Scales and harmony

A scale is a key laid out in a row. Almost all Western melody and harmony draws on one.

The major scale is defined by its pattern of steps: tone, tone, semitone, tone, tone, tone, semitone. Start on C and that pattern uses only white keys, which is why C major has no key signature. Start anywhere else and the pattern forces sharps or flats — that is where key signatures come from.

A scale uses each letter name exactly once: A major is A B C♯ D E F♯ G♯, never A B D♭ D… Spelling it that way keeps every interval correctly named.

The positions in the scale are numbered as degrees, and the first one is the tonic.

Degrees describe a note by its job rather than its name. In C major, G is the fifth degree; in G major, D is. The number stays put while the letters change with the key.

That is what makes them useful: a melody described in degrees can be moved to any key unchanged, and "it goes up to the fifth and falls back to the tonic" describes a shape you can recognise anywhere.

Each degree has a traditional name too — tonic, supertonic, mediant, subdominant, dominant, submediant, leading note — and the names hint at the pull each one has. The seventh is called the leading note because it leans hard into the tonic above it.

Degrees are also how chords are labelled, with Roman numerals: I, IV and V are chords built on the first, fourth and fifth degrees.

Play a scale and stop on the seventh note. Something feels unfinished. Go one more and it resolves: that resting note is the tonic.

It is the first degree of the scale and it names the key — the tonic of D major is D. Most pieces end on it, and a great many begin on it.

The tonic is not louder or longer than other notes; it is defined by context. The same note is the tonic in one key and a passing note in another. Finding it by ear is a trainable skill and one of the most useful there is — it is what lets you play something back without being told the key.

A cadence is how a passage arrives. The commonest is the dominant chord followed by the tonic — V to I — which sounds so final that almost every piece in the Western tradition ends on it.

Others stop short on purpose. Ending on the dominant leaves the music open, like a comma, and asks for an answer; pairs of phrases use that constantly, one leaving the question and one closing it.

In ear training a cadence has a second job: it establishes the key before a question is asked. A scale degree has no sound of its own — the same note is the tonic in one key and the leading note in another — so without a cadence there is nothing for it to be a degree of.

Start on C, which has no sharps or flats. Go up a fifth to G: one sharp. Up another fifth to D: two. Keep going and you pass through every key, adding one sharp at a time, until the sharps run out and the flats start coming off instead.

Go the other way from C — down a fifth to F, then B♭, then E♭ — and flats accumulate in the mirror order.

Drawn as a circle, the two directions meet at the bottom, where the same sounds are written two ways: F♯ major and G♭ major are the same keys on a piano and different pieces of paper.

What makes it worth learning is that it is not a list to memorise. It is one rule — a fifth at a time — that generates every key signature, tells you which keys are neighbours, and shows you where a piece is likely to modulate to next. The tool at /tools/circle-of-fifths draws it with both rings and the chords of each key.

A key is two things at once: a tonic to come home to, and a scale of notes that belong. Saying a piece is in D major says both that D is home and that F and C are sharp.

The key signature is how the key is printed, but it does not settle the matter alone — one sharp means G major or E minor, and only the music decides. What decides it is which note behaves like home.

Pieces change key, which is called modulating, and the change is usually the largest-scale event in the piece.

In Portuguese this is tonalidade, and colloquially tom — the same word as the interval tone, which is worth keeping straight.

The commonest chord is the triad: a note, the note a third above it, and the note a third above that. Built on C that gives C, E, G.

The quality depends on the sizes of those thirds. Major third then minor gives a major chord; minor then major gives a minor chord. That one swap is most of the difference between bright and dark in Western music.

Chords are named by the scale degree they are built on, with Roman numerals — I, IV and V are the three that carry most music, and their pull towards the tonic is why V to I sounds like an ending.

The notes need not be in that order or in one octave; rearranged, a chord is inverted but still the same chord.

Where melody is one thing after another, harmony is several things at once — and, on a larger scale, the order those combinations arrive in.

The smaller sense is a single chord: which notes are sounding together and what that sounds like. The larger sense is progression: why V leads to I, why a piece feels like it is heading somewhere long before it arrives.

Harmony is built from intervals and organised by key. Both senses depend on the tonic: a chord is heard partly as itself and partly as its distance from home.