hi Yahya,

--- In harmonic_entropy@yahoogroups.com, "yahya_melb" <yahya@...> wrote:
>
>
> --- 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?

Yes.

> 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?

Chords of the type 3:7:10 have the coherant difference tones --which
is pertinant to the list, yes?--- and are useful ways to arrange
chords, and wanted to know how the math worked. Or maybe I just need
a math tutor? Anyway, can you, personally, separate the love of math
(or numbers) from love of music?!

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