Designs on a grand scale

[John Delacour]

At 11:17 pm +1000 5/10/06, Overs Pianos wrote:

>Substituting the figures for the above speaking lengths into the 
>above multiplier equation we get;
>
>=(135/94)^(1/(26-1))
>= 1.014584831
>
>You can now take this multiplier and create your log-style speaking 
>lengths from Bfl26 to A1.
>
>Bfl26 = 94 cm
>A25 = 94 * 1.014584831  =  95.4  cm
>G#24 = 95.4 * 1.014584831 = 96.8 cm
>. . . etc. all  the way to A1 at 135 cm


So to complete the series we would have:

94.0, 95.4, 96.8, 98.2, 99.6, 101.1, 102.5, 104.0, 105.5, 107.1, 
108.6, 110.2, 111.8, 113.5, 115.1, 116.8, 118.5, 120.2, 122.0, 123.8, 
125.6, 127.4, 129.3, 131.1, 133.1, 135.0


Three questions:

1. I suppose that by "log-style" you mean you are aiming to produce 
an exponential curve.  If so, how can you do that by simply 
multiplying the numbers by x rather than raising them to a certain 
power?

2. Your example produces a line that bulges in the middle _towards_ 
the strike line as shown in the chart below, where the red line is 
straight and the blue is the graph of your lengths.  I hardly think 
this your intention.

3. What is the purpose of a curved bass bridge, no matter what the 
equation for the curve, other than to give extra length to the second 
octave and enhance the tone quality where it matters more?  To my 
mind there is no mathematical objection to a straight bass bridge.


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