Music,from zero.

00

Vibration

A sound is a push

Pluck a string and it swings back and forth, hundreds of times a second. Every swing shoves the air next to it. That air shoves the air next to it, and the push travels outward at about 343 metres a second until it reaches your ear and nudges your eardrum.

That's all a sound is. Air getting squeezed and released, over and over. The dots below are air next to a string, slowed down a lot.

Move the slider. More swings per second means the pushes arrive more often, and the sound gets higher. Fewer, and it gets lower. We count swings per second in hertz, written Hz. Human ears pick up roughly 20 Hz to 20,000 Hz.

Pitch is just speed. And notice the slider is smooth. Nothing in physics says where the notes should be. So where do notes come from?

01

Ratios

Some pairs sound smooth. Some sound rough.

Play two notes together and you'll hear it straight away. Some pairs blend. Others grind against each other. This isn't only taste. You can see it.

The low note below stays at 220 Hz. Drag the ball to move the second note higher. The square draws one vibration against the other. When the two speeds form a simple ratio, the drawing settles into a clean, still shape. In between, it tangles and drifts, and you can hear a wobble.

Every smooth spot sits on a simple fraction. At 3:2 the high note swings three times for every two swings of the low one, so they fall back into step every couple of swings. At a messy ratio they almost never line up, and the air gets choppy. Your ear hears that as roughness.

Two notes sound good together when their vibrations line up often. Simple ratios line up often. Almost everything else in music grows out of this one idea.

02

Octaves

Twice as fast is the same note

The simplest ratio, apart from playing one note twice, is 2:1. Double the speed and something odd happens. The new note is clearly higher, but it sounds like the same note. When an adult and a child sing a tune together they're usually an octave apart, and most listeners hear one tune.

That 2:1 jump is called an octave. It means pitch isn't a straight line. It's a spiral. Each time you double the speed you come around to the same spot, one floor up.

On a guitar, the open A string, the A at the 12th fret and the A an octave above that all sit on one line of this spiral: 110, 220 and 440 Hz. Same angle, same note name.

Because the octave repeats, music only has to decide how to split one lap of the spiral. How many notes should go in a lap? To answer that, we need to look inside a single note.

03

Harmonics

Every note is a chord in disguise

A plucked string doesn't only swing as one piece. It also swings in two halves, in three thirds, in four quarters, all at the same time. Each smaller piece vibrates faster, at exactly 2, 3 and 4 times the main speed.

These extra vibrations are called harmonics. You don't hear them as separate notes. You hear them as the character of a sound. A flute has few strong ones and a guitar has lots. That mix is why a flute and a guitar sound different playing the same note.

Now look at which notes are hiding in there. ×2 is the octave. ×3 against ×2 is 3:2, the smooth ratio from chapter 01. ×5 against ×4 is 5:4. Play harmonics 4, 5 and 6 together and you get a major chord. It was inside the string all along.

The smooth ratios aren't arbitrary. They're built into nearly every sound you've ever heard, voices included. Your ear has been soaking them up your whole life.

04

Twelve notes

Why there are twelve notes

Let's build a set of notes the simplest way we can. After the octave, the smoothest ratio is 3:2, which musicians call a fifth. So start on any note and keep stepping up by fifths. Whenever you go past the top of the lap, drop down an octave so everything stays inside one lap.

Press the button and watch where each new note lands.

Five notes give you an even spread with only two sizes of gap. That's the pentatonic scale, found in folk music all over the world. Seven give you the major scale. After twelve, the next fifth lands almost exactly on the note you started with. It misses by less than a quarter of a step.

Twelve is where the loop nearly closes, so that's where we stop. Modern tuning then cheats a little. It shrinks every fifth by a hair so twelve of them close the loop perfectly. Every step becomes the same size, 1.0595 times the one before (the twelfth root of two), so a song can start on any note and sound the same.

This is also where notes get their colours. Notes a fifth apart get neighbouring colours, so notes that get along look like they belong together. From here on, the page is in colour.

Twelve isn't a rule someone made up. It's the point where stacking the smoothest ratio comes back around to where it started.

