But it is stiffness that is the fundamental problem. Because it is proportional
to the width, diameter or whatever the lateral dimension is CUBED of the
vibrating body a small increase in d/l will produce three times the effect
'inharmonicity'-wise (don't let's get into the definitions of that again).
(Oh! for the 'light,inextensible, perfectly flexible strings of my applied
mechanics schooldays!)


RJC,
Edinburgh.


On Mon, 8 Jul 2002 01:51:22 -0400 Stephen Birkett <[log in to unmask]>
wrote:

> Margaret wrote:
>
> >The issue of the treble having to be stretched is entirely a matter of wire
> >stiffness.
>
> Well...actually....material properties really have little effect on
> inharmonicity. This does depend on frequency, stiffness, and density, but
> the range of these factors in normal practical circumstances on instruments
> is so small as to be quite insignificant compared to diameter/length. This
> is really the only important factor. You make shorter strings, or fatter
> strings, or both together and you increase inharmonicity.
>
> >B's Broadwood probably had very little problem.  When you tune by
> >ear you automatically match the fundamental of the top note to the
> >corresponding upper partial of the octave below, so stretch is the result when
> >needed.
>
> Exactly. _All_ stringed instruments are tuned with stretched octaves to
> compensate for inharmonicity, to a lesser of greater extent. As Margaret
> says it's simply the natural thing to do.
>
> >I think wire was stiff enough and heavy enough (heavy wire is always
> >stiffer) by late 19th century to make it an issue.  Stephen Birkett will
> >know more precisely.
>
> For plain wire strings I do believe that the stiffness of steel is an
> important tonal factor, but not because it affects the inharmonity (that
> effect is negligible), rather for a different reason (that is currently
> being explored experimentally as we speak/write).
>
> Wound strings are another issue, since the effective change in stiffness
> (compared to solid brass) is very large, and this does affect inharmonicty.
> Inharmonicty for big Viennese pianos with solid brass bass strings and
> short scales is extreme. It is actually _reduced_ in later 19th century and
> 20th century pianos with wound bass strings, not increased.
>
> All pianos have high inharmonicity in the treble (diameter to length ratio
> again - b i g ).
>
> The archives are full of stuff on inharmonicity....
>
> Stephen
>
> Stephen Birkett Fortepianos
> Authentic Reproductions of 18th and 19th Century Pianos
> 464 Winchester Drive
> Waterloo, Ontario
> Canada N2T 1K5
> tel: 519-885-2228
> mailto: [log in to unmask]
> http://real.uwaterloo.ca/~sbirkett

--
Roger Clarke
Computing & Electrical Eng.
Heriot-Watt University
[log in to unmask]