Let me break this down into very small pieces.

In the West we have a concept in music theory which is described as
"Harmony".  Harmony is centered around the idea that a particular section
of music can be regarded as having a unifying center - even theories of
sound organisation which move beyond the traditional recognise this
feature.  In traditional harmony the center was refered to as "the key" of
the piece.  This is not about simultaneous soundings of pitch, one can play
a line of melody and it will be in "a key".  Indeed the ability of a melody
to suggest a "key" or to suspend that expectation is a feature of the
melody which is generally remarked on.

Harmony is phrased around the concept of "chords" - "chords" *NOT* harmony
are are "simultaneous soundings of pitch".  InWestern Harmonic description
the Chord is the carrier of harmonic weight.  Even when the pitches are not
sounded simultaneously, we are expected to relate them into a "chord".  If
I play an arpeggio, then people are expected to take that arpeggio as if it
were sounded simultaneously.

To get from *chords* to *harmony* it is required to understand that within
the context of *a key* certain chords are followed by other chords.  The
sequence of chords are also refered to as "the harmony" of a section, and
how they establish, alter, or deny the "key" is the central concept of
tonal harmonic theory since at least 1900.

Because Harmony was conceived of as the "vertical" in music, and melody the
"horizontal" some means of connecting the one to the other was required.
This became the theory of "counterpoint".  The idea of counterpoint was
how one produced harmonic - supposedly vertical changes - with horizontal
effects.  One could build a theme which had the required features -
entrances for fugues and so on, but putting in the various artifices of
counterpoint, knowing that when played simultaneously with itself, or with
other material - it would produce the "harmonic progression" which was
desired.

The problem with all of this as a general description of harmony is
that the original "vertical versus horizontal" definition was always a
convenient fiction.  It had not even really been established before it was
attacked in music.  Bach can as easily establish a key with a single line
as with a set of chords, so too can Chopin.  Conversely the simultaneous
sounding of pitches does not assure a sense of harmonic center.  Any
reasonably competent composer can construct a progression which lends
itself to no key, and produces the requisite harmonic unsettling effect
known, for worse not better, as "atonality".  Yet one can use chords which
are all "triads and simple dissonances" to quote Schoenberg.

Clearly there is also a *horizontal* dimension to Harmony in how people
percieve it.  This inescapble fact, back by practice means something quite
simple:

   The description of Harmony as presented in Western theory is a
   description of *pragmas* - small units of practical symbolisation,
   and not of any universal physical or mental phenomenon.

These pragmas produce - in their implementation - produce the desired
effects, but they are not directly related to their basis in perceptual
or physical reality.  There is nothing wrong with this so long as one is
dealing with the vocabulary they were developed for.  But it leads to
intellectual problems when applied to other vocabularies.  People begin to
believe that because other musical cultures do not have a Western style
notion of harmony, that they have no harmony.  This is about as absurd
as declaring that because they do not have Indo-European Gramatical
structures, they don't have Gramar.

Since Western Harmonic Theory is not a description of an external thing we
are left with a few basic logical choices:

1.  It is a complete construction based solely on exposure.  That is people
don't hear harmony, but are trained to hear it.

2.  It is based on some universal physical phenomenon, which only the West
has discovered, leading it to be superior to all those cultures which have
not discovered it.

3.  It is based on a mental mechanism which, while the mental mechanism
is universal, its particular manifestation is the result of exposure and
development.  This would make harmony something akin to language - the
overwhelming percentage of people, if exposed to language learn language.
Almost all of those who do not can have physical defects pointed to, or
have suffered through extreme trauma.

The problem with 1, is that Western music seems to be acceptable to large
numbers of people not in the West.  If Western harmony were a construction,
we should expect it to be as bewildering as English is to a Japanese
speaker.  This is not what we observe, and hence makes this first
conclusion very unlikely absent much special pleading.

The problem with 2 is the converse, if Western Harmony were an advanced
form of a reducible physical fact, then we should expect Western Harmony to
overwhelm all other forms the way Western technology, when it has grasped
a physical fact unknown to other cultures, overwhelms the technologies of
other cultures.  Again, this is not what we see, instead many other
cultures have musical forms which are equally compelling to Westerners
as tonal harmony.

Which leaves us with 3 - Western Harmony is a manifestation of some basic
perceptual mechanism or mechanisms, but its specific form is by no means
deterministic from some simple physical fact.  This does not mean that
there are not physically measurable phenomena which relate to Harmony, but
instead that the particular use of those physically measureable processes
will not necessarily be duplicated in other societies which make different
choices about their balance and use.

This does not make Harmony "too broad to be of use", it merely means
that Harmony in any given context will mean "Harmony as it manifests itself
in the style of the particular culture." The same as manners, fashion,
language, morals and a host of other concepts we are familiar with being
both universal, and yet also variagated.

Stirling S Newberry [log in to unmask]