Tonality: Are we all Cagians, now?

Gary Morrison wrote:

** Speaking for my own opinions and experience, tonality is a useful tool
open
to a composer. Using that tool (or any other) is not mandatory but it can
be
useful, largely for the obvious purpose: creating that familiar "coming
back
home" sensation in your music. **

This is somewhat akin to the way in which Klarenz Barlough uses his
_Autobus_ programs. For Barlowe, **tonality** is a function or set of
functions whose parametric values can be set as desired by the composer; in
other words, you can turn the tonality on, up, down, or off. (The
simularity between this approach and the recent **principles and
parameters** approach of Chomsky is obvious; remarkably, Charles Seeger,
Cowells teacher - and Cage and Harrison's grandteacher - in his article on
_Dissonant Counterpoint_ (in _Modern Music_ca 1930), proposed a similar
usage of alternative parameter values in species counterpoint).

This contrasts with the traditional function of **tonality** which was to
structure a piece over time (although Gary alludes to this as **coming
back**). Functional harmonic analysis used exact returns over an (implicit
or explicit) tuning lattice to describe this structure, Schenker proposed a
model based upon linear diminutions of a single source chord (the Major
triad).

(Various **extensions** to **tonality** could be mentioned: increased
chordal density, altered chords, the Skyriabinist school, where a static
source chord is used both harmonically and melodically, Stravinsky's
playing off of diatonic and octotonic materials, or his dialectically
playful use of tonal **mistakes**; none of these, however, presents a
challenge to the essential mechanisms of **tonality** per se.)

Alternatives to **tonality** as an organizing principle include the
Schoenberg-Babbitt model of pitch class and aggregate (extended by Babbitt
to several levels and to other acoustical parameters) consumption, Carter's
exhaustive use of interval controls (which I believe were discovered by
Lou Harrison), Xenakis' set structure in _Herma_ (La Monte Young uses a
strikingly similar set organization - albeit sets with rational
relationships - in TWTP; Yuji Takahashi, indebted to both Xenakis and
Young, has also made interesting music - in Just intonation - using set
structures), Stockhausen's diminutions of motives (or, as he calls them:
formulas), and Boulez�s multiplications of a motive to create larger
structures. None of these approaches, however, has really found an enduring
following.

In contrast stands John Cage, who, partially following Varese's attempt to
integrate noises, proposed the divorce of a works division into temporal
units from a unique definition of those units by tonal means. It is perhaps
very difficult today to imagine how radical this suggestion was. Until very
recently in the western world (and still true in many places), the academic
study of music was largely identical with the study of functional harmony.
>From our present perspective - being able to splice in some **tonality**
with a sequencer, or turning the **tonality** on or off like a thermostat
with an algorithm, and the entire disjunctive tonal experience offered in
the media - Cage's proposal seems a commonplace. Even Cage's leading
European antagonist, Luigi Nono, while objecting to the use of
indeterminacy and chance operations as compositional abdication, used
composerly brute force to fill his large-scale forms with materials,
including tonal allusions or fragments, unrelated by functional tonal
schemes. In short, and in this regard, we have all become Cagians.

Daniel Wolf, Frankfurt

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Jonathan Walker has got his history right, but terminology often has a life
of its own, and now, following my Webster's Collegiate, the _wolf_ for
tuning is **a dissonance in some chords on organs, pianos, or other
instruments with fixed tones tuned by unequal temperament**, or **an
instance of such dissonance** (there is also a definition for the faulty
tones in certain stringed instruments, and the usual stuff about _canus
lupus_). I think we should accept the broader definition of _wolf_that
describes an effect or category of effects, rather than specific intervals,
and when we intend a specific interval it would be best just to give the
ratio itself.

This is tangential to another subject that has often concerned me: In
general, I am not a fan of invented terminology, and I think that an
informal neologism ban treaty within the tuning community would be of great
benefit to the public profile of our enterprise. The existing musical,
mathematical, and physical vocabulary is surely adequate and precise enough
for our modest needs!

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Re: Wolves

If I am correct, (and I have known to be wrong ) I believe that the
term "wolf" was originally used because the beating of an out-of-tune
interval was perceived to sound like the growling of a wolf. It this is
true, than any out-of-tune interval which produces beating fast enough to
"growl" (and I guess everyone would have to decide for themselves just how
much tolerance they have for beating) would be a wolf.

And for me, that includes major thirds in equal temperament. (Especially
in the tenor octave!)

Joe Downing,
in Syracuse
There are WOLVES EVERYWHERE!
(Just because you're paranoid doesn't mean that they're NOT out to get
you. I mean, even hypochondriacs REALLY get sick!)


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> Do we really want to use the same term "wolf" for these two very
> different intervals?

(And, as you very appropriately pointed out, different sources of tuning
errors.)

I tend to use "wolf" to mean either of two meanings: A note that is
conceptually correct in the tuning system but nevertheless has a systematic
pitch error from whatever source, and also the more specific case of the
break in the circle of fifths to make a diminished sixth.

I don't know whether to think that it's a good idea to use the same term
for those two meanings, but this sort of general/specific dual word usage
is certainly not unprecedented. For example:
Equal temperament:
General: A tuning based on single, consistent step size.
Specific: 12TET
Meantone:
General: A tuning based up on circle of a fixed size P5 wrapping within
an
octave.
Specific: Quarter-comma meantone.
Comma:
General: A pitch error between two systematically valid formulations of

what are conceptually the same pitch.
Specific: Syntonic comma.

I suppose one could take either of two camps in this question:
1. Music is not, and perhaps shouldn't become, an exact science. This
sort
of dual-meaning word is common, and it is poetic license, if not poetic

justice, that it should be accepted in the case of "wolf" as well.
2. Look, let's not make the same mistake for the ... what? ... sixth
time?!

Dan Wolf was, I think, insightful to point out that historically, "wolf"
has been used to describe far more divergent effects, like a note on an
instrument that, just by the acoustomechanics of the instrument itself,
tends to "stick out". I've even heard some violinists describe the open E
string on a "wolf".

So, the clear lesson here is that context is key.

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