Craig,  The nearest size you will find in cutting dies is the 1/16-inch
Whitworth.  This is the coarsest traditional thread and the 1/16-inch
size 60 threads per inch which equates to a pitch of 0.167 inch or 0.42
mm.  If you go for a metric die then the nearest to 1/16-inch is 1.6 mm
which has a pitch of 0.35 mm, smaller than the Whitworth thread.

Organ builders use their own standard for threaded wires, since all
the standard threads are too fine for the purchase (gripability) and
adjustability of Nylon or leather nuts.

Many organ builders have their own thread rolling machines, and one of
my acquaintance has a machine that rolls threads of 1 mm pitch on any
thickness of wire.  This is just about right for its purpose, and the
nuts will never slip.  Thread rolling also has the advantage that the
finished outside diameter is greater than the wire diameter, giving
additional strength to the assembly.

Professionals may wish to buy the thread rolling machine supplied by
Laukhuff, which produces a standard pitch of 1 mm.  Those with shallower
pockets could try the small hand held thread rolling die, also supplied
by Laukhuff.

Alternatively, I find it easier and cheaper all round to buy my threaded
wires as required, from my organ builder, since I only need a few,
occasionally.

Best wishes from the UK,
Nicholas Simons

 [ A Laukhuff screw-thread-rolling-machine (Gewindewalzmaschine) is
 [ at http://www.laukhuff.de/images/stories/downloads/katalog/0.pdf 
 [ The standard model rolls 40 threads per inch (40 Gänge auf 1 Zoll)
 [ on aluminum or brass wire of 1.5 mm to 2.5 mm diameter.  Laukhuff
 [ can also supply threaded wires made to request, see PDF page 7 at
 [ http://www.laukhuff.de/images/stories/downloads/katalog/1.pdf 
 [ -- Robbie