05

Scales

A scale is a handful of neighbours

You rarely use all twelve notes at once. That would be like painting with every colour in the box. A scale is a smaller set to work with.

Here's the neat part. The common scales are just runs of fifths, so on this wheel they sit next to each other. Five in a row make the pentatonic scale. Seven make the major scale. Every note is a fifth from the next, so they all get along.

Tap the pads, or use the keys on your keyboard. It's hard to play a wrong note here. Then switch to minor. It uses the same seven notes with a different one as home, and the mood changes completely.

A key is which slice of the wheel you use, and which note in it feels like home.

06

Chords

A chord is the hidden chord, played on purpose

Take every other note of a scale and play them together. That's a chord. In C major, the notes C, E and G make the C major chord.

Look at the numbers. C, E and G are very close to the ratio 4 : 5 : 6. Those are harmonics 4, 5 and 6 from chapter 03. A major chord is the sound hiding inside one string, pulled out and played on purpose.

On the clock of twelve notes a major chord is a triangle: 4 steps, then 3. Flip it to 3 steps, then 4, and you get a minor chord. The outer notes stay put, the middle one drops a single step, and the sound goes from bright to moody.

Major and minor are the same triangle, flipped. One note moves one step and the whole feeling changes.

07

Tension

Songs leave home and come back

Pick a key and one chord starts to feel like home. In C major, that's C. Every other chord feels like somewhere else, some nearby, some far, and your ear keeps waiting to get back.

The strongest pull comes from G. It contains B, which sits one small step below C. That small step is the least settled distance in music, and B leans toward C like a door that's almost shut. Play G, then C, and you hear it click.

Hundreds of hit songs loop these four chords: home, the pull, the sad cousin and the side-step. Let It Be, No Woman, No Cry, With or Without You and Don't Stop Believin' all use them, in different keys. Change the order, or build your own, and listen to how the story changes. Watch the coloured lines too. Good chord changes mostly move each note by one small step, or not at all.

Harmony is movement. Tension is being away from home. Resolution is getting back.

08

Rhythm

Now slow everything down

Every vibration so far has been far too fast to count. Music has a second half that lives at speeds you can tap your foot to. That's rhythm.

Rhythm works on the same idea. A steady pulse gets split into halves and quarters, and sounds land on those lines. Click the grid to build a beat, or start from a preset.

Try the swing slider. Straight notes split each beat 1:1. Swung notes split it closer to 2:1, long then short. That one ratio is most of the difference between a march and a shuffle.

Rhythm is ratios, slowed down. Which raises an odd question. What happens if you speed a rhythm up?

09

The big one

Speed up a rhythm and it turns into a chord

Here are two drummers. One plays 3 even hits in every cycle, the other plays 2. Drummers call this three against two. Listen to it at walking pace first.

Then press Accelerate. At around 20 hits a second your ear can't follow the separate clicks, and they blur into a buzz. Keep going and the buzz becomes two notes, a fifth apart. That's the 3:2 from chapter 01.

Nothing changed except speed. Three against two and a perfect fifth are the same pattern at different speeds. Rhythm is harmony slowed down, and harmony is rhythm sped up.

That's the whole idea in one place. Music is vibrations that line up. Fast, you hear it as pitch. Slow, you feel it as rhythm.

10

Your guitar

Now look at your guitar

Everything on this page is built into your fretboard. This one is drawn to scale. Tap anywhere on it to play.

The frets get closer together as you go up. Each one leaves 94.4% of the string that was vibrating before, which raises the note by one of the twelve equal steps from chapter 04.

Fret 12 sits exactly halfway, so half the string vibrates twice as fast: an octave. At fret 7, two thirds of the string is left, giving 3:2, a fifth. The dotted frets (3, 5, 7, 9 and 12) land on or very near 6:5, 4:3, 3:2, 5:3 and 2:1. Those are the smooth spots from chapter 01.

Try this on your real guitar. Rest a finger lightly on a string right above fret 12, 7 or 5 without pressing down, and pluck. You'll hear a bell-like chime. Your finger stops the string swinging as one piece, so only the harmonics are left: ×2, ×3 and ×4, the hidden notes from chapter 03.

You've been playing physics this whole time.