In any group, or collection of entities, whether it be the notes
of a chord, or members of an ensemble, the number n of implied
connections between the members goes up as the square of n.
This means that we do not have a smooth linear progression from
simple to more and more complex, but rather a dramatic exponential
increase as the number increases. Although this property is purely
mathematical, it has many interesting social and perceptual
consequences.
That makes for 16 relationships in a string quartet. Say, you have
four woman in the quartet. One might be heterosexual, for example,
and one gay, another bi-sexual, and the fourth an abstinent monk.
So, as we think things through and consider all the relationship
permutations of such a relatively small, simple ensemble, we
begin to see that it is actually quite complex and rich. This is
at the relationship level—which I’m suggesting is all important—
whether in terms of the interpersonal, or in terms of rhythm
and sound.
Let’s continue to explore larger sets of relationship.
For instance, there are 114 relationships in a 12-note chord.
Some modern progressive composers like Luciano Berio,
Iannis Xankis, and especially Edgar Varese, have used this
inherent natural complexity of many-note chords to great effect.
And there are 289 relationships between the sounds of a
simple 17-step poem, or haiku.
At this point, however, something extremely interesting happens.
We can no longer consciously “follow,” as it were, all the movements
of relationship. There are simply too many. Like when we count
the number stamens or male part of a flower, we tend to go,
as all botanists know, 1-2-3-4-5-many. In other words, at a
certain point, what we see resolves itself into a cluster of
indeterminate number. This is where I think we need the idea
of resonance. You might think of this as all the various
relationships in a space vibrating together, just the way the
notes or sounds of chord do. It is here where we transition
of thinking—indeed, I would argue that must be so—from
quantity to quality. In poetry, for example, this is what we
might call a poetry’s and a poet’s sense of sound, or
resonance. This is also where the ear and intuition do and
must take over from the marks on written page.
[part I]