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