Actually, I think the German notation uses "B" for "B-flat" and "H" for
"B-natural."  This is sometimes offered as an explanation of why our
modern natural sign looks like an "H" that lost a machete duel.

I agree with Robert Linnstaedt that string instrument notes can only be
sharpened, not flatted.  On woodwinds the special keys also sharpen notes,
but you can use the old recorder fingerings where you close a lower hole
to flatten some notes.  And brass instruments only allow flattening of
the pitch, and typically have natural scales in flatted keys, as Robert
mentioned.

Since band organs tend to play brass-band types of music, I think of the
black notes mostly as flats, not sharps.  My Raffin 31/84 is definitely
in the scale of Eb or Ab, so I would not notate its scale with sharps.

 [ However, band music has changed key within the last century.
 [ Previously the wind instruments were pitched in the "sharp keys",
 [ such as A, versus the modern B-flat pitch.  -- Robbie

And thanks to Melvyn Wright for a full and complete posting on organ
scales and the priorities of adding new notes.  I too mentally transpose
organ scales to C, as woodwind players do also.  My only disagreement
is that I consider the 20-note scale to begin where the notes become
continuous, so the lowest note is an "outlyer" and I'd notate it in the
key of C as:

  GG C D E F F# G A B C d e f f# g a b c d e

where I say F#, not Gb, since this note really is used for D-major and
D-7th chords.  Most music boxes and barrel organs likewise have "outlyer"
bass notes like this.  An instrument's "natural key" is best determined
from its set of chromatic notes.  The 31-note scale has enough of these
that two or three keys are almost equally natural.

Since a 20-note organ can play only in C, G, maybe F, and the related
minors, it really should be tuned in Just or Meantone Tuning, as were
most music boxes.

I have, in fact, considered building an organ with these tunings and
separate pipes for G# and Ab, etc.  Oddly, if you start off a Just
Tuning, you first run into trouble with the note D -- at which point you
may go to Meantone, which pitches the D halfway between its two possible
pitches.

Finally, there is a MIDI program, usable only with certain synthesizers,
that automatically recomputes the correct pitches for notes from chord to
chord, to keep all 3rds and 5ths in perfect Just Intonation.  I haven't
the equipment for it and haven't heard it, but it was recently reviewed
in Keyboard Magazine.

Mike Knudsen