Sound, Scales, and the Language

What Is Sound?

Sound is vibration. When something vibrates — a guitar string, a drumhead, your vocal cords — it pushes air molecules back and forth, and those pressure waves eventually hit your eardrum. Your brain does the rest.

We measure how fast something vibrates in Hertz (Hz) — the number of cycles per second. A guitar string vibrating 440 times per second produces A above middle C — 440 Hz. That number shows up everywhere: on tuners, on equalizers, on every EQ plugin you’ll ever open. When you see “cut at 200 Hz” or “boost at 3 kHz,” that’s a frequency — a specific speed of vibration. You don’t need to memorize numbers right now, but knowing that Hz = vibration speed makes those knobs a lot less mysterious.

When a string vibrates, it doesn’t just vibrate as a whole. It also vibrates in halves, thirds, quarters, fifths, and so on — all at the same time. These are called overtones (or harmonics), and they’re the reason music works at all. They’re not theoretical. They’re physics. They’re happening right now in every sound you hear.

The first overtone — the string vibrating in halves — is exactly double the frequency of the original note. That relationship sounds so natural to our ears that we gave it a name: the octave. Play any note on a piano, then play the same letter name higher up. That’s an octave. It sounds like the same note, just higher. That’s because it is — it’s the same vibration, doubled.

Why Pitch Is Logarithmic (Cents vs. Hertz)

The octave from A3 (220 Hz) to A4 (440 Hz) spans 220 Hz. The next octave — A4 to A5 — spans 440 Hz. Double the gap, same musical distance. That’s because pitch is logarithmic: equal musical intervals correspond to equal ratios of frequency, not equal differences. Every octave is a 2:1 ratio, every perfect fifth is 3:2, regardless of where you are on the keyboard.

This is why musicians measure pitch in cents — 100 cents per semitone, 1200 per octave — instead of Hz. Cents give you a ruler where equal distances sound equal. Hz give you the raw physics. Both are useful; they just measure different things.

The Harmonic Series

The harmonic series is the sequence of overtones that ring out from any vibrating object. It goes: the fundamental (your note), the octave, then a fifth above that, then another octave, then a third, and so on — getting closer and closer together as you go up.

Why does this matter? Because the harmonic series is where everything in Western music comes from. Chords, scales, keys, harmony — all of it traces back to the physics of how strings vibrate. The relationships between the first few overtones — the octave, the fifth, the fourth, the third — are the building blocks of everything you’re about to learn.

And one of the most beautiful things about the harmonic series: each note in the scale exists because it is contained within the note that came before it. The fifth is hiding inside the fundamental. The fourth is hiding inside the fifth. The scale isn’t arbitrary — it’s already there, ringing inside every note, waiting to be discovered.

Think of the relationship between the first note (the fundamental), the fifth, and the fourth like the sun, the earth, and the moon. The first note is the earth — it’s home. The fifth is the sun — the strongest gravitational pull, always reaching up. The fourth is the moon — always close, always orbiting. That trio — I, V, and IV — is the backbone of most of the music you’ve ever heard.

Building a Scale

A scale is just a set of notes organized by pitch. But it isn’t random — it comes from the harmonic series.

The short version: if you start on any note and follow the chain of fifths and fourths that the harmonic series gives you, and then squish all those notes into a single octave, you get a scale. The Western major scale — do, re, mi, fa, sol, la, ti, do — is what falls out.

There’s a catch, though. The intervals that nature gives us don’t divide the octave perfectly evenly. Over the centuries, we settled on a compromise that spaces all twelve notes equally, so you can play in any key on any instrument without retuning. Every piano, every guitar, every DAW — they all use this system.

Tetrachords: A Better Way to Remember

You may have seen the major scale written out as a pattern of whole steps and half steps: W W H W W W H. That’s accurate, but it’s a terrible way to memorize anything — it’s just a string of letters with no structure.

Here’s a better way. Cut the scale in half. The major scale is really two groups of four notes separated by a whole step. Each group is called a tetrachord.

The bottom four notes of the C major scale — C, D, E, F — follow the pattern whole, whole, half (or counted in semitones: 2-2-1). That’s the major tetrachord. Now look at the top four — G, A, B, C. Same pattern: 2-2-1. The major scale is just two identical tetrachords, placed side by side with a whole step between them.

That’s one pattern to remember — 2-2-1 — instead of seven. And it works in every key: find your starting note, play 2-2-1, step up a whole step, play 2-2-1 again. Major scale, every time.

This idea comes back later when we look at modes — because there are other tetrachords (minor: 2-1-2, harmonic: 1-3-1), and when you start mixing and matching them, you can build every scale and mode without memorizing each one separately. But that’s a Chapter 11 problem. For now, just remember: two groups of four, 2-2-1 twice.

Numbers Vocabulary: Intervals, Scale Degrees, Chord Tones

This is where the language comes in. Don’t worry — you don’t need to memorize all of this right now. This is the kind of thing that clicks over time, with repetition. But here’s the map.

