Americans would be better at math, science and many
other difficult abstract subjects if we played and listened
to more music
clock time | your
consciousness | chemistry
| quantum physics | spirals
and higher dimensions | thermodynamics
| mathematical ratios |
anthropology
Science at its heart consists of disciplined imagination,
and there are few better ways to discipline your imagination
than music. String theory evangelist Brian
Greene says:
The tantalizing discomfort of perplexity is what inspires
otherwise ordinary men and women to extraordinary feats
of ingenuity and creativity; nothing quite focuses the mind
like dissonant details awaiting harmonious resolution.
Sometimes other musicians get upset with me for
talking about music in scientific and mathematical terms.
Most of my artist friends didn't enjoy their math and science
class, and they don't like to sully their art with such a
cold, emotionless association. I, however, have been blessed
with great teachers and parents in math and science-oriented
fields, so I like that stuff, and its many convergences with
music are part of the big excitement of life for me. Several
of the best musicians I know are also lab rats or computer
programmers. Their respective fashion senses might not show
it, but my scientist friends and musician friends lead very
similar inner lives, and their jobs are more similar than
different.
clock time
It's not at all easy to keep track of time's passage
accurately without a clock around. We usually do it with some
kind of repetitive verbalization, one that takes the form
of a simple song. In America, there are two main versions:
Counted this way, each beat is half
a second long. To get accurate clock time, you can sing either
song at 120 beats per minute, a nice medium-up tempo. It's
no acccident that the default tempo on many drum machines
and sequencers is 120 bpm.
Marvin
Minsky elaborated on this idea considerably in his essay Music,
Mind, and Meaning. He focuses entirely on Western classical
music, but the ideas apply widely. Here's my favorite line:
Can one time fit inside another?
Can two of them go side by side? In music, we find out!
Time is a mysterious subject - linear
yet cyclic, symmetric yet asymmetric, rigid yet flexible.
It's likely that Albert Einstein's
insights into the nature of time were at least in part inspired
by his study of the violin.
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your consciousness
Damasio and Edelman tell us that human consciousness is comprised
of the interactions of different brain regions as they represent
the body's internal states to one another. Your experience
has a melodic foreground, the focus of your conscious awareness,
produced in long, causal-feeling chains, bounded at intervals
by sleep and punctuated by reveries and zoning out. This melody
line has a harmonic context - a euphonious one when all systems
are humming away optimally, and a dissonant one when your
stomach is empty or upset, or when you're experiencing any
of the other myriad forms of animal distress. Note that there
are many more possible dissonant states than consonant ones.
Your bodily processes are synchronized and ordered rhythmically,
from the Krebs cycle to respiration and pulse to sleeping
and waking. And your internal music is produced on the instrument
with its own unique timbre, your body.
Emotions
predate brains in evolution. Some people think emotion
is a magic force field of some kind, and it's easy to mistake
for magic, since it's so preconscious and thus resistant to
introspection. But emotions are real bodily happenings, wired
in at birth for good evolutionary reason. Antonio
Damasio thinks of an emotion as a preprogrammed hardware-level
routine that helps the body maintain homeostasis. He sees
emotions as big networks of reflexes. A reflex is a simple
automatic survival response, while an emotion is a coordinated
system of such responses.
Music is a much more concise and descriptive transmission
and storage medium of emotional states than language is. Consider
how many words it would take to convey the specific feeling-states
of a ten-second sample of Mood Indigo by Duke Ellington, Paranoid
Android by Radiohead, Angola by Cesaria Evora.
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chemistry
| subatomic particles |
overtones |
| atoms |
tones |
| molecules |
chords |
| a simple molecule like H2O |
a simple triad |
| a chemical reaction |
a chord progression |
| a cyclic chemical reaction, like the ATP cycle |
a cyclic chord progression, like a I-vi-ii-V turnaround |
| genes |
memes |
| an algorithm for generating systems of reactions |
a song |
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quantum physics
The longer a musical note is sustained, the more precisely
we can know its frequency, better known to musicians as its
pitch. The shorter the note is, the less precisely we can
determine its pitch. If we keep making the note shorter, eventually
it becomes a click with no particular pitch at all. This is
very similar to the way that the uncertainty
principle in quantum physics describes the limits on our
ability to simultaneously know certain pairs of particle properties.
There's a specific limit to the precision with which we can
simultaneously determine a particle's position in space and
its velocity. There's a similar limit to the possible simultaneous
knowledge we can have of a particle's angle of rotation and
angular momentum; also some weird thing to do with its intrinsic
spin.
Physicist
Lee Smolin considers the world to be a network of evolving
relationships, less a 'thing' than a series of causally connected
processes and events. That's a good way to think of music,
too. You can have all the sheet music, instruments and musicians
you want, but until air molecules start
vibrating in orderly ways, there's no music. Music is
a system of organized vibrations - of drum heads, vocal cords,
strings, air molecules. At the smallest scales we know of,
matter and energy are vibrations too. The equations describing
harmonics and overtones in music turn out to describe the
vibrations of matter and energy as well. For example, each
vibrational mode of the electron field gives rise to the orbitals
in an atom - you can get an interactive look at how this works
with this
fun Java simulation.
A more realistic view is Peter Falstad's nifty quantum harmonic
oscillator. Electron orbits aren't the circles in your
high school chemistry textbook, they're intricate three-dimensional
shapes. Here's
an exhaustive catalog; have a look, they're pretty.
