source file: m1587.txt
Date: Fri, 20 Nov 1998 11:12:34 -0500

Subject: Triads, tuners, tonality

From: Daniel Wolf <DJWOLF_MATERIAL@compuserve.com>

<Could someone explain to me why many on this list appear to be hung up o=
n
<the triad as a systemic harmonic basis?

One reason is that a large number of tuning enthusiasts are basically
committed to some traditional style of music making, but with an improved=

or enhanced (or, in some cases 'more authrntic') intonation. These
musicians are already committed to a triad-based harmonic style, prior to=

their interest in tuning.

Other musicians, however, have come round to a triadic basis after a deep=

consideration of the consequences suggested by particular musical
materials. I am quite fond, for example, of polyphonic music in pythagore=
an
intonation (c.f. Margo Schulter's postings to this list) or of Javanese
slendro (which is pythagorean in structure but not intonation). But neith=
er
of these systems lends itself to completely independent (i.e. non-paralle=
l)
part writing in more than two voices, and the introduction of an addition=
al
consonant tone within the space of the fifth is terribly convenient in th=
is
regard. If I were to work in some meantone tuning, for example, I would
probably would not reject the triadic attractions. =


Then there are altogether more experimental types and uses of 'triads'.
Partch pointed the way by cataloging the available species of triads with=
in
his tuning, each a three-member subset of the set of identities
(1,3,5,7,9,11) as well as all of the tetrads, pentads and hexads. Erv
Wilson, of ocures, has done the most consequent work along these lines,
which hold an interesting deep relationship to the partitioning problems
with which Babbitt has long been engaged.    =


With which I come to this passage by Paul Erlich:

<I haven't been taking about triads too much -- mostly "consonant"
<tetrads and pentads -- but suffice it to say that I feel the
<Balzano/Clough/Douthett approach to scales is bunk. The acoustical
<nature of simple intervals is a much stronger organizing force in music
<(at least the music I enjoy) than abstract set and group constructs.

Independent of Mr. Erlich's preferences, he certainly has to prove his ca=
se
better. I have witnessed both Balzano and Babbitt demonstrate virtuoso
aural command over the tonal materials in their respective systems (Balza=
no
in 20tet, Babbitt in 12tet), demonstrating convincingly that 'set and
group' properties are not just abstract constructions but real resources
for organizing musical works. Hearing highly structured, non-tonal music =
in
these temperaments may not reflect the modes of audition closest to the
biases of the physiological system, but it does remind one that the physi=
cs
of musical intervals has no such bias and that musical cognition, with
training, can be a far richer resource than the ear alone. (In different
domains, the works of Alvin Lucier are constantly demonstrating that the
frequencies in the margins between rhythm and pitch or pitch and timbre a=
re
both perceivable and musical rich.)

If Mr. Erlich has a formula for determining the relative strength of an
"organizing force in music", I would certainly like to know it. Naturally=
,
this should be independent of any local cultural biases. =


I can't help but note that I find it surpring that Mr. Erlich is framing
his argument in this way. His own work in 22tet is within a systwm whose
set and group properties are certainly more useful than the quality of it=
s
representation of ratios of small whole numbers.  =