Kyle Major asks about alternative tuning systems.  I am no expert, but I
am fascinated by such approaches, if not always pleased with the musical
results...I will leave reccomendations to those more knowledgable.  -I- am
all about theory, though (apparently, since that's what I'll be studying),
and welcome the opportunity to engage my brain...

Kyle writes:

>I recently pondered dividing the octave by means of the harmonic series.
>Using the first 31 natural harmonics of a fundamental I arrived at a 16
>note octave.

Why 31?

>(Half the harmonics are repetitions).  The relationship from one frequency
>to the next is mathematically arithmetic and not geometric; that is, the
>distance between pitches decreases as one ascends the octave.

I'm not sure exactly what you're saying, although I understand the
idea...Let's see.  If you measure the distances between notes by frequency,
in Hz, the distance between notes -increases- as one goes up in pitch, even
if the intervals are the "same".  The percieved interval is simply a ratio
of the pitches' frequencies.  Wouldn't having the notes get closer mess
this up? Or restrict you to one octave?

220 (Hz) is an octave down from 440, just as 440 is an octave down from
880.  Thus even though the octaves are the "same" [interval], the higher
one has "twice as many" Hz as the lower one.  To overcome this mathematical
necessity, the intervals would have to get much much closer together as you
ascend the octave, with the first interval being very large indeed.  Or do
I have it all wrong? Can you cite examples?

I will be thinking about this.  In any event it is an interesting subject.

Best wishes and luck,

Bob K.