Kelly,

--- In harmonic_entropy@yahoogroups.com, "traktus5" wrote:
>
[snip]
> >
> > Let's take your first example:
> > Sequence: 4, 5, 6
> > Double the middle term:
> > Sequence : 4, 10, 6
> > Rearrange: 4, 6, 10
> > so that : 4 + 6 = 10
> > Is that what you mean?
>
> Yes.

Good!


> > More generally, if we call the middle element m,
> > and the common difference d, we have:
> > Sequence: (m-d), m, (m+d)
> > Double the middle term:
> > Sequence : (m-d), 2m, (m+d)
> > Rearrange: (m-d), (m+d), 2m
> > so that : (m-d) + (m+d) = 2m
> >
> > Yes, the pattern holds for any values of m and d
> > that are integers.

Did you follow this reasoning? Do you see
that it means that "double the middle term
in an arithmetic progression is always equal
to the sum of the two outside terms"?

In other words, we've proved that the pattern
you suspected really does hold - always.


> > As I said, an interesting pattern. But I can't
> > help but ask myself: what does this have to do
> > with Harmonic Entropy?
>
> Chords of the type 3:7:10 have the coherant
> difference tones --which is pertinant to the
> list, yes?

Yes, I see.


> --- and are useful ways to arrange chords, and wanted
> to know how the math worked.

So, I hope it is clear now?


> Or maybe I just need a math tutor?

That'll be 5 bucks an answer, then ...! ;-)


> Anyway, can you, personally, separate the love of math
> (or numbers) from love of music?!

Oh yes, easily. They both draw on my love of pattern,
true, but each has also other dimensions and aspects
that the other doesn't share. And maths doesn't make
me dance!

Regards,
Yahya