Just a note on the stringing scales for wound strings: There are
many different ways to build bass strings, and they all have _slightly_
different characteristics. The software takes into consideration
basically the desired frequency of each string according to the length
prescribed and just uses the old high school formula plus a database to
generalize the desired sizes. It will compute the tension and then
search its data to find a core wire size that will give you a certain
safety factor for that, first. Then it will add the mass with copper
windings. No biggie. But there are tradeoffs, and they exist because
different pianos use different tensions in the same length scale.

    The "cello-like" tones of a Mason-Hamlin are built around a very
high tension scale. So you can build a somewhat thicker bass string
with more mass and stretch it tighter to raise the pitch. This changes
the partials and ideally puts them more equidistant along the string.
This, I believe, favors the even harmonics, strengthening them over the
odd harmonics. Even at that, you have tradeoffs, because you can give
the core wire an extra gauge or two and decrease the copper
accordingly, or you can go the other way.

    When you slim down the core wire to the bare minimum safety factor
and increase the copper, you change the anti-node width because you
have changed the shear angle. A higher shear angle supposedly perfects
the high partials of the string, which in turn resonate better with the
rest of the tenor and treble section. This sympathetic resonance
creates the quality that old timers named the "foundation section." It
colors the piano's tone, even when those notes are not being played.
The more balanced way in which they ring in sympathy, the more color
they bring to the scale.

    A good piano will have a rather "chameleon-like" bass section that
produces different coloration, depending on the intervals played and
how loud they are hit. Steinways are like this. They sound differently,
depending on who is playing them. As long as that instrument continues
to fascinate the ear, then it will never get tired of hearing it. That
means the tone must be both pleasing and very complex. A complex set of
partials means there are many overlapping partials and they are
therefore impure. So what seems, to a tuner, to be a perfect instrument
is not necessarily all that great to a musician.

    The overall point is this: It doesn't matter whose software or
books you buy.  None of them can give you the exact scale of the
original piano strings. But basically, unless you wind your own, what
good is that information going to do you by the time you have sent a
pattern to the string maker? He is going to use his own scale in any
event. And he isn't even going to mike the original strings! He has
what is called a "scale stick." Once he has laid out your strings, he
will know how to duplicate them.

    The redeeming factor of all this is, 90% of the tone in the
foundation comes from the scale of the piano and how the bass bridge is
cut, not the ratios of core to winding of the bass strings (unless
something is really wrong with those strings). The scale of the piano
is literally cast in iron (with its associated bridges). If you fitted
a Steinway plate into a Kimball piano and mounted Steinway bridges on
its board, it would have the coloration of a Steinway. As a matter of
fact, Kimball did just that with their Bosendorfer-- which I call a
Kimballdorfer, or a Bosenballer, depending on how I feel at the time.
The better  and more precisely detailed a piano scale is designed, the
less affected it is by string differences.

    The more important factor of a tenor/ bass section is the vowel
tones "spoken" during the decay of notes and intervals, but this gets
into another subject altogether.

Craig B.