Most modern physics is motivated by a search
for mathematical
symmetry. Music is all about the establishment and breaking
of symmetry.
| silence |
symmetry established |
a drum hit
|
symmetry broken |
| repeating drum hits |
symmetry established |
| accenting a certain beat |
symmetry broken |
| accenting every fourth beat |
symmetry established |
| section change |
symmetry broken |
| section change every sixty-four beats |
symmetry established |
| song ends |
symmetry broken |
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spirals
and higher dimensions
Music is particularly useful in translating the concept of
regular vibrations, oscillations, harmonics, sine waves, frequencies
and amplitudes into metaphors drawn from images of our own
bodies' states. It's a convention in nearly every known musical
culture that larger frequencies are 'higher' pitches, somehow
closer to the sky, and smaller frequencies are 'lower' pitches,
somehow closer to the ground. Also, larger frequencies are
usually on the right hand, and smaller ones on the left, as
on a piano keyboard, guitar or sitar fretboard, etc.
The really strange thing about musical pitches is that they
don't form a simple linear ladder, like the order of letters
in the alphabet. Musical pitches are cyclical, like clocks
and calendars. If you start on any piano key and go up or
down one key at a time, you'll encounter the 'same' pitch
every twelve keys. Middle C is the same pitch as the C twelve
keys higher, even though the higher one sounds, well, higher.
The pitches in the Western tuning system also show circularity
when you jump in increments of five or seven keys, producing
the so-called 'circle of fifths'.
These seeming circles are actually spirals. Viewed from above,
a spiral looks like a clock. Viewed from the side, it looks
more like a ladder. Both descriptions are true.
Some physicists are starting to
think that the universe has more dimensions than the four
we can see (three of space, one of time.) It's very difficult
to wrap one's head around this idea, and the pitch spiral
is a helpful visualization tool. In mathematical terms, the
circle of fifths is a two-dimensional projection of the three-dimensional
spiral of fifths. Writing the fifths in an ascending column
or scale is a different two-dimensional projection. Remember
that spatializing pitch is as arbitrary as 'spatializing'
higher dimensions, which by definition aren't located anywhere
in space. Higher dimensions are 'higher' in the sense that
C# is 'higher' than C, because of our arbitrary naming convention.
Spirals seem to
pop up a lot at radically different scales throughout the
natural world: DNA, the water going down the drain, seashells,
tornados, hurricanes, the solar system, our galaxy.
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thermodynamics
Musical tension is like potential energy, low entropy. Musical
resolution is like the release to equilibrium, the relaxation
to higher-entropy states.
For nearly all musical
instruments, the equilibrium state is out of tune. Fine-tuning
non-digital instruments requires close human attention, even
when assisted by tuning forks or computers. When an instrument
is in tune, it's in a very specific and usually delicate physical
state dependent on many factors. To keep a guitar in tune,
you need to continually adjust the strings' length and tension
to counteract the effects of changing temperature, humidity,
the strings' gradual stretching and slipping, random jostling
around, and so on.
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mathematical ratios
There are three different ways you can control the pitch
of a guitar. You can fret the strings, which effectively changes
their length. The frequency of the string's vibration (what
you hear as its pitch) is proportional to the string's length.
A longer string will result in a lower pitch, while a shorter
string will give you a higher pitch. Making a string half
as long (the twelfth fret on guitars) gives you a tone of
twice the frequency, one octave higher.
To tune a guitar, you loosen or tighten the strings, changing
their tension. Frequency is proportional to the square root
of the tension - a string under less tension (looser) will
result in a lower pitch, while a string with greater tension
(tighter) will result in a higher pitch. In theory, you could
also tune the guitar by changing the strings' density, which
has the same relationship to frequency as tension does, though
I can't think of how you'd do this in practice.
People
tend to prefer music based on simple ratios of the counting
numbers, and tend to find musical expressions of more abstract
numbers to be confusing or annoying. Ratios of frequencies
that nearly all humans find pleasing:
| 2/1 |
octave |
| 3/2 |
fifth |
| 4/3 |
fourth |
| 5/4 |
major third |
| 6/5 |
minor third |
| 9/8 |
whole tone |
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anthropology
Like Wynton Marsalis likes to say, jazz groups are models
of an ideal democracy, and symphony orchestras are models
of the European feudal systems of antiquity. Writing an orchestral
score is like making and executing a plan. Playing a jazz
solo is like going into a situation and winging it - both
jazz and real life are full of surprises, and the better prepared
and more relaxed you are, the better things are likely to
go. Opera is performance, heightened, carefully edited drama.
Psychedelic rock, electronica, free jazz and hip-hop all invite
you behind the psychological curtains.
Anthropologist Stephen Mithen
thinks that music predates language, that it forms the evolutionary
bridge between the calls and gestures of our primate cousins
and modern speech. His theory matches my own observations
closely. Semantic language is a product of the cortex, and
while the cortex is very good at understanding the world around
it, it doesn't do such a good job of understanding itself.
Our social consciousness is itself comprised of intricate
webs of emotional happenings deeper in the brain. Using the
cortex to understand your feelings is like trying to study
a microscope with the same microscope. Music is produced with
older evolutionary equipment than speech, so it accesses deeper
and older levels of feeling, often without the musician or
listener being consciously aware of what's happening. The
good news for us is that music offers a sideways look at our
own mental processes. I may not know how I'm feeling while
I'm feeling it, but I can look for clues in my iTunes playlists.
© ethan hein 2007 | back
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