The real answer to inharmonicity is...

[Ron Nossaman]

At 08:57 PM 8/15/98 -0700, you wrote:
>>Dick Beaton wrote:
>>
>>>Hi all.
>>>The real answer to inharmonicity is........a piano string acts like it is
>>>shorter than it really is....think about it......
>>>Dick MT
>
>I've thought about it, and initially agreed.  But now, not so.
>
>It came to me that I've always told customers just the opposite, at least
>when it comes to wrapped bass strings, saying, "The wrapping tries to make
>the string believe it's longer than it really is."
>
>Isn't that the whole concept behind scale designs...trying to fool the
>piano into believing it's bigger than it really is?  Or where have I gone
>astray?
>
>Keith McGavern
>kam544@earthlink.net
>Registered Piano Technician
>Oklahoma Chapter 731
>Piano Technicians Guild
>USA
>

You can tell just by tuning a piano that the bass strings are thinking
something entirely different from what the treble strings are thinking. %-)

All (*ALL*) piano scale designs are foreshortened from the theoretically
ideal logarithmic progression in order to get them into the case. The bass
strings are mass loaded with wrap to compensate for the length compromise.
Since you have to resort to larger diameter wire in the tenor section to get
the same effect, you introduce more stiffness. As someone already pointed
out, the diameter/speaking length ratio changes all along the scale so the
stiffness/length and inharmonicity change too. The wrapped strings are
easier to fool than the plain wire because you have control of a lot more
factors. This also means that you have more opportunity to screw up while
you are changing things, but that's another story. You can't do too much
with the plain wire except to make minor general tension and inharmonicity
changes unless you are willing to make new bridges.

So I think the answer is - yes, and no. The plain wires manifest
inharmonicity as if they were shorter than they are, and the wound strings,
as if they were longer than they are. 

 Ron