Inharmonicity in strings

[Jim Coleman, Sr.]

Hi Richard again:

In regard to your question about the higher coincident partials being
twice the speed of the lower coincident partials; this depends upon the
relative inharmonicity of the two. The higher order partials increase in
the amount of deviation from one partial to the next. As one progresses
up the scale, there comes a time when the the beat of the 4ths becomes
zero, and then reverts to narrow beating. The 3rds and 10ths do the same 
thing eventually. Whereas the narrow beating intervals eventually get much
faster. You have probably noticed by now that the 19ths beat faster than
the 12ths etc. and by more than just double.

Jim Coleman, Sr.

On Tue, 16 Jun 1998, Richard Moody wrote:

> Hi Jim, 
> 	I have always wondered about the series of harmonics above the primary
> ones.  I don't even know how to refer to them.  The interval the fourth
> with its 4:3 ratio, should have partials with a 8:6 ratio, and why not a
> 16:12 ratio as well? 
> The point is the 8:6 should beat twice as fast as the 4:3, so at the place
> in the scale where the fourth beats one per second, on paper we have the
> 8:6 beating at two per second. I don't hear these.  Do the coincident
> beats 
> reinforce each other and the peak geometry obscure the feebler more
> frequent beats? 
> 
> You mention the 8:6 ratio can be heard in ghost tone fashion.  I am
> not familiar with this term or concept.  Could you explain it further? 
> 
> Richard Moody.
> 
> ----------
> > From: Jim Coleman, Sr. <pianotoo@IMAP2.ASU.EDU>
> > To: Richard Moody <remoody@easnet.net>
> > Cc: pianotech@ptg.org
> > Subject: Re: Inharmonicity in strings
> > Date: Monday, June 15, 1998 12:13 AM
> > 
> > Hi Richard:
> > 
> snip
>  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.
> 
>