• Course intro: physical structures, temporal structures, and social structures
IMAGE: WIDE-VIEW SOUNDWAVE OF THE RITE OF SPRING ZOOMING IN TO SINGLE WAVE VIEW
This is a graphical representation of a soundwave, a visual plot of bunch of numbers that on their own wouldn’t mean much to someone reading them.
IMAGE: ANIMATION OF SPEAKER MEMBRANES UP CLOSE VIBRATING IN SLOW MOTION, PUSHING AIR MOLECULES FORWARD IN WAVES OF COLLISIONS
If we play the soundwave, then your speakers will vibrate at various frequencies and amplitudes, pushing and tugging at the air around them, conveying that wave across the room, through a given space, lasting a given amount of time.
This will change the air pressure quickly, like a little storm, but this wave won’t be primarily meteorological.
IMAGE: PICTURES OF PEOPLE DANCING, ORCHESTRA PLAYING, USE THIS (http://www.theartsdesk.com/sites/default/files/images/1916densmore.jpg); SHOW MUSIC BEING USED
The sonic storm that it brings is one where individual and collective experience collide, where memory and expectation blow wild, where pitch, color, musical time, and convention all play off of one another, where all the history and work and knowledge encoded in a musical work confront a new world every time its played.
This storm is important to study because it helps us to understand how this
IMAGE: GREGORIAN CHANT NOTATION—MAYBE SCROLLING/PANNING
differs from [this],
IMAGE: RITE OF SPRING SCORE
differs from this
IMAGE: EMINEM LYRIC SHEET (http://i960.photobucket.com/albums/ae81/theycallmerainman/Lyrics35.jpg)
, and more importantly, how the sounds and identities of those musics
IMAGE: PREVIOUS THREE IN SUCCESSION
and why we have such different reactions to each one.
IMAGE: SOUNDWAVE AGAIN
Soundwaves like this can lull us to sleep or they can cause riots.
They accompany our weddings and our seediest moments of excess.
If we want to understand how music has such power over us, and—importantly—how it bears so many simultaneous unities and diversities, then we’ll need to look at the levels it functions on.
IMAGE: ME SPEAKING, VIDEO
I’m Dr. Alex Reed, and this course, originally developed in 2009 at the University of Florida, is called How Music Works—a phrase that by coincidence shortly afterwards became the title of an excellent book by David Byrne.
The purpose of this course is look broadly and accessibly at musical structure, from soundwaves to rhythms, to pitches, notes, keys, harmonies, lyrics, and whole pieces.
But we don’t stop there; although it might seem like the class starts off as an introduction to some ideas from western music theory, we’ll come to understand that musical structure isn’t just the mechanics of what’s on a printed score.
Thinking critically about musical structure also means acknowledging the structures that any given musical work is part of—structures like genre, style, tradition, and even culture itself.
By the end of this class, after having spent some important time looking at musical nuts and bolts, we’ll be fostering a deeper, more contextual view of music—one that doesn’t deny or shy away from questions of politics, identity, or experience.
This matters because we all listen to music, and we owe it to ourselves and each other to know why and how we listen, to understand that we are part of the musical equation, that what something means relies on the people who experience it, and not just the composer’s intention.
IMAGE: RAPID ZOOMING OUT OF SOUNDWAVE, SCORE, COMPOSER PICTURE, PERFORMER PICTURE, AUDIENCE PICTURE, EARTH PICTURE
With an eye toward the various hierarchies on which music operates, we’ll start up-close with the acoustics of sound, and zoom out until we see as much of the big picture as we can.
Along the way, we’ll get at some useful answers, but more importantly, we’ll be asking some vital questions that will help us each to develop a fuller sense of how music works.
• The physics of soundwaves
IMAGE: TEXT “SOUND”
At some point you probably learned how sound works.
IMAGE: VIOLIN STRING BEING PLAYED; VIBRATING
An object is made to vibrate and in doing so, it excites the air around it into vibration too.
