Non-chord tones, and what the melody does between the right notes
The melody notes that do not belong to the chord, classified by how they arrive and leave; much of what sounds like a strange chord is only a passing note over an ordinary one.
Over a C major chord, the melody plays C, D, E. The D does not belong to the chord. Nobody changes the chord because of it: the D is a non-chord tone, a melody note passing between two right ones. Most melodies are made of this, and much of what looks like a complicated chord in a chart is a passing note over an ordinary one.
Classified by arrival and departure
Non-chord tones are not told apart by sound: a D is a D. They are told apart by how they arrive and how they leave — by step or by leap — and by where they fall in the bar. The names describe that movement.
Passing tone — arrives by step and leaves by step in the same direction, linking two chord notes. The D between C and E.
Neighbour tone — leaves a chord note by step and returns to it. The D between two Cs, or the F between two Es.
Appoggiatura — arrives by leap, lands on a strong beat, and resolves by step. It is the non-chord tone that hurts: accented, dissonant, and then resolved.
Over C major, the A arrives by leap on the beat, and falls to the chord's G.
Suspension — a note from the previous chord is held while the chord changes, and then falls to the right note. It is the prepared appoggiatura: it arrives by tie, not by leap.
F, a note of the F chord, held while the chord becomes C, and then resolved to E.
Anticipation — the next chord's note arrives before the chord. It is the opposite of the suspension: the melody goes ahead, and the chord catches up.
Escape tone — leaves by step and resolves by leap in the opposite direction. Less common, and the name says it all: the note escapes.
Why this matters for playing
Two practical reasons. The first is reading charts: a melody playing F over a C chord does not need a C eleventh chord; it needs a C chord and a passing note. Whoever knows the non-chord tones simplifies charts instead of complicating them.
The second is improvising: the chord notes are the resting points, and the non-chord tones are the path between them. A phrase made only of chord notes sounds like an arpeggio; one made only of non-chord tones sounds outside. The melody lives in the mixture, with the right notes on the strong beats and the foreign ones between them.
The strong-beat rule
The difference between a non-chord tone that sounds natural and one that sounds wrong is almost always in the timing. Passing and neighbour tones live on weak beats, between the chord notes; appoggiaturas and suspensions live on strong beats, which is why they hurt, and why they have to resolve. A non-chord tone on a strong beat with no resolution is what the ear calls a wrong note.
Over C major: E and G belong to the chord and fall on the beats; F and A are passing tones and fall between them. Swap the order — F and A on the beats — and the same sequence of notes sounds as though the chord were wrong.
What to take from here
Non-chord tones are the melody notes outside the chord, classified by arrival and departure: passing and neighbour tones by step on weak beats, appoggiatura and suspension on strong beats with resolution, anticipation arriving ahead of the next chord. Knowing them simplifies charts, organises improvisation, and explains why the same note sounds right on one beat and wrong on another.