Linear music notation is good for reading, but it doesn’t tell you everything you want to know about underlying musical structure. Notes that are close to each vertically are not necessarily the most closely related. The concept of harmonic relatedness is a complex one, but there’s an excellent tool for beginning to get a handle on it: the circle of fifths.
The left circle above shows the chromatic circle, the pitch sequence you find on the piano. The right circle shows the circle of fifths. Each note is a fifth higher or a fourth lower than its counterclockwise neighbor, and each note is also a fourth higher or a fifth lower than its clockwise neighbor.
Unlike a lot of music theory you learn in school, the circle of fifths is not some arbitrary Western European cultural convention. There’s actual science behind it. If two notes are adjacent on the circle of fifths, it means they have a lot of overtones in common. If you know what overtones are, you can skip the next few paragraphs. Otherwise, read on.
Before you can understand how digital audio works, you need to know a few things about the physics of sound. This animation shows a sound wave emanating through the air from a circular source — imagine that it’s a drum or cymbal.
As you can see, sound is a wave, like a ripple in a pond. Imagine that your ear is at the bottom center of this image. The air pressure against your inner ear is rhythmically increasing and decreasing. Your brain senses how wide those swings in air pressure are and how often they’re happening, and you experience the result as a sound.
The Major Scale, The Standard Chord Dictionary, and The Difference of Feeling Between The Major and Minor Triads Explained from the First Principles of Physics and Computation; The Theory of Helmholtz Shown To Be Incomplete and The Theory of Terhardt and Some Others Considered
Wilkerson begins with the observation that music theory books read like medical texts from the middle ages: “they contain unjustified superstition, non-reasoning, and funny symbols glorified by Latin phrases.” We can do better.
Wilkerson proposes that we derive a theory of harmony from first principles drawn from our understanding of how the brain processes audio signals. We evolved to be able to detect sounds with natural harmonics, because those usually come from significant sources, like the throats of other animals. Musical harmony is our way of gratifying our harmonic-series detectors.
I seem to have touched a nerve with my rant about the conventional teaching of music theory and how poorly it serves practicing musicians. I thought it would be a good idea to follow that up with some ideas for how to make music theory more useful and relevant. The goal of music theory should be to explain common practice music. I don’t mean “common practice” in its present pedagogical sense. I mean the musical practices that are most prevalent in a given time and place, like America in 2013. Rather than trying to identify a canonical body of works and a bounded set of rules defined by that canon, we should take an ethnomusicological approach. We should be asking: what is it that musicians are doing that sounds good? What patterns can we detect in the broad mass of music being made and enjoyed out there in the world?
I have my own set of ideas about what constitutes common practice music in America in 2013, but I also come with my set of biases and preferences. It would be better to have some hard data on what we all collectively think makes for valid music. Trevor de Clerq and David Temperley have bravely attempted to build just such a data set, at least within one specific area: the harmonic practices used in rock, as defined by Rolling Stone magazine’s list of the 500 Greatest Songs of All Time. Temperley and de Clerq transcribed the top 20 songs from each decade between 1950 and 2000. You can see the results in their paper, “A corpus analysis of rock harmony.” They also have a web site where you can download their raw data and analyze it yourself. The whole project is a masterpiece of descriptivist music theory, as opposed to the bad prescriptivist kind.
A musical pitch is a blend of many different frequencies beside the fundamental. Here’s a visualization of the different vibrational modes of an ideal string. The string’s movements are the sum of all these different modes simultaneously.
In high school science class, you probably saw a picture of an atom that looked like this:
The picture shows a stylized nucleus with red protons and blue neutrons, surrounded by three grey electrons. It’s an attractive and iconic image. It makes a nice logo. Unfortunately, it’s also totally wrong. There’s an extent to which subatomic particles are like little marbles, but it’s a limited extent. Electrons do move around the nucleus, but they don’t do it in elliptical paths as if they’re little moons orbiting a planet. The true nature of electrons in atoms is way weirder and cooler.
Pictures are a terrible way to understand the nature of quantum particles. Music theory is much better.
Gravity is the warping of spacetime by mass or energy. A mass like the Earth warps spacetime so that the shortest path, the “path of least resistance,” for inertial movement is towards the Earth’s center.
Using instruments like the Hubble Space Telescope, it’s possible to literally see the warping of spacetime by very massive objects like galaxies and huge conglomerations of dark matter. When you’re looking at a very distant object and there’s a large mass along your line of site, it warps spacetime to produce a visual effect known as gravitational lensing. Here’s a schematic diagram showing how it works.
I follow science news the way normal dudes follow sports. If you’re geekily inclined like me, you may have heard that the particle physics people are getting closer to producing the Higgs boson. You may have wondered what that is exactly, and why you should care. The science press has nicknamed the Higgs “the God particle,” which is poetic but doesn’t move me any closer to understanding. Here’s my best effort to wrap my head around the idea — maybe you’ll find it helpful, or at least entertaining. If you’re a real scientist and want to clarify or correct anything I’m saying here, please jump in on the comments.
In Annie Hall, young Woody Allen explains to his doctor that he won’t do his homework because the universe is expanding, so what’s the point? His mother exasperatedly tells him, “You’re here in Brooklyn. Brooklyn is not expanding!”
I post this because I’ve been reading Coming Of Age In The Milky Way by Tim Ferris, as good a summary of the state of cosmology between two covers as a person could ask for. Thinking about the horrifying enormousness and ancientness of the universe might have depressed Woody Allen, but it has a paradoxically calming effect on me. Reading books like Ferris’ is my favorite form of meditation.
The sun was on my mind today anyway, it being so nice and cloudless outside. But days like today also cause me anxiety. I’m a fair-haired sunburn-prone type, and my dad died from skin cancer, a combination of Scandinavian genes and long hours as a young guy on a ladder helping Grandpa paint houses, plus many more hours on boats and beaches with no sunblock. I stick to the shade, wear hats and generally play it very safe, but still, I feel some dread about the amount of radiation I’m getting from the great thermonuclear reactor in the sky.
My dread does have an upside. It’s fueled a lot of fascination. The sun is a bottomless source of interest if you’re a science geek like me. Continue reading →