String tension (was : Birdcage pitch raise)

[Stéphane Collin]

Hi Philip.

I'm a bit not at ease, as I'm not authority on this subject (neither on any 
other), and I'm just dealing what I know for now, which is subject to change 
without notice.
Comments below.

>Why wouldn't it be desirable to reduce inharmonicity ? Isn't it the reason
why one expect a full length grand piano to be better than an upright type ?

It is about how much is too much.  The grand design is there to counter the 
excessive foreshortening (that is : in the bass range, strings must be way 
shorter than their ideal length if you would use the same diameters of 
strings than in the middle of the keyboard : you would have to follow a 
logarithmic lengths curve, which would lead you to impossibly long strings) 
of the bass strings, which is, indeed, responsible for unacceptable 
inharmonicity in small grands bass strings.  Now, even the bass strings of a 
large grand have some inharmonicity, which proves to have two benefits : 1° 
give the piano a piano tone which is intuitively caracterized by some 
inharmonicity (if you try to imitate the sound of a piano on a synthesizer, 
and you put no inharmonicity in the upper partials you use, you get just 
that, a synthesizer sound, not a piano sound; seems that the human ear is 
used to consider complexity as a garant for liveliness; too simple sounds 
sound synthetic) and 2° make the equal temperament sound better than it 
would on a non inharmonic instrument (by alignin somewhat the discrepencies 
from "theoretical values" for the 10th intervals (plus one octave) of ET 
with the discrepencies of the 5th partial of a note).


> I also don't understand why higher tension shortens the sustain. I would
have expected the resonance factor to be more important in comparaison with
the losses by transmitting it's energy to the air or in the metal itself.
So, shouldn't it lenthen the sustain instead of shortening it ?

I must admitt that I have no obvious explanation here, but I first hand 
acknowledged the hard fact (which you can easily do for yourself) that when 
you raise the tension of a certain string in your piano, it's sustain 
shortens, and quite a lot.  Try and measure.  I suppose it is the increased 
internal restoring force in a high tensionned string that plays against the 
necessary possibility for the string to separate from it's rest position 
(elasticity) which is favourable to long sustain.



> Also, about the power... Am I correct, if I say that it give more energy 
> for
the same amount of vibrations, and so you may have a louder sound, on the
condition, that you have more weight in your hammer (so your keys will be
harder) ? I observed that on my piano, the keys are much lighter than on
some modern pianos.

Or may be, is the louder sound related with the shorter sustain, the weight
in the hammer having nothing to do with that ?

Interesting idea.  But again, following hard experimental facts, I heard no 
noticeable increase in loudness when raising the tension of a certain 
string.  Just a loss of sustain.  I believe it is the quantity of movement 
that can be stored in a thicker string that will make the difference in 
loudness.  Of course, you need a heavier hammer to produce that quantity of 
movement in the string.  I suppose there are limits where the losses (like 
the time the heavier hammer stays in contact with the string) exceed the 
gains.

Just my thoughts, hoping to raise some more comments.


Stéphane Collin.