String tension (was : Birdcage pitch raise)

[Stéphane Collin]

Hello Frank, Philippe.

I know that it wouldn't be the first time that I would have to change an 
idea that I have had for a long time, but I'm still thinking right now that 
everything else being the same, a string with more tension has less 
inharmonicity.
Intuitively, you can hear the bell like sound (that is with partials much 
deviated from the theoretical geometric progression, so lots of 
inharmonicity) of a string whose tension you release.
That being said, to achieve a desired pitch with a string of a certain 
length, the thicker the diameter, the higher the needed tension.  I believe 
(uptil now) that it is the extra mass of the thick string (not the tension) 
that is capable of storing more energy from the (thicker) hammer, and 
through a well designed impedance coupling with the board, producing louder 
sounds.
In my experience, when you raise the tension of a certain string, you raise 
of course the pitch of the sound, you lower the inharmonicity (which is not 
necessarily desirable) and you shorten the sustain (which is often not 
desirable).  No increase of volume, as far as I could hear.
I did extensive what if tests with 19th century Bechstein pianos, and 
ascertained that the designer chose exactly the good tension figures in his 
scalings, achieving best sound, which is best inharmonicity pattern (gives 
nice colours and helps, yes helps tuning ET) and best sustain values, for 
wire equivalent of Röslau blue today and diapason of A4 = 440.  According to 
controversial Roberts formulas, those tensions average between 30 and 45 % 
of supposed breaking strain, with a drop in the low tenor plain strings, and 
higher figures in the wound bass strings.

This is what I think now, until someone makes me doubt, in which case I'll 
contemplate thinking twice.

Best regards,

Stéphane Collin.




>> > ...what is the point in raising the string tension ?
>>>Does it reduce inharmonicity ?
>
> On the contrary, higher tension increases inharmonicity.
>
>>>or is there any other reason ?
>
> In the case of concert grands, higher tension produces a more powerful
> pianos that could compete better against an entire orchestra in concerto
> performance situations.  In the case of smaller pianos, higher tensions
> were used so they would not appear to be such "weak sisters" to the 
> concert
> grands in the some manufacturer's product line.  This was mostly an
> American phenomenon, while the Europeans remain somewhat more focused on
> building pianos primarily for the chamber music environment.
>
> Frank Emerso