--- In harmonic_entropy@yahoogroups.com, "traktus5" wrote:
>
> Hello. For chords such as 3:7:10, and 4:6:10, where the
> difference tones land on the chord tones (ie, 10-7=3, 10-6-4;
> Helmholtz commented on these, and I like them too!)...I had
> a question. This is probably axiomatic to the math adept
> (but an exciting mystery to me!):what math principle is it
> that accounts for the fact that if you take 3 adjacent
> numbers in a sequence (eg, 4,5,6...or 3,5,7) and double the
> middle one (to get 4,6,10...and 3,7,10), that you get 10-7=3,
> 10-6=4? (Don't laugh...)

Not laughing, Kelly; it's an interesting pattern.

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?

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.

As I said, an interesting pattern. But I can't
help but ask myself: what does this have to do
with Harmonic Entropy?

I almost think you need to join - or start! - a
list on numerology. ;-)

Regards,
Yahya