This object could be a drumhead in the case of a tympani,
IMAGE: TYMPANI HEAD CLOSEUP
or your lips in the case of a trumpet,
IMAGE: TRUMPETER’S LIPS CLOSEUP
or a clarinet reed
IMAGE: CLARINET REED
or a piano string.
IMAGE: PIANO STRINGS
But in most cases, this vibration doesn’t just go from the source and into the air; it also physically resonates in and is shaped by what we call the filter.
A tympani has the kettle of the drum,
IMAGE: KETTLE OF TYMPANI
a trumpet has feet of brass tubing
a clarinet has a wooden body that the reed vibrates
IMAGE: CLARINET BODY
and a piano string resonates the instrument’s soundboard.
This basic mechanism is what we call the source/filter mechanism.
IMAGE: TEXT OF SOURCE/FILTER
A source vibrates, and those vibrations are altered, amplified, and sometimes even dictated to a degree by the filter.
IMAGE: DIAGRAM OF VOCAL TRACT
The most human example of this is our vocal apparatus: the larynx—our vocal chords—vibrate at a given frequency, which creates a pitch.
IMAGE: ANIMATION OF SOUND RADIATING FROM THROAT TO THE RESTOF THE TRACT
But all the vowels and voiced consonants that make up our speech and our singing, and also the tone color that distinguishes my voice from yours—well, all of that comes from the way we move our mouth, lips, tongue, and cheeks, as well as they way we shape the resonating cavity of our throat, our sinuses, our chest, with our posture, and the mere act of being in our bodies.
So the resonances of a source and its filter move very quickly back and forth a minute distance, and this literally shakes the air.
IMAGE: RADIATIONS SHUDDER
Molecules and particles in the air then collide into one another at regular intervals, according to the frequency of the vibration.
IMAGE: ANIMATION OF MOLECULES PROGRESSIVELY COLLIDING
One bumps the next, and that one bumps the next, until the waves, and all the frequencies they carry, are conveyed from one point in space to another.
IMAGE: SOUNDWAVES BOUNCING OFF A WALL
And if they hit a wall or a surface, they can bounce right off, which is in a way just another level of filter, altering the sound of the source.
Eventually, the energy of these collisions dissipates, and the sound fades out.
IMAGE: SOUNDWAVES FADING OUT FROM PREVIOUS IMAGE
Anyhow, if you’re there in the room when these soundwaves are active, then the affected air is going to vibrate and pulse against your eardrum and excites a bunch of hair cells that line your inner ear, which will then move back and forth at more or less the same frequency and with a more or less comparable amplitude.
IMAGE: SOUNDWAVES VIBRATING EAR TIMPANUM
This is an energy—a very tiny vibrational bit of kinetic energy—and your nervous system converts that to an electrical signal that your brain understands as sound.
IMAGE: ELECTRICITY FROM INNER EAR TO BRAIN, AS IN THE FLASH OF A NERVE CELL
IMAGE: MICROPHONE NEAR SPEAKERS
Incidentally, this all is the same principle by which speakers and microphones work too: vibrational patterns of high and low pressure in the air, deriving from and colliding with the physical bodies that make and perceive sounds.
[cue lots of clanging noises]
Later on, we’ll talk about how soundwaves can bear lots of different frequencies at the same time, and how that relates to what we call timbre.
But for now, what I want us to remember is the relationship between sound and time.
IMAGE: SOUNDWAVE WITH AXES OF AMPLITUDE AND TIME CLEARLY MARKED
A sound wave—and indeed any sound at all that we encounter—is a perceived pattern of molecular motion: vibration itself relies on the passage of time, and vibration in fact divides time.
IMAGE: TUNING FORK
For example, this A natural, divides every second into 440 tiny periods of time, each marked by a fluctuation of tiny collisions, carried through the air, into and against our ear.
IMAGE: TUNING FORK STRUCK IN SLOW MOTION
We’re going to be talking about rhythm over the next several videos, and so it’s my hope that we might see a study of rhythm as a natural extension of sound itself.
Indeed, we can even hear the sound of a rhythm becoming a pitch as it moves from a slow repetition where we acknowledge each percussive sound to a much faster one where those repetitions are perceived as a comprising a continuous wave.
