scaling question

[PNOTNR@aol.com]

I have an upright piano (a Dyer & Hughes, made in Maine) that I am
restringing. The existing scale uses no half sizes.  I think I'd like to
improve the scale by smoothing out things with the half sizes.
My question is how do I determine where to make the changes.  Whether this
involves a lot of string formulas and/or computer run programs, and whether
this is likely to make a big enough difference to be worth the bother.  The
existing scale is:

13-----(8 unisons)
14-----(6 unisons)
15-----(6 unisons)
  ---break---
16-----(8 unisons)
17-----(6 unisons)
18-----(8 unisons)
19-----(8 unisons, 2 on treb. side of break, 6 on tenor)
20-----(6 unisons)
21-----(4 unisons)

60 unisons

My first thought was to simply divide each size in half, but I run into a
problem when it comes to the hitch pin arrangement in sizes 14, 15, 17, and
20.  The old stringing was straight forward with no single strings.  If I
divide a section of 6 unisons of a size into 3 and 3, I end up with an odd
number of strings, so it seems that things won't work out so easily.
Any help would be appreciated.  If anyone wants to help me out on this, I can
furnish more information if need be.  Thanks

Gordon Large
Mt. Vernon, ME