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Intervals: the distance between two notes
An interval is just the gap between two pitches. Almost everything else in theory is built out of them, so it is worth half an hour, and it is the only bit of theory I would call genuinely unavoidable.
The numbers count letters, not semitones
This trips people up more than anything else, so here it is first. To name an interval you count letter names, starting at 1 on the bottom note.
From C to E: C is 1, D is 2, E is 3. That is a third. From C to G: C, D, E, F, G, so a fifth. From C to the next C: eight letters, an octave.
Notice you count the note you start on. It feels wrong the first time, because C to D looks like one step but is called a second. Blame the people who named these things centuries before anyone thought about it properly.
Hear them
Each button plays two notes together, starting from middle C. Play them in order and the change in character is obvious even if you have never thought about it before.
The second and the seventh sound tense, like they want to move. The fifth and the octave sound settled, almost empty. The third and the sixth sound sweet, which is why they carry most of the harmony in pop music.
Why the fifth sounds so solid
There is a physical reason and it is not mystical. A vibrating string does not produce one frequency, it produces a fundamental plus a stack of overtones at whole-number multiples. The first overtone is an octave up, the second is an octave and a fifth up.
So when you play a C and a G together, the G is already present in the C, quietly, as an overtone. The two notes share a lot of their sound. That shared material is what your ear reads as agreement.
A second shares almost nothing, and its two frequencies are close enough that they beat against each other. That roughness is the tension you hear.
Major, minor, perfect
Seconds, thirds, sixths and sevenths come in two sizes. The bigger one is major, the smaller one is minor, and the difference is one semitone.
That single semitone is the whole difference between a happy chord and a sad one, which gets its own page: major and minor.
Fourths, fifths and octaves do not come in major and minor. They are called perfect, a name inherited from medieval theory that has stuck around long past its usefulness. Treat it as a label, not a claim.
The tritone
One interval sits exactly in the middle of the octave, six semitones, halfway between the fourth and the fifth. It is the only interval that stays the same if you flip it upside down.
Medieval writers were suspicious of it and the phrase "the devil in music" got attached to it later, mostly by people repeating each other. What is true is that it is unstable and wants to resolve, which is exactly why it sits at the heart of every dominant seventh chord and every blues.
Where to go with this
Stack two thirds and you have a chord. Line up a specific pattern of seconds and thirds and you have a scale. Go round the circle in fifths and you get the circle of fifths, which is the fifth doing its work on a larger scale.
How the notes fit together
Start anywhere. Each of these stands on its own, and they all end up back at the circle.
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You are here
Intervals: the distance between two notes
A third, a fifth, an octave. What the numbers count, and why a fifth sounds settled while a second sounds like an argument.
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02
Scales: seven notes and the gaps between them
A major scale is a pattern of steps, not a list of letters. Once you know the pattern you can build one from any note.
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03
Major and minor: one note of difference
Move a single note down a semitone and a bright chord turns dark. Here is which note, and what it does.
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04
Chords: notes stacked in thirds
Triads, sevenths, and why the chords in a key are not a random assortment but a family with jobs.
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05
Key signatures: why sharps arrive in that order
F sharp, then C sharp, then G sharp. The order is not arbitrary, and once you see where it comes from you never have to memorise it.
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06
The circle of fifths, explained by ear
The most looked-up diagram in music, and the one most often taught as a thing to memorise rather than a thing to hear.
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07
Pentatonic scales: five notes that cannot clash
Take two notes out of the major scale and something odd happens: everything left over sounds good together. Handpans and guzhengs are built on it.
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08
Transposing: the same tune in a different place
Why a song moves when it changes instrument, what stays the same when it does, and what a hundred real melodies show about which instruments have to move most.