Nonlinear string density (was: Convert a 12-tET guitar to JI)

Hi, John,

> Here's a wacky thought: could piano strings be made to have more
> harmonic overtones (offsetting the effect of string stiffness, at
> least partially) by careful invocation of nonlinear string density?
> If so, would the result sound more pleasing, or less? Has this
> ever been done?

Bass strings, yes. We adjust the lengths of the un-, or less wound
sections at the ends of bass strings at the design stage of
scaling/rescaling to tailor inharmonicity. Partly this is for effect,
but far more often better to match the less adjustable plain wire at
change-overs and to even out variations in the original. Here, a shorter
length between the end of the winding and terminations predicts results
of lower inharmonicity (alias, higher harmonicity - also, overall
length, core wire size and tension affect this). Dave Sanderson holds a
patent for additional nonlinear loading, I think in the form of 'bumps'
or thickened winding at the bridge end. As to nearly harmonic partials,
his father Albert (I think who developed the standard bass string
inharmonicity formula, along with the Sanderson Accutuner family) wrote
that his experiments made alien and lifeless sounding strings, but I
really prefer the more harmonic, nearly organ-like sound of old
Chickering scales to the more bell-like Steinway type. The latter may
'project' better, but possibly in the same way stretched treble tuning
does.

Clark

[I wrote:]
>>Here's a wacky thought: could piano strings be made to have more
>>harmonic overtones (offsetting the effect of string stiffness, at
>>least partially) by careful invocation of nonlinear string density?
>>If so, would the result sound more pleasing, or less? Has this
>>ever been done?

[Clark wrote:]
>Bass strings, yes. We adjust the lengths of the un-, or less wound
>sections at the ends of bass strings at the design stage of
>scaling/rescaling to tailor inharmonicity. Partly this is for effect,
>but far more often better to match the less adjustable plain wire at
>change-overs and to even out variations in the original. Here, a shorter
>length between the end of the winding and terminations predicts results
>of lower inharmonicity (alias, higher harmonicity - also, overall
>length, core wire size and tension affect this). Dave Sanderson holds a
>patent for additional nonlinear loading, I think in the form of 'bumps'
>or thickened winding at the bridge end. As to nearly harmonic partials,
>his father Albert (I think who developed the standard bass string
>inharmonicity formula, along with the Sanderson Accutuner family) wrote
>that his experiments made alien and lifeless sounding strings, but I
>really prefer the more harmonic, nearly organ-like sound of old
>Chickering scales to the more bell-like Steinway type. The latter may
>'project' better, but possibly in the same way stretched treble tuning
>does.

That's really fascinating; thanks much, Clark! Now I really wish I
could run some numbers thru a finite element program. It strikes me
that a single "point mass", x distance from the bridge and y mass,
(x and y to be solved for) could effectively counteract the
inharmonicity of piano strings. O'course, the strings are VERY close
together once they double and triple up, so could an actual mass be
found that would both fit and make a difference?

And, from what you're saying there could be patent issues. Exactly
what Dave K, was hoping to head off!

Senior thesis, anyone?

JdL