A few responders to this thread have said essentially "stick to what
the makers did in olden times, for they surely knew best".  However,
there is at least one reference book from olden time that flatly
contradicts this, with explicit reasons.  This was written by Samuel
Wolfenden, chief piano designer for Aeolian in London.  What he says
is fascinating, and written in 1927 is a call to arms for the computer
designed bass string, more than 50 years before the maths of the
subject was cracked!

In Wolfenden's Supplement to "A Treatise on the Art of Pianoforte
Construction" (reprinted in the 1970s by Unwin in London), chapter
XVIII starts with the startling assertion that:

  "It is remarkable that, at this date, after spun strings have been
  in use for, say, a matter of two centuries, neither in this country
  nor any other, as far as many enquiries have shown, is there in trade
  use, a method by which the tensional stress upon a spun string, tuned
  to a given pitch, can be approximately ascertained.

  "What is needed, then, is some simple process by which given
  vibrating length (i.e. distance between bridges)frequency and length,
  the required diameter can be calculated.

  "It does not comport with the dignity of such a trade as ours that
  there are items in use which are not understood.

  "In former years more British piano makers spun their own covered
  strings than is now the case, but it is plain that their methods,
  and those of professional string spinners, were empirical,  a state
  which has continued to this day."

Wolfenden then quotes piano-makers' symposia (21st December 1916,
Chicago, and 5th March 1919, New York) that show "a real desire to
cooperate in the improvement of the tone of American pianos" but
"it is evident that just the same conditions rule there as here".
(The reports of these symposia were reprinted by Vestal Press as
"Piano Tone Building".)

He then notes the improvements to overall piano scaling where even
string tension has been found to be desirable in treble and tenor and
how it needs extending to bass design.

  "The common custom has been to decide that a set of covered strings
  shall have a certain gross weight.  This settlement often has regard
  merely to the matter of cost.

  "Even when a happy guess as to the gross weight approximates to that
  which would result from calculation, the distribution of that weight
  is often exceedingly irregular; there is frequently a considerable
  excess of weight (and therefore of tension) in the middle part of the
  range.  Sometimes this excess of weight extends to the whole set.

  "Naturally, such excess, whether partial or total, tends to aggravate
  the characteristic defect of bass piano tone, viz., the preponderance
  of the first overtone, often so pronounced as to eclipse the pitch of
  the fundamental, particularly when the strings are very short."

Wolfenden then proceeds to report his measurements of wire and windings,
and proposes his rules for spun [wrapped] string design.  Radically for
1927, he gives his results in millimetres.

Anyhow, my own take on this is that a master of the piano trade spelled
out his concerns about the unscientific, and illogical, process of bass
string design and the need to do something a whole lot better.  These
days, we're lucky that we can indeed do a lot better, and vindicate
this writing of over 90 years ago!

I'm just in the process of fitting my third set of computer-scaled new
bass strings, and am sure that Wolfenden at least would wholeheartedly
approve.  I've used the computer-scaled strings made by Barney Unwin of
the Deben Wire Company, and the results have been highly satisfactory.

Julian Dyer