IMAGE: SOUND WAVE OF LOW SQUARE WAVE SWEEP
This shift happens, by the way, at about 20 cycles per second, and it’s a totally human, perceptual thing.
Nothing in the sound is changing except its frequency; your ears and brain are doing all the mind-bending.
There are a few composers and musicians who have been really interested in this perspective that privileges rhythm above other musical considerations—Henry Cowell was famously one of them
IMAGE: HENRY COWELL WITH CAT (http://www.nypl.org/sites/default/files/henry_cowell_assisted_by_pepper_on_symphony_no._14._nyc_1959-60.__sidney_cowell_photo..jpg)
—but for our purposes,
IMAGE: TICKING CLOCK
let this understanding of sound’s reliance on time serve as a gateway to a study of musical structure and hierarchy, a study that’s situated in the space between the musical abstract, experiential listening, and human reflection.
• Tempo: pulse, subdivisions, and hierarchies
IMAGE: TEXT “TEMPO, PULSE, SUBDIVISION”
IMAGE: CLOSEUP OF COUNTING CLOCK TIMER ON ITUNES PLAYER
One important factor that differentiates music from certain other forms of artistic expression is the way that we experience it through time.
Although we can reflect on musical events long after they happen, their actual durations and temporal juxtaposition are part of the artform itself—so much that it might be more useful to say that we experience time through music than the other way around.
IMAGE: CLASSIC-STYLE METRONOME
Most music charts our passage through time by way of a more or less constant pulse, like the ticking of a clock.
This is what we commonly call the beat.
The beat is not the same thing as a particular rhythm in a piece of music, and when we use the word “beat” in this context, we’re not talking about a looped drumbeat like you’d talk about in hip-hop.
Instead, in this context, beat is a regular, simple division of musical time.
It’s the ceaseless pulse that we tap our feet to.
The rate at which it occurs is called the tempo, traditionally measured in beats per minute.
IMAGE: TEXT OF “BEATS / MINUTE”
Here’s 50 BPM.
IMAGE: TEXT OF “50 BEATS / MINUTE”
Here’s 100 BPM.
IMAGE: TEXT OF “100 BEATS / MINUTE”
Here’s 150 BPM.
IMAGE: TEXT OF “150 BEATS / MINUTE”
Here’s 200 BPM.
IMAGE: TEXT OF “200 BEATS / MINUTE”
We can notate rhythm graphically.
IMAGE: QUARTER NOTE WITH TEXT OF “QUARTER NOTE”
Western music notation often privileges this symbol—a quarter note—as equivalent to the beat.
A written note implies that an instrument is playing; if instead a musician waits in silence this is called a rest.
IMAGE: QUARTER REST WITH TEXT OF “QUARTER REST”
A quarter rest is designated by this symbol.
By the way, we’re using the American naming system here; in other countries, this note is sometimes called a quaver, and there are a few other pieces of terminology that vary from place to place and from time to time; feel free to look it up on your own.
The American system is not necessarily better—and I want to make sure that we’re getting a globally applicable sense of western music here, inasmuch as that’s possible—but since this course is offered through the University of Florida, we’ll go with how it’s done in the university’s classrooms.
Now, later on we’ll get into why these are called quarter notes and rests, but for the time being let’s wrap up our exploration of how we perceive beats and tempo.
IMAGE: SHOT OF VOLUME GAUGE LIGHTS ON A STEREO, SYNCED TO 120BPM BEAT
Sometimes the beat very easy to hear, like in a lot of modern pop music.
Other times it has a sense of ebb and flow to it.
IMAGE: BUST OF CHOPIN
In other cases, we might hear different possible tempos in seeming competition with each other.
IMAGE: MARCHING BAND
In a march, you can imagine tapping every time the bass drum hits, or you could also hear the snare drums as hitting on beats as well.
IMAGE: SHOT OF VOLUME GAUGE LIGHTS ON A STEREO, SYNCED TO 160BPM BEAT
Just listen how this clicking can fit into 160 beats per minute with one musical setting [plays] and 80 beats per minute with another.
