Learn music

Music theory.

Taught slowly, from nothing, with a picture for every idea. I am not going to assume you know what a semitone is, or that you can read music, or that you have ever touched a piano. If you can count to twelve you can follow this.

25 min read

Part one: why twelve notes?

You can skip this and go straight to the practical theory if you want. But if you have ever wondered why there are exactly twelve notes and not ten or twenty, this is the part that answers it, and it makes everything afterward make more sense.

The octave is not an opinion

Play a note. Now play a note that vibrates exactly twice as fast. Your ear says those are the same note, just higher. Not similar. The same. Every musical culture on earth, independently, arrived at this.

That is because it is physics, not taste. If a string vibrates at 110 times a second and another at 220 times a second, every single peak of the slower wave lines up with every other peak of the faster one. They agree constantly. Your ear hears that agreement as sameness. We call that doubling an octave.

So the octave gives us a box. Everything in music happens between a note and its double. The only question left is how to divide up that box.

The overtone series hands us the next note for free

When you pluck a string it does not just vibrate as one whole string. It also vibrates in halves, thirds, quarters, and so on, all at the same time, quietly, underneath the main note. Those quieter extra notes are called overtones, and they are why a guitar and a trumpet playing the same note still sound different.

The first overtone after the octave is the string vibrating in thirds, which gives you three times the original frequency. Bring that back down into our octave box and you land on a note we call the fifth. It is the second strongest relationship in music after the octave, and again, nobody chose it. It falls out of a vibrating string whether you want it or not.

Pythagoras stacks fifths and runs into a wall

Here is the old approach. Start on a note, go up a fifth, then a fifth from there, and keep going. Because the fifth is so strong, every step sounds good. Do it twelve times and you arrive back at what should be your starting note, seven octaves up.

Except you do not. You land slightly past it. Stacking twelve pure fifths overshoots seven octaves by a small amount, about a quarter of a semitone. That gap is called the Pythagorean comma, and it is not a measurement error. It is a mathematical fact: powers of three and powers of two never line up exactly.

Equal temperament: everybody gives up a little

The solution we settled on is blunt. Take the octave, divide it into twelve exactly equal steps, and accept that almost nothing is perfectly in tune anymore.

Every fifth is now very slightly narrow. Every third is noticeably off. But here is what you buy with that compromise: every key sounds the same as every other key, and you can play in any of them on the same instrument without retuning. Your guitar's frets are permanent, so this matters enormously. Without equal temperament, a guitar in tune for one key would be out of tune for another.

So twelve is not magic. Twelve is the smallest number of equal divisions that gets you acceptably close to those natural relationships. That is the entire reason.

And other cultures made other choices

Worth knowing, because it makes clear that twelve is a decision rather than a law.

• Indian classical music uses shrutis, commonly counted as twenty two divisions of the octave, and keeps intervals pure rather than evenly spaced.
• Arabic and Turkish maqam use quarter tones, notes that sit between the notes on your fretboard. They are not out of tune. They are notes you simply do not have.
• Indonesian gamelan uses scales that do not match our system at all, and each ensemble is tuned to itself, so two gamelan orchestras are not expected to match each other.

Part two: the twelve notes

Now the practical part. Everything from here is stuff you will actually use.

There are twelve notes. Then they repeat. That is the whole system, and here it is on a piano keyboard, because a keyboard shows the pattern more clearly than a guitar does.

Look at the names. Seven of them are plain letters, A through G. The other five have a sharp sign after them. A sharp just means "one step higher than the letter it is attached to." So C♯ is one step above C.

The smallest step there is

Moving from any key to the very next key, with nothing between them, is called a half step. On a guitar, that is one fret. Moving two of those is a whole step, or two frets.

Why is there no black key between E and F?

This trips up nearly everyone, and the answer is simpler than it looks.

Everything on a keyboard is a half step from its neighbor. Between most letters there is a black key to fill that half step gap. But E to F and B to C are already only a half step apart, so there is nothing left to put between them. No gap, no black key.

The letters were named long before anyone worked out the theory, so the naming is a bit of a historical accident. The pattern itself is perfectly regular. It is only the names that are uneven.

The same twelve notes on a guitar

On a keyboard the notes lay out left to right. On a guitar, one string does the same job going up the neck, one fret at a time.

That is the thing worth understanding about a guitar: the twelfth fret is always the octave. Whatever the open string is, fret twelve is the same note, twice as fast. That is true on every string, in every tuning.

