Inharmonicity

[Richard Moody]

One topic that should be mentioned in the discussion of inharmoanicity
(sic) is that in aural tuning, it is not a theoritical concern.  By that I
mean, we can only tune by what we hear, we don't know how much or how
little inharmonicity there is.  It automatically takes care of itself when
tuning by ear.   
	Now when machines came along, they discovered that tuners tended to tune
the upper octaves sharper than measured. This turned out because of
inharmonicity. Octaves are tuned according to their coincedent partials.
Second partial of the lower note to the first partial of the upper note.
So if the second partial is a little sharp, the first partial being tuned
to it, in order to sound beatless will turn out to be a little sharp, from
the 2:1 theoritical.  We as aural tuners don't know how much sharper this
really is. We tune octaves beatless in a  basic manner of speaking. 
	It is well known that tuning octaves three and four up can produce the
top note beating flat with the starting note.  . The EFFECTS of
inharmonicity come into play with aural tuners when say C4, C5, C6, C7 is
tuned by octaves.  C7 can be beatless with C5 but beats flat with C4. 
When C7 is tuned beatless with C4, it beats sharp with C5.  Some pianos
are more of a problem than others.  This is how aural tuners get grey
hairs. 
	Now in the bass it gets WORSE, the octaves are on, but the fifths are
off, and then it becomes a test of sanity, and the hair gets gray.  On
high quality instruments this is less, but since it is the experienced
tuners who get to tune these, also explains why the  concert tuner is
often the grey haired soft spoken gentleman type.

Richard the Ramblin Ric