Many thanks to Melvyn Wright for his explanation of small organ scaling
(MMD 970829).  His simple suggestion of transposing the scales into C for
comparison has solved a puzzle that has been entertaining me for ages.

Here's how I've applied Melvyn's suggestion to the two organette scales
I have at the moment: a 14-note McTammany style, and a 20 note Celestina.
The 14-note is scaled in A with a compass over 2 octaves from A to F#.
Transposed to C, this becomes C to A.  The only sharp is a single A# in
the middle, as predicted.

The Celestina is in A-flat over 3 octaves, Ab to F.  Not quite the same.
But transposed to C, it's still C to A.  It has C, F, G and A# in the
bass, C to C in the middle octave with F#, G#, and A#, and C to A in the
top octave with no sharps.

OK, I'll admit to a total lack of experience in this area.  Modulations in
A-flat are beyond me, but with it all transposed to C the how and why of
it becomes much clearer.  Thanks again to Melvyn for the insight.

John Wolff
Melbourne, Australia.