source file: m1585.txt
Date: Tue, 17 Nov 1998 16:31:35 -0500 (EST)

Subject: Re: TUNING digest 1584

From: Stephen Soderberg <ssod@loc.gov>

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