OMS Essay
[1]
Helix induces an actual “mathematical experience” in the
listener; and it does this more intensely than any other musical work
that I have found.
[2] What is the nature of the “mathematical experience” induced by Helix?
According
to the OMS model, music stimulates a large number of musical
“receptors” (also sometimes called “processors”, “mental-resources”)
which react to various aspects of the music. Most of these receptors
are primitive in nature rather than being highly analytical. They cover
a wide range of human experience, for instance: “rhythm”,
“contrapuntal”, “loud/soft”, “high/low”, “harmonious/dissonant”,
“spiritual”, “religious”, “ordered/chaotic”, “symbolic”, “emotional”.
When a large number of these receptors are stimulated in a systematic
way, the effect on the listener is massive and deeply satisfying.
There
is a category of receptors which are “mathematical” in nature: They
detect/signal effects of music which (informally speaking) are
“mathematical” in nature. For example, there are receptors that
detect/signal “componentry”, “formulas”, “structure”, “topology”,
“infinite/finite”, “simple/complex”, “order/chaos”,
“architecture/logic”, etc. These receptors are quite primitive;
and their reactions represent a mathematical intuition or reaction
rather than a precise mathematical analysis. From the listener’s point
of view, when these receptors are stimulated, the listener has an
actual mathematical experience, to a degree: The listener will
experience “componentry”, “formulas”, “structure”, “topology”,
“infinite/finite”, “simple/complex”, “order/chaos”,
“architecture/logic”. For an average listener, this experience is not
up to the level of a professional mathematician, and these experiences
may be somewhat inaccurate if evaluated from a formal mathematical
point of view. But this is besides the point – it is still a rich and
satisfying part of the musical experience, and although primitive, it
is still “genuine”.
These receptors are “truly mathematical” in
the sense that even a professional mathematician has these same
receptors; and some mathematicians will at times make use of intuitions
or primitive thoughts to assist them in their actual work. Of course,
in many cases of course a mathematician’s intuitions are more acute
than those of a non-mathematician. But when these receptors are
stimulated, the listener literally partakes of an actual mathematical
experience – primitive, but genuine.
As per the above, Helix
enables a listener to partake of an actual mathematical experience –
not as extensive as that of a professional mathematician, but genuine
as far as it goes. What is distinctive about Helix is the high degree
to which it stimulates the key mathematical receptors that are
sensitive to music.
[3] Some detailed comments on the mathematical experience in Helix:
Components:
There is a bewildering variety of componentry in this work. At times, I
think of flotsam scattered on an ocean – a tremendous amount of random
“stuff” with no obvious relationship (but then again maybe it is
related?). E.g. at the beginning we hear rhythmic pulses from various
percussion (different pulses, varying), and then a piccolo playing
against a contra-bassoon (two strange and different melodies). Probably
the composer has designed relationships among all these different
things; but if so, the relationships are not highly-evident (it is up
to us to intuit or suspect that there are relationships).
Formulas:
We sense that things are moving, accelerating, compressing, in some
kind of ordered/mathematical way – although we cannot articulate what
the formulas are. (Compare to seeing a very slow whirlpool in a large
body of water – there is a sense of formula, but only a scientist or
mathematician could determine what formulas might actually be involved.)
Structure: The work seems to be highly organized and unified from beginning to end.Salonen
describes it as a “nine-minute accelerando” with two phrases “being
pushed through constantly narrowing concentric circles …”. It is “very
rigidly structured, and based on essentially one continuous process.”
Topological: This work has a massive spatial aspect – the “helix” is a big evolving shape “in” the concert hall.
Infinite/finite:
For the most part, the “helix” feels large and finite. But as it speeds
up and compresses to its demise, there is a sense of a process that
accelerates to the infinite.
Simple/complex:
This work encompasses an exceptionally broad range on the scale of
simple-to-complex. Simple: The work can be grasped as one idea, one
“thing”, the “Helix”. Complex: The work contains a massive variety of
components, and the complexity thereof (the way the components move and
integrate) increases greatly as the work proceeds.
Order/chaos:
The work feels highly organized; but when examined in detail it looks
highly dis-ordered, chaotic. As the work evolves, both of these
impressions are intensified (it feels even more organized, but the
detail seems even more dis-ordered).
Additional comments
from Salonen: “The form of Helix can indeed be described as a spiral or
a coil; or more academically a curve that lies on a cone and makes a
constant angle with the straight lines parallel to the base of the
cone.” (This language sounds like language from the abstract of an
article in a mathematics journal).
[4] There is more to Helix than only a mathematical experience:
[a] It is a “celebratory and direct overture-like piece” (Salonen).
[b]
It is flattering to the listener: Atonal, very complex and
“mathematical”, melodies that are difficult to grasp; however it is
designed so that an ordinary listener can easily perceive the major
elements – the work is enjoyable even on first hearing.
[c]
A termination which is easy to grasp and even fun: The listener can
witness the piece terminate/self-destruct in a gigantic acceleration –
a death spiral that hits a big brick wall! Once the listener realizes
that the termination is taking place, it becomes fairly clear that the
accelerando stretches all the way backwards to the beginning of the
piece.
[d] Rich detail:
Orchestration and tone color. And there what seems like an overwhelming
amount of melodic material: A great variety of 3 and 4 note
phrases that are joined into longer phrases and melodies. The melodic
lines are relatively simple in terms of rhythm and shape (mainly small,
singable intervals); but I also find them “unfamiliar” and difficult to
assimilate. So Helix is fairly easy to hear on the “macro” level but
elusive on the detailed level. As the piece proceeds, the detail
becomes increasingly complex and “overwhelming”; but the macro level if
anything becomes clearer and simpler.
Having listened to a recording many times, I am now able to focus more attention on the detail, and I find it very interesting.
[e]
Helix is appealing and even “user-friendly” – but the appeal is without
much use of conventional methods (such as emotion, melody,
drama/narrative, harmonic structures, etc.). Salonen makes use of
less-used kinds of stimulation (mathematics, “ideas”, novel
colorations, an individualistic working of simple against complex, his
invention of “the Helix”, the death-spiral, …) and gets a compelling,
memorable result.