Robbie, I was curious about the use of MIDI note numbers in formulae
and the application you have in mind.

I use MIDI note numbers in my music roll punching software to define
notes so that they appear in the correct tracker-bar order as the
machine punches them.  Most roll playing street organs have an orderly
sequence of notes from bass to treble,  but which is usually not
chromatic.  The use of MIDI note number definitions makes it easy to
relate music notes with hole positions.  The file is scanned for active
notes which are identified by their numbers, and this data is
translated into hole positions for punching.

This method is particularly useful with non-sequential scales such as
the 26-note scale used as an extension of the Carl Frei/Raffin 20-note
scale.  Here the additional six notes, which are some of the missing
accidentals in the main scale, appear either side of the sequential
20 notes in a complex order.

This is referred to as the Alderman scale here in the UK, but I am
told that Jaeger und Brommer have either adopted this scale for their
26-note organ or use one similar.  If this is true perhaps those good
folk will tell us about it.

Transposed to a basic C major scale this 26-note tracker bar lineup,
with MIDI note numbers below, is:

  d' c' f' g' a' a#' b' c'' d'' e'' f'' g'' a'' a#'' b''
  50 48 53 55 57 58  59 60  62  64  65  67  69  70   71

  c''' d''' e''' f''' g''' a'''   c#'' f#' d#'' f#'' a#''
  72   74   76   77   79   81     73   66  75   78   72


The beauty of this complicated arrangement is that a 26 note organ will
play both 26 note and 20 note music rolls, which use only the notes
from c' (48) to a''' (81) in the above sequence.

Getting back to Robbie's thread, I spend many hours re-arranging MIDI
music, using Cakewalk pro, to fit various organ scales.  Much of this
is routine work transposing to the correct key, clipping low octave
notes and shifting notes that are not in the particular organ scale.

After that comes a whole lot of tricks to substitute notes that should
be there, but are not.   I have often thought that a good Macro would
do most of the donkey work.  Is there such a thing, or some software
which would do the trick?  What are Robbie's mathematical formulae, I
wonder?   Tell us, please!

Happy Christmas to all MMDers and as much of the new Millennium as you
can manage.

Bob Essex
Warwickshire, England

 [ A common use of the note number is in an equation to compute
 [ the frequency of a given piano key (note), or organ pipe:
 [
 [   f(n) = 440*2^((n-69)/12) , where f is the frequency (Hz)
 [ and n is the MIDI note number.  (A=440 Hz is note 69.)
 [
 [ It's useful for tuning a piano or designing an organ pipe, but
 [ not much use for predicting which notes to substitute -- trust
 [ your ears and good musical sense for that!
 [
 [ It seems that you easily equate the two nomenclature schemes for
 [ the small organ.  I hope that folks who work with 98- and 125-key
 [ organ scales do too.  ;)   -- Robbie