One thing to know upfront: music uses numbers in multiple ways, and this is a genuine source of confusion. We use numbers to describe intervals (the distance between two notes), scale degrees (a note’s position in a scale), and chord tones (a note’s role within a chord). The same number can mean different things depending on context. We’ll flag this as it comes up — for now, just know it’s a thing.

To keep chord functions clear, we use Roman numerals. Upper case means major, lower case means minor. Here are all the chords you can build on the white keys — every chord diatonic to the key of C:

I – ii – iii – IV – V – vi – viiø

Three major chords (I, IV, V), three minor chords (ii, iii, vi), and one diminished (viiø — we’ll talk more about that one later). This notation tells you two things at once: where the chord lives in the scale, and whether it’s major or minor. You’ll see it throughout the rest of this course.

Scale degrees are how we number the notes of a scale. In the key of C major:

You don’t need the fancy names yet. What matters is the numbers. When someone says “the five chord,” they mean the chord built on the fifth degree of the scale. Numbers let us talk about music in any key without getting tangled up in letter names.

For this entire course, we’re going to live in C major — and its relative minor, A minor. Every major key has a relative minor that shares all the same notes but starts on a different home base. C major and A minor use the exact same white keys on the piano — the only difference is which note feels like “home.” We’ll come back to this relationship later. For now, just know they’re roommates.

Think of it like learning chess. The first time you sit down to play, you learn with one chess set. The pieces look a certain way. You learn the rules, the moves, the strategies. Later, someone hands you a different set — taller king, heavier pieces, marble board. But it’s the same game. Same rules, same moves.

Keys work the same way. Everything you learn in C — the chord numbers, the functions, the pulls, the relationships — works identically in every other key. The note names change (the pieces look different), but the game is the same. C major is our chess set. Once you’ve learned to play here, you can play anywhere.

Intervals describe the distance between two notes. A second is one step. A third is two steps. A fifth is four steps. You get the idea. Intervals can be major, minor, or perfect — those words describe the quality of the distance, not just the size.

Chord tones are the notes that make up a chord. The most basic chord — a triad — is built by stacking two thirds: the root, the third, and the fifth. Change the quality of those thirds (major or minor) and you change the entire character of the chord. That’s coming in the next chapter.

Structure vs. Function

One of the most important ideas in this whole course shows up right away, in the very first class:

What a thing is is not necessarily what a thing does.

A C major chord is a structure — it’s made of the notes C, E, and G. That’s fixed. But its function changes depending on context. In the key of C, it’s home base — the tonic. In the key of F, it’s the dominant — the chord that wants to pull you back to F. Same three notes, completely different job.

This idea — that context determines meaning — is the thread that runs through everything we’ll talk about. Keep it in the back of your mind. Every time you see something highlighted in orange, we’re talking about what something is. Every time you see blue, we’re talking about what it does.

Hey Jude: Two C Chords Walk Into a Bar

Listen to “Hey Jude.” The verse sits in the key of C:

F → C → G7 → C → C7

That’s IV → I → V7 → I → I7. The C chord is home — the tonic. But that C7 at the end? Same chord with one extra note (B♭) — and that note changes everything. It turns the C into a dominant seventh pointing at F. The song slides into a new section where F is home:

F → Fmaj7 → Dm → Dm/A → Bdim → C

Now C is the dominant — the V chord, pulling back to F. Same three notes in the C chord. Completely different job. That’s structure vs. function in action. (Hey Jude comes back in Chapter 3 — that C7 trick has a name, and it’s one of the most useful tools in the toolkit.)

Try both progressions below. Hit the SUB button on the verse wheel to see the key shift to F — watch how C moves from the tonic position to the dominant.

The Claw

If you have a keyboard nearby (and you should — it doesn’t need to be fancy), try this: put your thumb on C, skip a white key, put your middle finger on E, skip another, put your pinky on G. That shape — thumb, middle, pinky with gaps between them — is the claw. It’s how you grab a basic chord on a keyboard. (To be clear — this is bad piano technique, and you’ll need to unlearn it later. But it gets you started.)

Move the claw up and down the white keys and you’ll hear different chords — some major, some minor, one that sounds a little crunchy (that’s the diminished — we’ll get to it). These chords may all look the same, but they’re different — because the piano keyboard is not symmetrical. The spacing between notes changes, which changes the chord quality. The claw is your starting point for everything that follows. Put it under your fingers — get comfortable with it.

The Harmony Wheel

Throughout this course, we’ll use the Harmony Wheel to hear the concepts we’re discussing. It’s an interactive tool — you can press the orange play button to hear a chord progression, or click individual chords to play them yourself.

We’re going to start simple — just a few chords — and add more as we go. By the end of this course, the wheel will be fully loaded with everything in your toolkit. Here’s what the full wheel looks like:

Don’t worry about all those chords yet. For now, we only need three — I, IV, and V. Try it:

Open the full Harmony Wheel →