source file: mills2.txt
Date: Mon, 9 Jun 1997 09:58:18 +0200

Subject: Re: Comments on the importance of tuning in New Scientist.

From: mr88cet@texas.net (Gary Morrison)

I found Lucy's quotation from James Iliff in the New Scientist very
interesting.

   Some comments:



>An alternative basis for deriving musical intervals may be of great
>acoustical and mathematical interest in itself.  But its musical
>significance may be slight.

   I'm inclined to expect something more like the reverse.  Lucy's belief
that pi has anything to do with tuning, best I can tell, holds marginal
interest at best both scientifically and musically.  Still, in my admittely
brief experimentation with LucyTuning, it struck me as an interesting
tuning with definite musical possibilities.

   But I should qualify that by saying that it strikes me as one of a long
list of interesting tuning possibilities, and at a quick glance, it seems
to me to be somewhere in the lower middle priority-wise of that list.




>For most of us, the difference between the "cooked" [tempered] and the natural
>[just] version is so slight that it becomes lost in the idiosyncracies of
>performance.

   I believe that to be both thoroughly true, and thorougly false in two
different ways.  Anybody who has played an indefinite-pitch instrument
(e.g., virtually all orchestral instruments) can easily confirm that the
pitch-biasing imperfections of these instruments, combined with the time
and attention limits of normal-speed music, make it extremely difficult to
precisely perform in, for example, 12TET vs. QC meantone, much less the
subtle variations of different well temperaments.  There's not doubt in my
mind that that's true in all but sustained chords, and I think it's
important for mathematical theorists to bear that in mind.

   But there are very important limits to that argument.  Firstly,
sustained chords certainly do occur occasionally in normal-speed music, and
they probably get the most attention in the audience's mind, at least when
it comes to how the tuning affects them.  Second, there certainly are
plenty of definite-pitched, and at least much-more-definite-pitched,
instruments out there.  Guitars and pianos are extremely common examples of
these, along with electronic instruments.

   But certainly the most important caveat to this argument, is that it
applies only to distinguishing temperaments (or not) of traditional pitch
relationships, and entirely ignores nontraditional pitch relationships.
The difference between, for example, a 9:7-frequency-ratio supramajor third
and a normal major third is very easily audible in normal-speed music.
Also, that large a pitch discrepancy from "normal" tuning (nearly a
quartertone) is well outside the semirandom deviations due to instruments'
pitch indefiniteness.

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