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Decatonic Harmony

🔗Kalle Aho <kalleaho@mappi.helsinki.fi> <kalleaho@mappi.helsinki.fi>

2/28/2003 2:47:34 PM

I wrote:

> > What I find quite interesting about all these dissonant chords is
> the
> > fact that they would probably sound even more dissonant in just
> > intonation.

Paul wrote:

> it seems to me their tuning in just intonation is "undefined". do
you
> see it differently? hold on, this isn't really a making microtonal
> music question -- reply on tuning.

Yes, you are right. I think that their tuning is undefined in the
sense that you have more than one choice for the different intervals
in the chords.

I wrote:

> > In the tempered intonation of 22-equal the Augmented
> > tetrad has all its intervals within 9-limit and both Ma-mi and Mi-
> ma
> > tetrads have their intervals within 11-limit.

Paul wrote:

> well, you don't hear these tempered intervals as 11-limit unless
> they're part of larger 11-limit otonal chords, do you?

I can't hear the limit of an interval.

Kalle

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com> <wallyesterpaulrus@yahoo.com>

2/28/2003 9:43:31 PM

--- In tuning@yahoogroups.com, "Kalle Aho <kalleaho@m...>"
<kalleaho@m...> wrote:

> Paul wrote:
>
> > well, you don't hear these tempered intervals as 11-limit unless
> > they're part of larger 11-limit otonal chords, do you?
>
> I can't hear the limit of an interval.
>
> Kalle

if you're listening to a dyad, and the upper note reminds you of the
11th in a harmonic-series chord, you're probably hearing a ratio of
11. if that does work, the 11th harmonic of the lower note is the one
that will be beating slowly . . .

🔗Alison Monteith <alison.monteith3@which.net>

3/1/2003 10:23:17 AM

on 1/3/03 1:55 pm, Alison Monteith at alison.monteith3@which.net wrote:

"wallyesterpaulrus " wrote:
--- In tuning@yahoogroups.com, "Kalle Aho <kalleaho@m...>"
<kalleaho@m...> wrote:

> Paul wrote:
>
> > well, you don't hear these tempered intervals as 11-limit unless
> > they're part of larger 11-limit otonal chords, do you?
>
> I can't hear the limit of an interval.
>
> Kalle

if you're listening to a dyad, and the upper note reminds you of the
11th in a harmonic-series chord, you're probably hearing a ratio of
11. if that does work, the 11th harmonic of the lower note is the one
that will be beating slowly . . .

Hmmm. Just like that!

a.m.