Re: [tuning] practical kook [was:] Re: nutty professor has me confused (JI)

Paul Erlich schrieb:
>
> --- In tuning@y..., klaus schmirler <KSchmir@z...> wrote:
> >
> > For instance, you can derive an improper structure like the
> > hexachord (almost) directly from a pair of lures.
>
> What's a lure, in this context?

An old germanic brass instrument modelled on mammoth tusks and with
a kind of disc around the bell said to symbolize the sun. Kind of
like a slender sousaphone. The point is, they were alway used in
pairs, presumably tuned a fourth apart.

>
> > One plays 4, 5, 6
> > -- c, e, g; the other 3, 4, 5 a fourth higher -- c, f, a.
>
> There's that fourth!

I won't deny it.

> You mean propriety? I never was a huge fan of propriety -- the
> Pythagorean diatonic is improper. Anyway, you pondered where the D
> comes from -- I think D tends to creep in because it is both an
> approximate 3:2 below A and an approximate 4:3 below G (in strict JI,
> it can't be both simultaneously, but I don't think musical intuition
> is tied so strongly to strict JI -- "temperament" of various sorts
> enters the picture in as primitive a stage as this).

But JI is built into the instruments, whatever musical intuition
says. For the pair of lures, there is only a 3/2 above G or a 10/7
below A. The question may be put differently: Why is the D, which is
only available as a ninth harmonic, used, but not the seventh?
Because it is not in a 3/2 relation to anything else?
(It begins to dawn on me that this was the point of your objection.
But then again, very strange alphorn ditties involving all those 7
and 11 ratios do exist: there's an artistic decision.)

>
> > Which in turn
> > implies that there is something in the brain that shys away from
> > higher primes... :o)
>
> Or in the way the brain tends to construct musical systems, yes
> you're absolutely right.
>
> > And Guido used 5-limit intonation. :O)
>
> Not sure what you're getting at . . . ??

Just testing the limits! (You would suppose that music from the
Middle Ages would be 3-limit. And it is probably true, since the
structure of Gregorian chant differs from the songs I would derive
from the repertoire of a lure or mouth harp duet.

Thanks and good night,

klaus