Re: lattice applet; Beware of McLaren part deux

Joe Monzo wrote,

>What is useful about Ming's applet is that it
>portrays visually the 'finity' displayed by Partch's
>theory of odd-limit Tonality Diamonds
[...]
>Ming wrote the Java code so that it starts with my lattice
>representation of the 5-Limit Tonality Diamond.

>Each subsequent higher-odd-limit lattice is centered
>on the same 5-Limit Diamond, and if you hold the cursor
>over the links that specify the different limits,
>you can see the addition of ratios to the system visually.

>You can see how the complexity *and the finity* of the
>system as a whole increases as the odd-limit is increased.

>So I like it because of my interest in finity.

Not that I could get Ming's applet to work, but it seems you are using
'finity' in a sense quite inconsistent with your own definition of the term.
At least I thought I had a grasp on your conception of finity when we were
discussing the Fokker stuff. Since diamonds don't tesselate to fill ratio
space, this use of the word seems quite incorrect.

Joe Monzo also included a quote from Brian McLaren, which as usual merits
harsh criticism. The passage is guilty of wild exaggeration, facile
reinterpretation of thousands of years of history, incorrect mathematical
formulae (n^2-n-1 is only correct for n=5, 6, or 7), and worst of all, a
very poor, mathematically abstract justification for Partch's procedure,
which is about as far removed from Partch's philosophy as one could get, and
lacks the slightest hint of a connection to the concept of Monophony.

I will not spend more time dissecting McLaren's piece, but I must say that
in 10 years of studying tuning theory and 4 years on this list, I have never
seen a higher garbage-to-insight ratio than in the work of McLaren. Let him
not take personal offense and may he rest assured that I hold him in the
highest regard for his efforts in favor of microtonal music and his fine
musical compositions.