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

Paul Erlich schrieb:
>
> Klaus,
>
> I think one of the important points you're missing in your
> ruminations is the psychological similarity of pitches at 2:1, and
> the lesser but still significant similarity obtained at 3:2 and 4:3.

abstractabstractabstract! ;)

I just wanted to make a point that historically tunings weren't
systems but somehow inherent in the instruments, their tunability
and their ways of playing. And that there was a time before MIDI
keyboards.

Admittedly, it is more than likely that some of the qualities of
harmonic sounds like the human voice enter into other acoustical
artefacts too. But that doesn't necessarily mean that e.g.
equidistant tunings have to, or have always consciously included the
octave.

As I said, that stuff isn't exactly what I know, it's just the kind
of questions I ask (skeptic and spoilsport that I am).

For instance, you can derive an improper structure like the
hexachord (almost) directly from a pair of lures. One plays 4, 5, 6
-- c, e, g; the other 3, 4, 5 a fourth higher -- c, f, a. The d is
still missing, and you'd have to assume either that the melodic
8-9-10 is somehow ingrained in the melodic culture anyway, or (more
likely) that the lures really played an octave higher. This means
they could also play the seventh and the 11th harmonic, but didn't.
(Today's alphorns play in this range and often skirt them; "minor"
pieces making heavy use of the 7th and 11th harmonic are rare).

This would have two implications:

You don't have to derive a hexachord from a pythagorean pentatonic
with one leading note or from a diatonic with one note missing (*).
It also means that property (how I hope to have this term right) is
not an issue for this music, since it would have been so easy to
include the 7th harmonic of the lower instrument. Which in turn
implies that there is something in the brain that shys away from
higher primes... :o)

And Guido used 5-limit intonation. :O)

(And if this looks like an attack on the theoretical concepts y'all
have worked out: it isn't. It is (probably similar to the start of
this thread) for a good part getting the attacks of a certain
individual
on a certain sister list out of my system. And it is calling
attention to a way of seeing things that I think is not well
represented - maybe for a reason, since it involves that much
speculation.)

klaus

(*) Aside to Haresh if you read this:
You probably know many more hexatonic melodies than I do, and at
least South Indian theory gets all kinds of six-note scales by
applying the 7-minus-1 principle to any note of a diatonic. I'm
interested: Is there nevertheless some kind of preference for
hexachord-like six tone ragas?

What is "hexachord-like" in my definition? In Western white-note
terms: the gamut is c d e f g a. The A is introduced in stepwise
motion from below and falls right back to g -- this can be delayed
by an intervening f (and further by the high c, i.e. the whole F
triad).
In other words, an A always goes down, either by a 9/10 or a 4/5.
A-E and A-D don't occur; A-D would be 27/20 in my derivation, but
there is actually nothing that would prohibit A-E except maybe the
strong harmonic implications of a fourth in this context (sounds of
4:5:6,
implying a c# to come).
The finals I know of are C (German children's songs) or D (Guido's
example for the hexachord, "Ut queant laxis", which not unlikely is
from a different tuning tradition: there is a D-A, although between
phrases.
Structurally important tones are C and G (childrens' songs) or D and
G (Guido's hymn). In other words, "Ut queant laxis" does not make a
great distinction between CDE and FGA: everything tends to the
central note. In the childrens' songs, this is true for FGA only.
CDE tends towards C or extends itself to G via F.

--- 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?

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

There's that fourth!
>
> You don't have to derive a hexachord from a pythagorean pentatonic
> with one leading note or from a diatonic with one note missing (*).
> It also means that property (how I hope to have this term right) is
> not an issue for this music, since it would have been so easy to
> include the 7th harmonic of the lower instrument.

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).

> 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 . . . ??

> From: klaus schmirler <KSchmir@z.zgs.de>
> To: <tuning@yahoogroups.com>
> Sent: Wednesday, July 25, 2001 6:12 PM
> Subject: Re: [tuning] practical kook [was:] Re: nutty professor has me
confused (JI)
>
>
> And Guido used 5-limit intonation. :O)
>
> (And if this looks like an attack on the theoretical concepts y'all
> have worked out: it isn't. It is (probably similar to the start of
> this thread) for a good part getting the attacks of a certain
> individual
> on a certain sister list out of my system. And it is calling
> attention to a way of seeing things that I think is not well
> represented - maybe for a reason, since it involves that much

Hi Klaus,

*I* believe that Guido may have used 5-limit, but how did
you come to that conclusion? Any evidence? I'm really
curious about this. I've done quite a study of Hucbald,
Guido, and Hermannus Contractus and am interested in
your ideas.

-monz
http://www.monz.org
"All roads lead to n^0"

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