lincoln@eosp1.UUCP (Dick Lincoln) (03/12/84)
The smaller the piano, with shorter strings and less string tension,
the more you must tune the top sections increasingly (with pitch) sharp
in order to get them to *sound* in tune. Every piano tuner I know has
told me that and I have found it true myself (I occasionally have to
tune pianos). This is because:
(1) The shorter and looser the string (or string set), the less
energy is can store from the hammer strike, and
(2) The less energy a string stores, the more its sound is dominated
(in the listener's perception and memory) by the time the hammer
remains on the string (the "strike" sound), as opposed to the
time the string continues to impart "significant" acoustic power
after the hammer falls away.
As all you linear feedback - servo mechanism types out there remember,
the Laplace Plane locus with damping of a two-pole, one zero (at the
plane origin) transfer function resonates at a *lower* apparent
frequency (projection on the imaginary axis) as the damping increases.
Thus the strings actually sound lower in pitch while the hammer remains
damping them.
This is a technical explanation of why spinet pianos and the like must
be tuned sharper in the high registers than 9ft. grands - their top
notes are more dominated by the lower pitch sound while the hammer
remains on them because they can't store as much strike energy and
continue to vibrate as long after the hammer leaves as can longer,
higher tension "grand" strings.
Thus tuning spinet treble sections with a "tuning machine" sounds (ha)
to me like an exercise in complete frustration.
I know of no reason why bass sections should be tuned increasingly flat
with decreasing pitch, nor am I aware of anybody who actually tunes a
piano that way. Of course, I haven't met every piano tuner in the
world. I'll discuss this at length with my piano tuner when next I see
him.
Dick Lincoln - EOSC, Princeton, NJ
{decvax!ittvax,allegra,princeton}!eosp1!lincoln