Was OnlyPure not P12ths Tunings

[Stephen Birkett]

Bernhard:
>No. this method does not ensure at all, that those four combinations sound
>the purest possible (i.e. to get the smallest amplitude modulation).
>You must do a nonlinear beat summation (numerically or by 
>measurement or by ear)
>of the whole spectra of the three notes invovlved.

What is a "nonlinear beat summation"?

A single slow but loud beat will be more offensive to the ear than 
several faster almost inaudible beats, regardless of the position in 
the spectrum of coincident partials. Based on the definition of 
"purity"
as:
>the state, where the sum of the beats is minimal
the former will be judged more "pure" than the latter, since the beat 
amplitudes are not taken into consideration in this defintion. In 
other words, "purity" in this context is a moving target. So why 
bother to lock in on one particular artificial representation of the 
chimera?

>And this method is new, and that is what i filed for patenting. One 
>can not patent maths or an idea or a system, but a method you can.

This is true of course. US patents are granted for claims related to 
either methods or devices. In the old days, you couldn't patent 
software (i.e. an algorithm) directly. You had to get around this by 
patenting the software "installed on a computer [device]".  Of course 
that is now much freer. However, a method is usually patentable only 
when its application LEADS to something new. In this tuning case the 
patent would be for a new method to arrive at a public domain tuning 
formula that is already well-known. This isn't really any different 
from me coming up with a new "method" to empty garbage cans and then 
trying to get the city to licence my garbage slinging kinesthetics 
when I see the guys at the kerb infringing my patent.

>and with all that, with a usual frequency measuring ETDs is not 
>possible to measure beats correctly.
>Tuning the three notes for pure state is like tuning with unison 
>tuning precision.
>Try doing this with an ETD on one note with three strings one after the other.
>The difference you hear, is what the ETD lies. And this lie is in 
>every ETD temperament.

Unless the ETD can directly compare frequencies without using an 
intermediary target reference, in the same way the ear detects beats.

>Piano sounds are nonlinear in frequency AND time.

What  do you mean by "nonlinear in time"?

And while I'm asking for clarifications, I hope I'm not the only one 
here wondering about:
>fractal symmetry of the beat-relations to the interval relations in 
>the "stopper-tuning"
and
>Since due to the extension of the tuning matter from two dimensions 
>to three (and more) dimensions the octaves/fifths problem 
>dissappears,
What is fractal symmetry of beats and three dimensional tuning matter?

Stephen

-- 
Dr Stephen Birkett, Associate Professor
Department of Systems Design Engineering
University of Waterloo, Waterloo ON Canada N2L 3G1
Director, Waterloo Piano Systems Group
Associate Member, Piano Technician's Guild

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