Contact Ratio over a scale

Bernhard Stopper b98tu@t-online.de
Thu, 26 Aug 2004 20:01:44 +0200


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Contact Ratio

Is the ratio between the time the hammer touches the string and the time =
the wave traveling along the string from the strike point to the bridge =
and back to the strike point.

If this two times are equal, one have a ratio of 1. This means that the =
hammer moves away from the string as the string wave returns from the =
bridge and gives therefore the maximum of energy into the first =
harmonic. This contact ratio is highly dependent of the string tension =
and of the hammers stiffness. Assuming a smoothed stiffness in the =
hammer set will show any differences in the scales strike point =
stiffness.=20

Unfortunately strike point stiffness of the strings of a key can not be =
taken in correlation to contact time (and therefore contact ratio) on =
the break from bichords to trichords, since the hammers damping loss is =
different if there are 2 or 3 strings. So any theoretical calculation of =
contact time with static formulas go far off from whats happen real.

With the dynamic model of Mensurix one can measure a realistic contact =
time.
The Reference Graph allows you to make a sound classification of two =
different instruments.
Or you can use the contact ratio to set your string diameters at the =
breaks to achieve a better sound balance.

On the graph below, the Example 1 curve is from a Hamburg grand piano, =
and Example 2 is from a Vienna grand piano (modern scale). One can see, =
that around the break the contact ratio of the Hamburg piano (a scale =
from 1880) lies nearly on a straight line indicating a well balanced =
sound that will keep its line also if the hammers intonation becomes =
lost in time. A jump at the break of the the contact ratio may be =
needled out to some amount, but when the hammers intonation has gone, it =
will return.

A relative sound classification can be seen in the Graph 2 (with Hamburg =
as grey curve in reference) directly since around the break and the =
upper bass region on the Hamburg model the contact ratio is higher =
(produces a more bass pronounced sound), wheras on the Vienna model has =
less contact ratio resulting in a more harmonics pronounced sound in the =
bass region. This must not be a question of quality, but shows the =
instrument specific sound characterization.

The blue line in the graph marks the break, (on the keyboard the red =
marker)



best regards,

Bernhard Stopper
more info:
http://www.piano-stopper.de/html/mensurix_51.html
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