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<div>At 11:17 pm +1000 5/10/06, Overs Pianos wrote:</div>
<div><br></div>
<blockquote type="cite" cite>Substituting the figures for the above
speaking lengths into the above multiplier equation we
get;</blockquote>
<blockquote type="cite" cite><br>
<blockquote>=(135/94)^(1/(26-1))</blockquote>
<blockquote>= 1.014584831</blockquote>
<blockquote><br></blockquote>
</blockquote>
<blockquote type="cite" cite>You can now take this multiplier and
create your log-style speaking lengths from Bfl26 to A1.</blockquote>
<blockquote type="cite" cite><br>
<blockquote>Bfl26 = 94 cm</blockquote>
<blockquote>A25 = 94 * 1.014584831 = 95.4
cm</blockquote>
<blockquote>G#24 = 95.4 * 1.014584831 = 96.8 cm</blockquote>
<blockquote>. . . etc. all the way to A1 at 135 cm</blockquote>
</blockquote>
<div><br>
<br>
So to complete the series we would have:</div>
<div><br></div>
<div>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<br>
</div>
<div><br></div>
<div>Three questions:</div>
<div><br></div>
<div>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?</div>
<div><br></div>
<div>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.</div>
<div><br></div>
<div>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.</div>
<div><br></div>
<div><br></div>
<div><img src="cid:p06240606c14c54020961@[10.0.0.1].1.0"></div>
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