.com

4/21/1999 10:55:59 AM

[Erlich/aka Barbaro:]
> Your lattices do not make it possible to see the order of
> pitch of the notes in a scale. So in my view,
> the use of angles derived from pitch ends up serving
> no useful purpose.

There is a very good reason why I calculate the angle
measurement as a function of the prime's cents-value:
it is that because each prime produces a unique interval size,
using that information enables me to represent every prime
number with a unique angle.

This is important to me because my lattices grew out
of my desire to diagram all the different tuning systems
I came across in my research. These systems have not
just 3, 5, 7, and 11 as factors, but sometimes 19, 23,
31, 37, 211, 499 - all different kinds of prime-factors.

The only way I could put *all* of these on the same type
of diagram in order to compare them is to use a method
that gives each prime a totally unique representation.

As I've said in the past, this is not to say that
the lattices the rest of you use, or Canright's pitch-plotting
algorithm, don't serve their useful purposes.

But my lattices are certainly the only way I've found
that enables me to make accurate representations of Ptolemy's,
Marchetto's, Partch's, and Robert Johnson's pitch resources
*all on the same diagram*, with absolute consistency
in all the diagram measurements. I think there's value in that.

-monzo

Joseph L. Monzo....................monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
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🔗Paul H. Erlich <PErlich@xxxxxxxxxxxxx.xxxx>

4/22/1999 12:59:16 PM

Joe Monzo wrote:

>The only way I could put *all* of these on the same type
>of diagram in order to compare them is to use a method
>that gives each prime a totally unique representation.

Every lattice method we've been talking about gives each prime a totally
unique representation.