Kyle Major wrote:

>So the intervals between pitches decrease as you ascend the octave.  There
>are many pitches between A and E as there are between E and A.  But this,
>I believe, will happen on any finite harmonic series ending on an octave of
>the fundamental.  If we go from 1-4 we have pitches in the ratio, when put
>in a scale, of 1, 1.5, 2.  From 1-8 we have 1, 1.25, 1.5, 1.75, 2.  And
>that same crazy additive business always happens.  I didn't plan any of
>this, it simply works mathematically.

I've just written a quick and dirty program illustrating these "arithmetic
scales" on the PC beeper. It's really interesting! So if anyone still has
an old Borland Pascal and wants to try it, I can supply the source code.

Having heard several of these scales I'd agree that 16 is a fine number of
pitches, 8 being quite similar to the diatonic scale (especially in the
lower part) and 32 being a bit too much to actually distinguish (especially
in the higher part).

- Hagen