The turnaround, and the return that sounds like a consequence
The short sequence that closes a section and hands the music back to the beginning, and why a well-chosen return makes the repeat feel inevitable instead of like starting over.
One section of a song ends on the tonic, and the next section begins on the tonic. If the last two bars just sit on the C chord, the repeat sounds like starting over: the music stopped and began again. The turnaround is what goes in those two bars so that the return sounds like a consequence — a path that leaves the tonic and arrives at it again with intent.
The basic formula
The simplest turnaround is I–vi–ii–V: tonic, sixth degree, second degree, dominant. Four chords, one per beat or one per half bar, and the closing dominant is what hands the music back to the beginning.
It works because it is a whole sentence in miniature. The tonic and the sixth degree are rest; the second degree is departure; the dominant is tension; and the resolution is the first chord of the next section. The ear reaches the start of the repeat already expecting it.
With secondary dominants
Swap the diatonic chords for dominants, and each step starts pushing the next. The sixth degree becomes the V7 of II; the second degree becomes the V7 of V:
Now the roots fall by fifths the whole way — A, D, G, C — and each chord is the dominant of the next. The return gains urgency: three tension chords in a row before the rest. It is the turnaround of the blues and of a good part of American music in the first half of the twentieth century.
The middle ground, with a minor sixth degree and a dominant second degree, is the commonest of all:
Starting from the third degree
The turnaround's first chord can be the third degree instead of the tonic. E minor shares two notes with C major, so it fills the same function, and it avoids repeating the chord the section has just ended on:
That III–VI–II–V is the reference turnaround of jazz and bossa nova. Notice that, read another way, it is two chained II–V–Is without the I in the middle: E minor and A7 point at D; D minor and G7 point at C. The three-chord formula of the previous reading, applied twice in a row.
Where it lives
The turnaround lives in the last two bars of a section that repeats: the end of a blues chorus, the end of a song's A section before it comes round again, the end of a head before the solo. When a section ends on the tonic and the next begins there, there is room for a turnaround; when the next section starts on another chord, the turnaround points at that one.
In a twelve-bar blues in C, the last two bars are the classic place:
The first version returns; the second returns with intent.
What to take from here
The turnaround is a cadence stretched over two bars that leaves the tonic and returns to it, and what makes it work is the same thing that makes everything else work: functions in order, roots by fifths, dominants that push. I–vi–ii–V is the basic formula, III–VI–II–V is the jazz one, and secondary dominants are the seasoning added as the style asks. With it, the reading of functional harmony closes the circle: the sentence, the cadence, the preparation and the return.