Five progressions that reliably sound sad: vi–IV–I–V, i–♭VI–♭III–♭VII, i–♭VII–♭VI–V, i–♭VII–♭VI–♭VII and I–iii–IV–iv. Four start on a minor chord; the fifth turns sad on its last chord, where a major IV becomes minor. In every case the sadness comes from one of three things: a minor tonic, a ♭VI, or a borrowed minor iv.
Each is shown below in a key where the chords are open shapes on a guitar, with why it sounds the way it does and a link to the family page where it is compared with its relatives and given the scales that fit each bar.
Pop-Punk / Sensitive
vi – IV – I – V
The same four chords as the brightest progression in pop, I–V–vi–IV, started from the minor chord. Beginning on the vi makes the ear take the relative minor as home, so every arrival on the I feels like leaving rather than landing. It still resolves, which is why it carries ballads: sad without being hopeless.
Natural minor with nothing borrowed. The drop from the tonic to the ♭VI is immediate and lands a third lower, and the ♭III and ♭VII that follow are the relative major's I and V, so the loop keeps glancing at a major key it never settles in. In A minor these are Am, F, C and G: the chords of the progression above with the tonic moved.
A descent by step from the tonic to the V, and the V is major. That raised seventh (G♯ in A minor) is a note the natural minor scale does not have; it gives the last chord its pull back to the top and the whole line its drama. This is the sad that sounds Spanish.
The Andalusian descent without the raised V. It turns back at the ♭VI and never resolves, so it broods instead of landing. In E minor every chord is an open shape, which is why alt-rock reaches for it first.
Starts in a major key and turns sad on one chord: the IV becomes minor, one note dropping a half step (A to A♭ in C). Everything around it is diatonic, so the ear hears exactly one moment of loss and remembers the song by it. The most efficient sad turn in pop.
A minor and C major share the same open chords (Am, C, Dm, Em, F, G) and E minor adds D, which is why the five above are shown in those keys: every chord except the E in the Andalusian cadence and the Fm in the soul climb is a first-position shape. To sing them higher, put a capo on and keep the same shapes.
The first two progressions are the same four chords, Am, F, C and G, and which one you are playing depends only on which chord the ear takes as home. Over either, the scale is the same seven notes: A natural minor, which is C major started from A. The family pages show that scale on the fretboard bar by bar.
On piano
All five sit on the white keys in C major and A minor with two exceptions, and the exceptions are where the sadness is: the G♯ in the E major chord that ends the Andalusian cadence, and the A♭ in the Fm that ends the soul climb. Play the progression on white keys, then add the one black key, and you can hear exactly what each borrowed note does.