Part three: the major scale

Out of those twelve notes, we almost never use all twelve at once. We pick seven and call it a scale. The most important one is the major scale, because nearly everything else is described by how it differs from it.

The major scale is a fixed pattern of steps. Not fixed notes, a fixed pattern. Here it is:

Start on C and follow it, and something convenient happens.

C major uses no sharps and no flats. That is not because C is special musically. It is because our keyboard was laid out with C major as the plain, all-white-keys option. Start the same pattern anywhere else and you will need black keys.

Start on G instead, and watch what happens

Count it yourself. G to A is a whole step, A to B whole, B to C half, C to D whole, D to E whole, then E to F is only a half step. That breaks the pattern, which needs a whole step there. So we raise it to F♯, and now the pattern holds.

That is where key signatures come from. They are not arbitrary. Each key needs exactly the sharps or flats required to keep that pattern intact, and no others.

You do not need to memorize that table. The circle of fifths tool shows you every key and its signature, and it will make the pattern obvious faster than memorizing will.

The scale on a guitar

Part four: intervals, and what a third actually is

An interval is just the distance between two notes. That is all the word means. But you need it, because chords are built out of intervals.

There are two ways to count, and mixing them up is the single most common source of confusion in all of music theory.

So a "third" is named for counting letters, but its actual size is measured in half steps. Both numbers describe the same distance. Here it is:

Major third and minor third, and why it matters so much

Here is the part almost nobody explains properly. There are two sizes of third, and the difference between them is one single half step. That one half step is the difference between a chord sounding bright and sounding sad.

That fifth is the one your power chords are built from. A "C5" chord is just C and G, a perfect fifth apart, with no third at all. That is why power chords sound neither happy nor sad. You removed the note that decides.

Part five: how chords are built

A chord is three or more notes played together. The standard way to build one is beautifully simple once you see it.

Start on C. Skip D. Take E. Skip F. Take G. You now have C, E, G, which is a C major chord.

Now do the one thing that changes everything. Move that middle note down a single half step.

Every one of those is the same idea: stack thirds, then adjust one note to change the color. If you want to hear any of them, the chord library plays every chord in every key, and the chord identifier works backward if you are holding a shape and want to know its name.

Part six: keys, and which chords belong together

Here is where it all pays off. If you build a chord on every note of the major scale, using only notes from that scale, you get seven chords, and they always come out in the same pattern.

Those Roman numerals are just a way of saying "the chord built on the first note, the second note," and so on. Capital means major, lowercase means minor. This pattern is identical in every major key. The first, fourth and fifth chords are always major. The second, third and sixth are always minor. The seventh is always diminished.

The key finder tool does this in reverse: give it chords you already know and it tells you which key they belong to and what else fits.

Part seven: minor scales, and the trick that saves you work

The minor scale has its own step pattern: whole, half, whole, whole, half, whole, whole. It sounds darker because the third note is a minor third above the root rather than a major third. Same reason a minor chord sounds darker. It is always that third.

But here is the shortcut worth knowing.

These are called relatives. A minor is the relative minor of C major. To find any relative minor, count up six notes in the scale, or go down three half steps from the major root. It means learning one set of notes gets you two scales.

Part eight: modes, without the mystery

Modes get treated as advanced and difficult. They are neither. You already did one in the section above.

A mode is what you get when you take a scale and start on a different note, treating that note as home. Same notes, different center of gravity, different feel.

All seven of those use the exact same white keys. The only thing that changes is which note feels like home, and that is decided by what the music underneath you is doing.

Part nine: rhythm, the half everybody skips

Everything above is about pitch. But you can play all the right notes and still sound wrong if the timing is off, and timing is at least half of what makes music work.

A time signature like 4/4 tells you two things: the top number is how many beats are in a bar, and the bottom is which note value gets one beat. So 4/4 is four quarter notes per bar, which covers most popular music. 3/4 is three beats, which gives you a waltz feel.

Reading and counting rhythm properly is covered in the sheet music lesson, and the metronome is the tool for actually practicing it.

Where to go next

If you followed all of that, you know more theory than most working guitarists. Not an exaggeration. Plenty of good players never learn why a minor chord is minor.

The useful next step is applying it rather than reading more of it:

• Writing riffs and melodies, taking these notes and building something with them.
• Soloing over chord progressions, which is where knowing your thirds actually pays off.
• The circle of fifths, which turns all the key signature stuff above into one picture.
• The note trainer, for getting the fretboard into your hands rather than your head.

And if any part of this did not land, that is a fault in how I explained it rather than how you read it. Tell me which part and I will rewrite it.