This is a working reference for how far notes sit from one another (intervals), and what happens when you stack several of those distances at once (chords) — worked out, with numbers, across all twelve keys and nine scales. Click the keys. Everything here makes sound.
An interval is the distance between two pitches, measured in semitones (half-steps). That's the whole idea — everything else is naming convention. A piano has twelve semitones before a pitch repeats an octave higher, so there are thirteen interval sizes worth naming, from standing still (0 semitones) to a full octave (12 semitones).
| Semitones | Short name | Full name | Character | What it's doing |
|---|
Choose any starting note and any interval. The keyboard shows both notes, plays them, and the table below shows what that same interval produces starting from every one of the twelve notes — because an interval is a relationship, not a fixed pair of pitches.
| From | Interval | To |
|---|
Every scale is a formula of whole-tone (W) and semitone (H) steps from the tonic. Change the root and the notes change, but if the formula is the same, every interval relationship inside it — tonic to 3rd, tonic to 5th, 3rd to 5th — stays exactly the same. Pick any root and any scale below to see (and hear) the formula worked out in real notes.
| Degree | Note | Step from previous | Interval from tonic |
|---|
Take a root, add a note a third above it, add another note a third above that, and you have a triad. The only thing that changes between a major, minor, diminished, or augmented triad is which size of third gets stacked where. Do it once more and you have a seventh chord.
Root, third, fifth. Four possible qualities, defined entirely by two interval choices:
Take any triad and stack one more third on top. Eight qualities show up in common practice and jazz harmony:
Pick a root and a chord quality. The keyboard highlights every note, and the breakdown shows exactly which intervals — from this table above — are stacked to build it.
Pick any note in a scale as a root, and stack the notes a third and a fifth above it — using only notes already in that scale. Do this on every degree and you get that scale's diatonic chords: the built-in harmony of the key. Choose a root and a scale to generate its full set, triads and sevenths, for every degree.
| Degree | Triad | Quality | Notes | 7th chord | Quality | Notes |
|---|
Once you can hear the difference between a major 3rd and a minor 3rd, you can identify almost any triad by ear — the fifth barely varies, but the third decides everything.
Move the lower note of an interval up an octave (or the upper note down one) and you get its inversion. Every interval and its inversion add up to 12 semitones. This is also why a major 3rd below a note sounds like a minor 6th above it — same two pitches, same relationship, viewed from the other end.
| Interval | Inverts to |
|---|
Each scale is a distinct formula of intervals from the tonic. The coloured bar shows which of the twelve chromatic pitches belong to that scale, starting from C — root in red, scale tones in gold.
Both circles arrange the twelve major keys around a clock face. The circle of fifths moves clockwise by a perfect fifth (7 semitones) at each step; the circle of fourths moves clockwise by a perfect fourth (5 semitones) — the same circle, read in reverse. Relative minor keys appear in the inner ring; key signatures in the centre.
Each step clockwise raises the key by a perfect fifth (+7 semitones) and adds one sharp — or removes one flat.
Each step clockwise raises the key by a perfect fourth (+5 semitones) and adds one flat — or removes one sharp.