My life has always had a soundtrack. My earliest memories are backed by Alicia de Larrocha’s “Mostly Mozart.” Or Ray Charles’ “Anthology.” Anything by the Beatles. I fell asleep to “Golden Slumbers,” and woke to “Good Day Sunshine.” Family gatherings were jam sessions. Uncles on guitar, cousins on makeshift table drum kits, aunts singing in harmony, each piece beautiful in its own way.
I remember watching my mother gracefully work the keys of her 30-year-old flute. The silver still showed where her fingers pressed down and where her bottom lip rested on the embouchure. But the body was tarnished and dented, a sign of the many years of love rather than disrespect. So I picked up the same instrument at eight-years and have been dueting with her ever since.
Dana started working with me in private lessons when I was eleven. She was a talented musician and mastered the flute exquisitely. She didn’t rely solely on her own raw talent; she understood more than the simple fingering and embouchure position. Throughout my lessons, I heard time and again the prevalence of numbers in music. Each note is a number, a unique frequency vibrating through the air. An “A” rings out at 110 vibrations per second. An “A” one octave higher oscillates 220 times per second. Like waves in an ever-stormier ocean, this cycle continues—the higher the note, the more vibrations per second. The same goes for any C, which presses towards our ears in multiples of 65 cycles per second. Or E notes, at a frequency of 82.
Numbers rule over the rhythm of a piece, too. A waltz is one two three, one two three, instruments mirroring swaying steps, swirling skirts. All the action in jazz and blues happens on the upbeat, on a one-half fraction of a note, syncopation grooving the melody along.
My favorite live show breathes rhythm. Tab Benoit, Cajun blues dreamboat, perches on a solitary stool on the stage that’s more a foot-high platform, hardly more illuminated than the dusky lighting on the faces crowding around dinner tables. He’s surrounded by a drum kit, huge speakers, and a couple amps, one of which is the resting place for a fearsome plastic gator head.
Tab’s sweating. He’s coming down off the high of the first set. He’s a few cognacs in and perched on the edge of that stool, guitar strapped to his neck. He flashes the crowd a roguish, half-drunk smile, a shock of white teeth showing through his dark scruff beard. A few cheers, a few clinks of glasses. By this time everyone is finished their eggrolls. They just want more Tab.
It’s the same routine every time he plays at Chan’s Chinese Food. He’s alone on stage, just him and his guitar. A solo interlude before another round of cranking bayou blues.
He starts to tap his foot.
One two three four…Two two three four. Thumping on the old pine floor, echoing in our eardrums. The first few picks of the strings.
His guitar is worn at the bottom and he looks comfortable with it, like he really fits it.
A strum.
He strums and picks, sometimes so sparsely that all that fills the emptiness in between is the thump thump thump thump of his booted foot on the floorboards and something intangible, like his soul is coming out through the amp instead of the electrified vibrations of his strings. I want to be his guitar.
Soon he is cranking chords. We are swimming in his blues. Everything is improvised. He harmonizes with himself, eternal runaway solos moving through his arms, his legs, his toes, his hair. And the pulsing, two, three, four, underneath.
The strings are perfectly in tune, humming together into euphoria in my ears. The pressure shifted in the air by the vibrating strings melds together. The “As” oscillating 110, 220, 330 times per second. The “Cs,” at 65, 130, 195 times. “Es” at multiples of 82, blending together in perfect consonance. Faster and faster the strings vibrate as he moves up in octave, so high the strings could break. And they do, frequently. It’s not a Tab concert if he doesn’t replace at least three strings.
Tab makes ample use of these notes and more, blending them together into the pain of a New Orleans man. Sometimes, an improvised note goes wrong—it’s just a little off, there’s a bit of dissonance. But Tab brings it home, resolves it into beautiful harmony.
These freezing cold, rainy winter-into-spring days make me yearn for Tab. I searched for some solos online to put me in a balmy mood. As I listened to his fingers smoothly work up and down the neck of his worn-out guitar, plucking out those bluesy harmonies, I wondered what makes them sound so good? What makes those slight deviations from what we expect so jarring? Numbers dictate the rhythm of music, the frequency of the notes. Why shouldn’t it explain this, too?
I searched for days, in books, on web sites. Nothing came up on any of the many Google searches I conducted. All I found in one book was the fact that the very basic, primal part of our brain recognizes these differences in sounds. Why we like the consonance, those beautiful harmonies, is unknown, but it seemed like there is a bit of math in the mix.
I turned to a friend of mine, an engineer with a much better mind for math than I. We sat down and looked up the frequencies of all these notes. I know that notes three whole steps apart ring beautifully, as do fifths. Fourths are alright. Seconds, however, come together with a dissonance only pleasant when it’s resolved into one of the harmonies.
We found the frequencies of C and it’s third, E. I wanted to know—what do these frequencies look like? I was hoping that a visualization of the wavelengths would help me see what makes them ring harmoniously. My friend worked his Excel magic, giving me the graph I wanted. Nothing stood out to me, just two sine waves overlapping with a slight repetition in their joined pattern.
So next, I wanted to know—what would it look like if we overlapped a C and the next note up, a D? Again, nothing staggering. The pattern seemed longer; it didn’t repeat itself in the short cut we made. So could that have something to do with it?
We broke it down into ratios to see if there was something in that. Music theory tells us that in the well-tempered scale, each note’s frequency is 21/12 higher than the note before. This makes for nice, even sounding thirds and fifths no matter the key of the piece of music. The frequency of E to C, three notes apart, was 5 to 4. It turns out that all major thirds have the 5 to 4 ratio. Fourths are 4 to 3, and fifths are 3 to 2. Those dissonant seconds though—the D to C—that ratio was 9 to 8. Still whole numbers, just larger. Maybe that was the magic math that made it sing (or not)? Maybe smaller integers in the ratios sound better to us?
Perhaps the math makes sense in our brains in a way we can’t articulate. Maybe my family’s harmonies and Tab’s guitar strings vibrated through the air, into my eardrum, worming into specially attuned stadium arenas of my brain.
We turned to another friend, a music aficionado psychologist, for some answers. He told us what we had already assumed: no one really knows what makes our brain interpret thirds as ringing so pretty. It turns out, in the case of what we think of as dissonance, that there is some overlap in the parts of the brain that register two successive notes, and sometimes the resonances of those will conflict with each other and cause a beating sound.
But why that beating is so unpleasant to Westerners is a mystery. In other cultures, seconds to them are like thirds to us. Seconds are treasured in a piece of music. It’s subjective, like all art. What is appealing to one person in one culture may not gel with the artistic standards of another. The sweeping symphonies of Mozart may pale in comparison to the driving beat of African drums. The staccato steps of a tap dance may fall short next to the lyrical flow of a contemporary ballet. The scattered squares and smeared paint of modern art hold deep meaning for some. Beauty is apparently in the brain of the beholder.
Tab’s solo set is over. His band comes back on stage. They kick right into a rocking remake of an oldie: Tab on guitar, bass player walking his notes up and down the scale, grooving to his own rhythm, drummer jumping his body up and down in time with the slams of his snare. The three musicians are one, reading each others’ every movement, traveling in unison through the song.
Maybe some things don’t need explanation. I know what I like. And all I can say for sure, backed by the years of musical training in this American culture, is that Tab’s gravelly voice sailing over the harmonies of his electric guitar and the bass and the drums—it’s a beautiful thing to me.
This post first appeared on MIT Scope in March 2011