Quantum Harmonics

Jo Monzo wrote:

>My idea was that quanta would specify
>a range of possibility for interpretation
>of a ratio. I'm way out of my league here -
>how about some of you physics professors
>explaining whether or not I'm on the right
>track?

I'll gratefully yield to any real professors out there. I think, though,
that you are on the right track. It's something I have thought about
before.

The first idea would be to specify a ratio in coordinates or whatever, and
also specify it's uncertainty in cents or whatever. So, instead of "play a
3/2" say "play within 3 cents of a 3/2". Or even, say "play 3 cents flat of
3/2" but in a way a computer would understand. Here, the "error" would be
an extra column in the matrix. See
http://www.cix.co.uk/~gbreed/matrices.htm for what a matrix is in this
context.

The other idea is to express the probability that a given interval will
represent a given ratio. So, 400 cents could be 60% a 5/4, 30% an 81/64 and
10% a 9/7. These figures are only examples. All sorts of algorithms could
be defined to score ratios according to nearness and simplicity. I think
this could be useful for adaptive tuning as well. You could take all the
different just interpretations of the new note, and score each according to
how consonant the resulting chords are, by whatever method you use. Then,
each value will have a probability assigned to it. The note assigned can be
either the most probable, or a sort of quantum superposition of them all.

In the example given, the pitch would be 13.7*0.6 - 7.8*0.3 - 35.1*0.1 =
2.37 cents flat of equal temperament. A more useful algorithm would score
simplicity much higher than nearness, and so give something very close to
5/4. The idea of averaging rather than taking the highest is so that
"ambiguous" notes like the D in C major can end up being tempered.

I am interested in getting my MIDI Relay program working with adaptive
tunings. One reason it doesn't yet is that I'm finding myself doing things
in fixed tunings that a dynamic algorithm would stomp all over. I'll be
glad to assist anyone working on this sort of thing. I can explain how to
get MIDI working in Windows if nothing else.

Graham

p.s. This weeks New Scientist says that the uncertainty principle in QM may
all have been a big mistake!