Inharmonicity

[Richard Moody]

----------
> From: Jim Coleman, Sr. <pianotoo@imap2.asu.edu>
> To: Richard Moody <remoody@easnet.net>
> Cc: pianotech@ptg.org
> Subject: Re: Inharmonicity
> Date: Tuesday, August 18, 1998 2:27 AM
> 
> Hi Richard:
> 
> No one has shown any evidence that the nodes of a piano string take up
> space thereby shortening the segments of the various partials. 
..................................
> The Inharmonicity formulas which you showed in your last post do not 
> completely describe what goes on in piano strings. For those who have 
> the RCT, the Pianalyzer shows varying amounts of inharmonicity for
different
> partials (especially for the lower order partials). Dean used standard
> formulas similar to the authorities cited in your post to calculate the
> inharmonicity constants derived from successive pairs of partials.. 
> There are yet unknown factors which are needed to account for these 
> variations. At least, these formulas get you in a good ballpark.
> 
> Jim Coleman, Sr.


Good point.  As far as tuning is concerned the inharmonicity is already
there. Unless there are techniques I don't know, ih cannot be changed by
the tuner. From the aural side, we don't hear it, but do  tune according
to it, because of the partials involved in the intervals we choose to tune
and or check and retune to get the "best" sound.  To acheive the optimum
results according to beat rates, and to "fudge" certain intervals to get
the best "blend" of "intuneness" is the skill and "art" of the tuner. 
	The provence of ih math formulas then would seem to belong to the piano
builders and rebuilders, and the designers of tuning machines, and their
users. 
	For me it is professional curiosity to look at ih formulas and theories.
Whether it is stiffness that accounts for sharp partials, or space taken
by nodes making the vibrating segments shorter, it is intersting to hear
both ideas. 

	A question I would like to ask regarding the varying amounts of ih esp
"lower order partials" is, in which strings is this found? My hunch is
that some strings have less variance amoung lower # partials, while others
(shall we start with wound strings?) have more.  

Richard Moody