The full-length vibration is called the fundamental note,
and it's the loudest note you hear. But the other vibrations
have pitches of their own, quieter than the fundamental but
still quite audible, especially if you silence the fundamental.
The first harmonic is the sound of the guitar string vibrating
in halves. Its frequency is twice the frequency of the fundamental,
and it produces the pitch one octave higher than the fundamental.
Every world culture we know of uses the octave, and just about
everyone experiences it as a gratifying sound.
The second harmonic is the note produced by the string vibrating
in thirds, and it makes the note a perfect fifth higher than
the first harmonic. The fifth, and its inverse, the fourth,
are cornerstones of Western music and are ubiquitous elsewhere.
The overtone series also gives an approximation of the major
third and flat seventh, and from there you can derive pretty
much all the harmonic components of all of the music you like.
The important point here: frequency ratios of the counting
numbers make for the most euphonious sounds. For example,
the notes in the major triad have the frequency ratio 3/4/5.
Other world cultures do use scales based on more complex
intervals. For instance, Middle Eastern and Arabic musics
have a characteristic half-step (the interval between two
adjacent piano keys) as the first scale tone. Think of Hava
Nagila or the songs from Fiddler On The Roof. The half-step
is a complex interval for sure - in Western tuning, the ratio
of the two frequencies is one to the twelfth root of two.
How can such a sound be pleasing to the ear? I think it's
because a lot of Middle Eastern music uses drones, single
notes heard or implied throughout an entire piece of music.
Your ear uses the drone as a baseline to compare other pitches
to, balancing out the processing challenge of the complex
interval. In Western music, where the roots move around a
lot, complex intervals are a lot more work - your ear is continually
having to readjust to new contexts as the notes roll in, so
to add crunchy harmony on top of that can be overwhelming.
How about rhythm? Here, too, the math tends to be the kind
you can do by counting on your fingers. Just about every rhythmic
cell or motif in Western music is two, three or four beats
long, and they almost always repeat a binary number of times:
twice, four times, eight times, sixteen times, etc. Music
from other parts of the world use complex rhythms with some
larger prime number of beats involved, five or nine or eleven,
but you generally feel them as groups of smaller primes, so
you experience eleven beats as three plus three plus three
plus two, or whatever. Even the complex polyrhythms of Afro-Cuban
music are based on simple ratios - three against four, for
example, or two against three. Also, rhythmically complex
music tends to be static harmonically, balancing out the information-processing
burden on your ear. Conversely, Western classical music tends
to balance its harmonic and melodic complexity with simpler
rhythms.
People usually like music that's friendly to the formation
of memory schemas, with lots of repetition to assist with
rehearsal, modular forms to assist with chunking. In the West,
we also like alternating questions and answers, tension and
resolution, to create a feeling of cause and effect, a narrative
with a beginning, middle and end. Nearly every Western musician
is trying to achieve that delicate balance of predictable
to unpredictable, reassurance to challenge, comfort to surprise.
The ratio has been steadily changing over time. Back in the
Mozart era, life was a lot more predictable and orderly than
it is now. Musical culture has changed along with its environment.
Our attention spans are shorter, but we're also a lot more
sophisticated and demanding. Back in the 1700s, composers
were given to multiple-hour-long systematic explorations of
simple and predictable ideas to every possible logical conclusion.
Now you have an audience's attention for only a few minutes
or seconds, so you have to make your point fast and make it
stick. That means a lot more novelty and surprise combined
with a lot more insistence and repetition.
Not everyone likes music friendly to their bodies. Angry
people (like nearly every young person in America, for example),
have been seeking out increasingly large amounts of jaggedness,
grating textures, unresolved tritones and so on. My grandmother
grew up on Glenn Miller and Artie Shaw, and she lived long
enough to be utterly horrified by Kurt Cobain and Trent Reznor.
Recent classical and academic music is full of deliberate
attempts to avoid conventional methods of gratifying people,
which naturally results in music that takes an enormous amount
of labor to make and listen to, and which doesn't result in
too much pleasure for anyone involved. I think that the making
and supposed enjoyment of awful music is a strong indication
of America's
epidemic unhappiness.
What makes music 'good' to Americans in the year 2007, as
a general thing, is: internal contradiction over a strong
beat. One of the most important developments on the cultural
scene lately is the spread of the 'Jimi Hendrix chord', the
crunching E7#9 at the heart of many of his classic tunes:
Purple Haze
Voodoo Child
Here's the chord I'm talking about.
Non-musicians, bear with me, it's not as bad as it looks.
Let's take this chord from bottom to top. First there's E,
the root, home base. (In fact, there are two of them the way
Jimi Hendrix plays it - one is the guitar's open low E string,
the lowest note you can play on guitar.) Then there's G sharp,
the major third, understood throughout the Western world as
establishing a bright and happy mood. So far, so good - this
chord would sound fine in a nursery rhyme.
