Kelly,

--- In harmonic_entropy@yahoogroups.com, "traktus5" wrote:
[snip]
> 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.

What you call "height" would seem to be what
mathematicians call "Greatest Common Divisor"
or "GCD".


> You have to admit that, according to Paul's theories, the height
> of a chord in a series is related to its harmonic entropy, ...

??? I don't think I can admit what I don't understand ...!


> 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