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From: sandell@ils.nwu.edu (Greg Sandell)
Newsgroups: comp.music
Subject: Re: Musical Frequencies
Message-ID: <505@anaxagoras.ils.nwu.edu>
Date: 21 Dec 90 17:38:13 GMT
References: <35111@netnews.upenn.edu>
Sender: news@ils.nwu.edu
Reply-To: sandell@ils.nwu.edu (Greg Sandell)
Followup-To: mercuri@grad1.cis.upenn.edu (Rebecca Mercuri
Organization: The Institute for the Learning Sciences
Lines: 30

In article <35111@netnews.upenn.edu>, mercuri@grad1.cis.upenn.edu
(Rebecca Mercuri) writes:
> jbovitz --- 
> 
> I'm sure that at least a half dozen people have informed you that although
> your formula is "correct", it will sound like hell. Most instruments are
> "stretch tuned" (higher in the high octaves, lower in the low octaves) to
> accommodate for the nonlinearity in the hearing process. String players do
> this "automatically" as they are playing. If you need more info (references
> on this), get back to me.
> 
> R. Mercuri

Rebecca, I think you are criticizing too quickly.  Whether the notes
will sound "like hell" or not depends on what timbre is used to
instantiate them.  If you did your best to create a piano-like timbre
while using this formula for your fundamental frequencies, yes, your 
listeners will note the attempt at imitation of a piano sound but
find the pitches to sound flat in the high range...but mainly for
associational reasons (i.e. when you hear a piano timbre, expect it
to be accompanied by stretch tuning).  If the sounds involved were
merely sine tones, or an impoverished harmonic sound (like a square
wave), I would think that the formulaic tuning would sound appropriate.
Sound right to you?

- Greg
****************************************************************
* Greg Sandell (sandell@ils.nwu.edu)          Evanston, IL USA *
* Institute for the Learning Sciences, Northwestern University *
****************************************************************