Semi-log scale design

BobDavis88@aol.com BobDavis88@aol.com
Sun, 27 Apr 2003 15:36:51 EDT


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Okay, so I set up a spreadsheet in which I started arbitrarily with a 52mm 
note 88, took the natural log (Ln), added an increment, used the EXP function 
to return the length of the next note, repeated it down to note 21, and 
graphed it all to show a picture of the long bridge shape.

I dinked around with increments by trial and error until I found one, 0.0528, 
that gave me a note 40 that was very close to that of a Stnwy B, and overlaid 
that shape on the graph of a B bridge. I also overlaid speaking length scales 
from several other pianos onto the same graph, and they all were surprisingly 
close to the same shape, except where you would expect them to diverge in the 
low tenor, around note 28 or thereabouts.

My question is, so what? What does this mean? Why would I choose a different 
increment? I guess with a higher increment the scale would be longer as it 
went down, higher tension, lower inharmonicity or louder (depending upon wire 
size), but would "run out of case" sooner, or have to be compromised earlier 
with wound strings, third bridge, etc. Might this heavier scale be expected 
to have a slightly shorter sustain, all other things being equal?

Thanks,
Bob Davis 


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