But then comes D natural, the flat seventh. The interval
between G sharp and D is called a tritone. Some fun facts
from Wikipedia:
The tritone is a restless interval, classed as a dissonance
in Western music from the early Middle Ages through the
end of the common practice period. The name diabolus in
musica ("the Devil in music") has been applied
to the interval from at least the early eighteenth century.
It's probably a myth that you could get excommunicated from
the church for using a tritone, but it's an important myth.
Heavy metal musicians use the tritone to signify evil, Satan,
a big middle finger to America's
dominant faith. Hendrix himself uses a bare tritone as
the intro to Purple Haze.
The tritone was exploited heavily in the Romantic period
as an interval of modulation for its ability to evoke a
strong reaction by moving quickly to distantly related keys.
Non-musicians: a sudden change to a distant key feels like
being flung unexpectedly
into another dimension.
One of the oddities of the pitch spiral is the equivalence
of different pitches separated by an octave. Going up, say,
a major third gives you the equivalent pitch to going down
by a minor sixth. 'Mirror-imaging' intervals in this way is
called octave inversion. The tritone is the only interval
that's 'left-right' symmetrical with respect to the pitch
spiral. All the way around, this is a sound with all sorts
of deeply mysterious psychological significance. The tritone
has lost a lot of its bite from common usage, the way profanity
has, but its impact remains unsettling.
So then on top of all that, the real shocker is the top
note, G natural, the sharp ninth, or in its more common name,
the minor third. The minor third between E and G feels dark,
somber, tragic, exactly the opposite of the major third's
brightness. It is not, to say the least, a common practice
in Western music to use major and minor tonality simultaneously.
It would be like a
comedy about AIDS - a glaring clash of contexts. Blues
music and its many descendants are based on delicately juggling
this strange new tonality, simultaneously bright and dark,
tragic and joyful. The signature sound of blues is the minor-sounding
blues scale over major chords. The most daring and foreward-thinking
blues musicians do it the other way, too, slipping major thirds
carefully into minor tonality. Alabama
by John Coltrane is my favorite example. It's a piece based
on a Martin Luther King Jr speech. Over an ambient minor rumble
from his band, Coltrane intones the rhythms of the words with
a minor pentatonic sax melody. At the climax of the increasingly
intense outtro, he plays a triumphant and unexpected major
third before winding back down to the ending in minor again.
Alabama
Back to the Hendrix chord. Note that the interval between
D and G is a perfect fourth, a calmly consonant sound when
you hear it by itself. So dig the amount of contradiction
tied up in this chord. It's major, it's minor, it's joyful,
it's angry. It has a huge, strong, stable base and a friendly
ingratiating top, but the top doesn't agree with the base,
because it's sitting on that unresolved tritone in the chord's
center. Very much like America. Jimi Hendrix didn't invent
the seventh sharp nine chord - it's one of the defining sounds
of blues music and all of its relatives, from bebop to hip-hop.
But Jimi really knew how to throw it in your face. And what
makes Jimi so cool is that he wasn't trying to be chinscratchingly
avart-garde; he was making dance music, pop music, music for
everyday use.
I worked on a
musical theater production at NYU with a rock drummer
named Michael Horrigan. Michael calls himself a 'primitive'
in a self-deprecating way because he does nearly all of his
playing by ear. The thing is, this cat is one of the best
drummers I've ever had the privilege of playing with. His
ear is so sensitive that when I sped a click track up from
141 bpm to 143, he could instantly tell I had, and by how
much. His rock playing really rocks, hard, and he can play
many other styles, with subtle, quiet shadings that have the
same intensity as his loud stuff. If this guy is a 'primitive'
musician, what on earth could possibly be expected of an advanced
one? Rock and roll primarily exists for musicians who aren't
well-served by our current system of music education, which
I would say is about ninety-nine percent of Americans.
I genuinely believe that Western classically-centered music
pedagogy is one of our civilization's major pathologies. It
lays a regimented, anxiety-governed structure onto kids' natural
music-making instinct, frightening a substantial percentage
of them away from ever participating in music again. The ones
who hang in treat music as a competitive sport, except without
the joy and excitement people get from sports. There's something
willfully perverse about drilling kids with a system of rules
developed on another continent hundreds of years ago. Our
current interpretation of classical music's rules is probably
a lot more narrow than it was back when the rules were devised.
Most people are surprised to learn, as I was, that JS Bach
was famous in his lifetime as an improviser, and that a great
deal of his work was centered around hymns functioning as
his era's equivalent of ubiquitous Top Forty songs. Elaborate
though Bach's embellishments may have been, he was effectively
an interpreter of pop and folk songs. The best musicians of
the modern era have all been shaped by popular culture, and
have been shapers of it: Duke Ellington, Björk, Lennon
and McCartney, Thelonious Monk, take your pick. Too many
well-educated people mistakenly believe that 'profound' cultural
experiences have to be difficult and unpleasant. The truth
is, though, that the really good stuff is friendly, utilitarian,
and exists to make you feel good.
Update:
I discovered a great paper by Marvin Minsky on this very subject,
well worth a read.
© ethan hein 2007 | back
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