--- In harmonic_entropy@yahoogroups.com, "yahya_melb" <yahya@...> wrote:
>
hi Yahya - thanks for the math correction. I'm terrible at it, though
love numbers...

By 'height', I was referring to how, for example, the major third in
the chord c-e-a is 12:15, whereas it's "height" in the chord
d4-f#4-b4-e5 (spelled one way) is 36:45. So, I still consider that
the first major third has a height, in a manner of speaking of 3
(though I realize 3/3 = 1), and the height of the second third is 9,
in a manner of speaking.

You have to admit that, according to Paul's theories, the height of a
chord in a series is related to its harmonic entropy, so I'm just
trying to 'tabulate' the 'heights of the intervals. How would you do
it?

thanks, Kelly

> Hi Kelly,
>
> --- In harmonic_entropy@yahoogroups.com, "traktus5" wrote:
> >
> >
> > > > > Do you think this could have any acoustical significance?
> > > > > It's a very nice sounding chord!
> >
> > > > ... no, I don't think it guarantees an overall
> > > > "nice" sound.
> >
> > But there is a correlation between the 'height' of the
> > interval in the series (ie, eg, 5/4 x 3 = 15/12) and
> > the difference tone, so there could be a connection...
>
>
> You do *very* strange arithmetic! ;-)
>
> You often write things like:
> 5/4 x 3 = 15/12
>
> This should be, instead,
> 5/4 x 3/3 = 15/12
>
> since
> a) you can always multiply any number by 1 without
> changing it, and
> b) 2/2 = 3/3 = 4/4 = 5/5 = ... = 1 = n/n for every
> natural number n.
>
> These facts mean you cna legitimately multiply BOTH
> top and bottom (numerator and denominator) of any
> fraction by the same number.
>
> Enough of the maths ... what do you mean by "height"?
>
> Regards,
> Yahya
>