TUNING digest 1582

> From: Kraig Grady
> The question of Native American tuning is something I have been looking
> into for quite a while having a potent amount of Chipewa blood. For
> years I have been collecting transcriptions (mainly Francis Densmore) as
> well as listening to the recordings at the southwest museum which is
> about 3 miles from where I am. There they have tape from the edison
> cylinders. Still by the time these recordings were done, she was only
> able to get solo recordings where as much of this music was sung in
> groups. This music is gone for the most part or greatly corrupted by
> 12et.etc.

I once read a 19th century book on native american music out of my public
library. It was written by some missionary, who brought a piano out to
North Dakotah or some such place. He would have the native singers sing
him their favorite songs, and then he would figure out how to 'harmonise
them properly.' So thrilled would they be by finding out thereby what
their music was supposed to sound like, he reported, that they would
immediately begin to drum along. Sometimes, they would be so transported
into ecstasies by the revelation of his piano playing, that they would
drum louder and louder -- sometimes to the point where he could no longer
HEAR his piano playing!

Judy

Could someone explain to me why many on this list appear to be hung up on
the triad as a systemic harmonic basis? -- sometimes (so it appears to me)
even to the point of seeing an "abstract triad" as some sort of Platonic
object for which we should be trying to find the closest real-world
approximation (in one universe or another)? Is there something musically,
physically, or logically sacred about a triadic foundation?

Puzzled,
Steve Soderberg

A follow-up to my previous, too -brief post asking "Why triads?" It
wasn't meant to be testy, but on re-reading it came off that way to me --
so my apologies... and some explanation.

Paul Erlich describes a couple of very interesting systems. Let me talk
about the max-even 22@41. If we call this a first order max-even
structure and, forgetting about triads, follow the hint provided by the
usual diatonic that the basic (triadic) harmonic units are second order
max-even (3@7@12), then we might play around with second order max even
structures within 22@41. One interesting system is formed by 5@22@41
which would take 22@41's interval string <2222221222222122222221> and form
pentachords by superimposing the string <44545> on it (this is analogous
to superimposing <223> on <2212221> to get the usual diatonic triads).
You can work it out yourself, but what you get is five basic pentachord
types:
A <87t79> (t=10)
A' <7897t>
B <87989>
B' <78989>
C <77t7t>
where the prime indicates a rotated inversion of its original. What we
have then is two inversionally related pairs of basic pentachords (5 each)
and two penachords that seem to suggest a "diminished triad" function.

If you then draw a circle with 22 marks on it to represent the 22@41
scale, the order of the chords built on successive scale-degrees around
the circle is:

A B B B' B' A' C A A B B' B' A' A' A A B B B' A' A' C

To see the compositionally suggestive pattern this creates, draw lines
across the circle to connect identical chord types.
There's MUCH more in this system, but this should suffice to explain why
I asked "Why triads?" (Next week: "JI is a red herring")

Steve Soderberg

There is one thing about the diatonic and pseudo-diatonic scales I
mentioned which seems important but is not shared by other similar
scales such as 19 out of 22: in the scales I mentioned, a given
consonant interval is always approximated by the same number of scale
steps. This seems like an important grammatical feature without which
the sense of the scale as a fixed melodic basis could be very difficult
for a composer to convey. Stronger requirements such as Rothenberg
propriety (which requires that a given number of scale steps always
subtends an interval smaller than the smallest interval subtended by
that number plus 1 scale steps) seem less useful as they exclude such
common scales (such as the Pythagorean diatonic) from consideration.