Z Formula

[John Delacour]

At 9:11 AM -0800 12/3/01, Joseph Garrett wrote:

>I have been using the "Z" formula as criteria for scale evaluation, for many
>years.... I hope that you will avail yourself of the possibility 
>that the Z formula does have some merit and try it...

Thanks, Joe.  That's what I've been after from the beginning.  I 
would be most grateful if you would let me have the DOS program and 
from that I shall be able to get the drift of the thing and work out 
an Excel formula to do something similar.  I've been doing all my 
calcs in Multiplan/Excel on the Mac since 1984 and DOS always reminds 
me why I got a Mac!

>using your previous scales records and re-run them using the original scale,
>(with the Z formula), and then a comparative with your "end" scale, (also
>using the Z formula). When you look at the graphs you will probably find
>that you have, intuitively been doing much the same, but without the math
>aid of the Z formula. Of course, this is speculation on my part, but I
>suspect, through trial and error, you have become intuitive in this regard.

That's almost certainly so, as in so many things to do with the 
piano.  As a stringmaker I have the advantage of having worked on a 
huge variety of scales from the finest pianos to the most awful from 
every period, and by studying the original scales, revising them, 
listening to the results, you get a sort of mental slide-rule build 
up, learn all the pitfalls and end up by looking at a rubbing and 
sying to yourself "now this one is going to be a beauty" or "oh well, 
it certainly won't sound worse"  and it's very gratifying when a 
customer has ordered a set for a 4'9" piano and phones you to say it 
now sounds really good.  Small grands are the most difficult to apply 
rules to and you have to guess from the original empirical scale what 
sort of soundboard they have and rescale on that basis.  Anything 
over 6'3" is a breeze.

But it's good to know the reasons for things and that's why I'm 
interested in this question of impedance applied to strings and would 
very much like to see how the numbers work out.  Most pianos won't 
allow an ideal "blending" of all the parameters, so however much I 
might like all the strings in a bass scale to be at 60% of their UTS, 
it's not possible on most pianos and not desirable on some where it 
is.

Thanks for the offer, but please expect a few queries while I get the 
hang of it.

JD