IMAGE: SHOT OF VOLUME GAUGE LIGHTS ON A STEREO, SYNCED TO 80BPM BEAT
What this means is that the way that we hear the beat is to some degree determined by melody, harmony, percussion, and other musical components.
IMAGE: SHOTS OF THE FOLLOWSING BOOK COVERS: Sloboda's Exploring the Musical Mind, Lerdahl and Jackendoff's A Generative Theory of Tonal Music, London's Hearing in Time, and Hanninen's A Theory of Musical Analysis
Music theorists have modeled the ways we perceive rhythmic pulse, but whether we hear a piece of music at a tempo of 80 or 160 is the result of certain competing preferences and likelihoods produced by the musical whole, so the hierarchical level that we assign the beat to is not exactly an either/or proposition.
IMAGE: LINE SHOWING A CONTINUUM OF TEMPOS FROM 40 TO 200, INDICATING SWEET SPOT FROM 60 TO 160 AND CORDONING 100 TO 140 OFF AS DANCE TEMPOS
That said, we tend to perceive most music as having a tempo of between about 60 and 160.
Too slow and we try to find faster subdivisions; too fast, and we focus instead on groups of beats.
When we walk or run, our feet are hitting the ground at a tempo usually between about 100 and 140 beats per minute, so those tempos are good for certain kinds of dancing or exercise.
If we want to sway our whole bodies gently back and forth, either alone or if we’re slow dancing, then tempos like that are too high; we might want something more like 70 beats per minute.
Don’t lose sight of the fact that the way music sounds and the ways that people use it are closely linked to one another.
IMAGE: TEXT OF “The way music sounds and the ways that people use it are closely linked.”
Anyhow, this all leads us to a more immediately useful idea in discussing rhythm—namely, the operations of rhythm at levels smaller and larger than the beat.
IMAGE: THREE HORIZONTAL LEVELS—IN THE MIDDLE ARE SEVERAL CONSECUTIVE QUARTER NOTES; ON TOP IS “GROUPINGS” WITH A BRACKET OVER THE QUARTER NOTES; ON THE BOTTOM IS “SUBDIVISIONS” WITH A TRIANGULAR ARROW IMPLYING THAT SUBDIVISIONS ARE TO BE HEARD WITHIN A SINGLE QUARTER NOTE.
For now let’s look at those smaller levels—I used the word subdivisions just a moment ago to describe them.
Nearly all music uses beat subdivisions, and the easiest way to cut a beat into smaller sections is to divide it in half.
Remember how we’d used quarter notes and quarter rests to describe the beat earlier?
IMAGE: TEXT 1/4 ÷ 2 = 1/8
Well, recalling that in math, one quarter divided in half is one eighth, the name for these split subdivisions are eighth notes (for when a note hits) and eighth rests (for when an instrument waits silently).
The eighth note looks like this—it has a head and a stem like a quarter note, but it also has a flag.
IMAGE: EIGHTH NOTE
When multiple eighth notes are organized in succession, we usually turn those flags into beams, like this.
IMAGE: TWO EIGHTH NOTES IN BEAMS
An eighth rest, by the way, looks like this.
IMAGE: EIGHTH REST
Now, listen to how a quarter-note kick drum holds down the beat here while the eighth-note hi-hat cymbal strikes twice for each beat.
IMAGE: KICK DRUM QUARTER NOTES (STEM DOWN) AND HI-HAT EIGHTH NOTES (BEAMED IN FOURS, STEM UP)
Let’s say that we’re counting the kick drum hits in groups of four, which is a common idea that we’ll talk more about in the next video.
This hi-hat cymbal might be classified by rhythmically inserting the word “and” between the beats: one-and-two-and-three-and-four.
IMAGE: ADD COUNTS AND “AND” TO BEATS OVER PREVIOUS GRAPHIC
One advantage of considering music hierarchically is that we can get at a lot of rhythmic complexity very easily.
IMAGE: TEXT 1/8 ÷ 2 = 1/16
For example, if we can divide a quarter note in half to get eighth notes, then we can divide eighth notes in half to get sixteenth notes, and the notation here follows an easy formula—just put another flag (or beam) on the stem.
