Inharmonicity in strings

[Jim Coleman, Sr.]

Hi Richard:

Well, I stand corrected again. This time so does Kent. We should have
said the 8:6 relationship. It is there and can be heard. It is very
easily measured. My D3-G3 measures 2.1 cents wide at that coincidence.
It is easily heard in ghost tone fashion.

Jim Coleman, Sr.

On Sun, 14 Jun 1998, Richard Moody wrote:

> 
> 
> 
> 
> ----------
> > From: Jim Coleman, Sr. <pianotoo@IMAP2.ASU.EDU>
> > To: Billbrpt@aol.com
> > Cc: pianotech@ptg.org
> > Subject: Re: Inharmonicity in strings
> > Date: Saturday, June 13, 1998 10:33 PM
> > 
> > Hi again Bill:
> > 
> > I stand corrected by Kent Swafford. You can hear the 8:3 relationship.
> > 
> > Jim Coleman, Sr
> 
> Actually I don't think you can HEAR the 8:3.  If you can, what's the first
> thing that strikes you about the beats?  You can hear an 11th, but to
> split a hair, I don;'t think the beats that are supposed to be there (from
> the 8 and 3 partials) can actually be heard. 
> 
> 	To be truthful, I can hear the 8:3 on a synthesizer, and yes I did have
> to check the math to make certain the rate was what I thought.  This was
> starting at a -- d" (a3--d5). Still they are pretty damn weak, and given
> the difficulty (comparative) of hearing 4:3 fourths on the piano, I doubt
> they could be heard at all there.    
> 
>  I believe the original question was about sine waves having no partials
> execpt the fundamental, and the implications of that in tuning.   
> 
> But to address the postulation... no coincedent partials--no beats...
> consider the following.... 
> 
> 	These tests were conducted on an analog synthesizer, harpsichord type
> patch,(tweeked to give clearest beats)  with unlimited sustain. 
> 
> It can be demonstrated, that clear audible beats disappear out side the
> simple ratios, (non doubled)(lowest numerators)  of the intervals. 
> 
> For instance, a third, 5:4 with root at c# (3) beats 5.5 /sec.  the tenth
> at 5:2 with the F now at f' (4) beats the same.  at  17th  the ratio is
> 5:1 the beat is the same. However at the 24th or c# - f'' (F 6) no beats
> are readily descernable. In fact they seem vanish.   Now there should be a
> 10:2 but can they be heard enough to be usefull, if at all? There was
> always a doubt if I was hearing any beats  there. 
> 
> Consider the 5:3 ratio, the 6th.  Observe the ratio is composed of 2 prime
> numbers. Take f--d'  (f 3 -- d4)  Pert'near 8 bps, and very distinct.  
> What about f--d"  (f3--d5) ? NO BEATS ! !   The nearest coincedent
> partials would be 10--3. The beats should be doubled, but they are not
> nearly (if at all)  audible to hear that.
> 
> Richard Moody     
> 
> 
>