[pianotech] Tuning the duplex sections

[George F Emerson]

Regarding a formula for calculating the longitudinal mode partial, this is 
what I am using:
LM=100355/(SQRT(((OD^2/CD^2)*(WM/100))+0.11)*L)

where LM is longitudinal mode frequency in Hz
OD is the overall diameter, including wound string wrap, in thousandths of 
an inch
CD is the core wire diameter, in thousandths of an inch
WM is a constant specific to the wrap material, for copper, 89
and L is speaking length., in inches
I'll let you deal with the metric conversions.

I am in China at the moment, and do not have access to my library, but I 
believe I got that formula from a book on longitudinal mode partials, 
written by Ellis? and available, I think, from the PTG store.  I am not a 
mathematician, so I cannot confirm the veracity of this formula, but you can 
take it for what it is worth, or buy the book from PTG.

Regarding Harold Conklin's work, I worked for Baldwin for 10 years and had 
access to Mr. Conklin's research notes, fascinating material.  His winding 
machinery was rather complex, but Baldwin's string maker, at the time, did 
produce strings to his specifications, although the more practice machinery 
that they used to make the strings was not as precise as he had envisioned 
in his design.  A weakness of his wound string design was that the core 
wires were of an unusually small diameter, and prone to breaking more easily 
than "typical" bass strings. To some extent, what was gained in avoidance of 
conflicts between longitudinal partials and harmonic transverse partials was 
lost in string longevity in heavy use environments (that is, very heavy 
handed pianists).

Frank Emerson