IMAGE: SIXTEENTH NOTE
Similarly, the sixteenth rest takes a second flag.
Give it a listen.
Musicians sometimes count sixteenth notes like this: one-ee-and-a-two-ee-and-a-three-ee-and-a-four-ee-and-a.
IMAGE: KICK DRUM QUARTER NOTES (STEM DOWN) AND HI-HAT SIXTEENTH NOTES (BEAMED IN FOURS, STEM UP), WITH COUNTS AND “EE-AND-A” ABOVE
Hear how much more active the beat sounds with sixteenth-note hi-hats over the quarter-note kick drum? Throw in a few rests and eighth notes and you’ve got a lot of rhythmic variety.
IMAGE: SHOW BEAT AS PERFORMED, AS PER THE SCHEME THUS FAR
IMAGE: 32ND AND 64TH NOTES
Now you can theoretically go even further, past sixteenth notes and into thirty-second notes and sixty fourth notes—and indeed these subdivisions sometimes show up in music: hi-hat programming in drill and trap music within hip-hop, tends to use thirty-second notes, and bagpipe music will sometimes notate its fastest, most inbetween notes as hundred-twenty-eighth notes, but for the most part, sixteenth notes are just about the smallest subdivisions that we encounter and use regularly across western musical styles.
IMAGE: HIERARCHICAL DIVISIONS BY TWO: QUARTER NOTE INTO TWO EIGHTH NOTES INTO FOUR 16TH NOTES
Everything we’ve talked about so far comes just from dividing the beat into progressive multiples of two equal parts.
That’s not the only way to do it, of course.
We can also divide it at any level into three, called triplets.
IMAGE: TEXT “TRIPLETS”; SHOW UNBEAMED TRIPLETS (WITH BRACKETED “3” ABOVE” AT QUARTER, EIGHTH, AND 16TH-NOTE LEVELS)
We use the name and the symbol of the divide-by-two scheme to indicate what level of triplet we’re dealing with.
Listen to the quarter-note kick drum pulse and hear how the various triplets sound on hi-hats.
Quarter-note triplets squeeze three equal notes into the space of two quarter notes.
IMAGE: 2 KICK DRUM QUARTER NOTES (STEM DOWN) AND 3 HI-HAT QUARTER-NOTE TRIPLETS (WITH BRACKETED “3”, STEM UP)
Eighth-note triplets squeeze three equal notes into the space of two eighth notes.
IMAGE: 2 KICK DRUM QUARTER NOTES (STEM DOWN) AND 2 SETS OF 3 HI-HAT EIGHTH-NOTE TRIPLETS (WITH BRACKETED “3”, STEM UP)
Eighth-note triplets are, incidentally, a rhythmic hallmark of jazz music, in which a swing rhythm focuses on the first and third of those triplet subdivisions, sometimes with a little bit of rhythmic flexibility, depending on whether you want what’s called a hard or a soft swing.
IMAGE: SAME GRAPHIC AS BEFORE BUT WITH MIDDLE EIGHTH-NOTE TRIPLET OF EACH SET REPLACED BY AN EIGHT-REST TRIPLET
And here are sixteenth-note triplets, which squeeze three equal notes into the space of two sixteenth notes.
IMAGE: 2 KICK DRUM QUARTER NOTES (STEM DOWN) AND 4 SETS OF 3 HI-HAT 16TH-NOTE TRIPLETS (WITH BRACKETED “3”, STEM UP)
This, by the way, is also sometimes called and notated as a sextuplet.
IMAGE: 2 KICK DRUM QUARTER NOTES (STEM DOWN) AND 2 SETS OF 6 HI-HAT 16TH-NOTE TRIPLETS (WITH BRACKETED “6”, STEM UP)
To sum up, nearly all music has a steady beat, and there are reliable, notatable, hierarchical ways that this beat gets divided—mostly in powers of two, but we can divide into threes—and even other numbers, if we want to.
IMAGE: HOW MUSIC WORKS LOGO (IS THERE ONE?)
Now it’s time to go and do some listening and beat-finding on your own.