Following Dave Vincent's query about these registers (Dutch name:
Bifoon), I have an answer from Judith Howard, maker of the pipes
on our Dutch-style organ, "De Witte", located in Pennsylvania:

  Interesting question!  I used to think it was just to distinguish
  between first and second Bifoon, if you like, but I don't think this
  is correct, as it seems to reflect the number of ranks.

  Carl Frei 90-key organs tended to have a single stopped rank at 16 ft
  on the Melody on the Bifoon register, which is a contradiction in
  terms in a way, as the name suggests two ranks!  (I think the open
  8 ft flute on "Cementmolen" uses that key instead.)  The 16 ft was
  often used together with the Violin (not sure if ever used with the
  Bourdon similarly?), rather than on its own, to vary the string sound
  a bit (Violins/Celestes of course could be used mainly without it).

  The Counter-melody Bifoon is always two ranks, and should be both at
  8 ft.  But modern examples (and, I'm sad to say, some rebuilds of Carl
  Frei organs) have an 8 ft plus 4 ft, to make it brighter and more
  audible against the Melody Violins, etc.  That isn't really correct.

  Some newer organs and rebuilds have multiple mutation Registers,
  e.g., Trifoon on the "Arab", which I think has three ranks including
  what we would call a Nazard (i.e., quint pitch) -- probably with an
  8 + 4, or even 8 + 2 (I need to check that out!).  I have come across
  similar on some of Elbert Pluer's organs, and others.

"De Witte" has a counter-melody Bifoon of two ranks, both 8 foot
(one octave lower than the 8 foot ranks on melody), tuned to celeste
tuning.  They are under the usual tremulant register control.

John Page, UK - Organ Builder
http://www.johnpage.co.uk/organs/