Harmonic rhythm, and how fast the chords change
How fast the harmony changes is a decision separate from how fast the music goes; speeding it up before a cadence is one of the most reliable signals that a phrase is ending.
Two songs at the same tempo, with the same chords. In one, each chord lasts a bar; in the other, two. They do not sound alike: the second is calmer, the first moves more, and neither changed speed. What changed is the harmonic rhythm, how fast the harmony changes, and it is a decision independent of everything else.
A layer of its own
The melody's rhythm says when the notes attack. The tempo says how fast the pulse goes by. The harmonic rhythm says when the chords change, and it can be slower than the melody, nearly always, or faster, rarely.
The two progressions have the same four chords in the same order. In the first, each occupies two places; in the second, one. Play them at the same tempo and the second seems to be in a hurry. No chord changed; the frequency did.
The acceleration before the cadence
The most important use of harmonic rhythm is signalling the end of a phrase. Many songs hold one chord per bar through a phrase and, in the last two bars, put two chords per bar. The harmony accelerates, and the ear understands that the phrase is ending before the cadence arrives.
Here the ii–V or IV–V cadence usually comes in tight, two chords where there was one, and the closing tonic returns to the broad rhythm. It is the same mechanism as the turnaround: the return gains urgency because the chords tighten, not because the tempo rises.
Harmonic rhythm and style
Every genre has a typical harmonic rhythm, and it is part of what makes the genre sound as it does.
Rock and folk change slowly: one chord per bar, sometimes per two, and many whole songs with four chords. Bossa nova and jazz change fast: two chords per bar is the norm, and the II–V–I fits in two bars. Choro changes faster still, and the samba-canção sits in between.
That sequence, at two chords per bar, is bossa nova; at one chord per bar, it is a ballad. The chords are the same.
Passing chords and rhythm
When the harmony accelerates, the extra chords are usually passing ones: diminished chords between two degrees, secondary dominants before a degree, the sixth degree sharing a bar with the tonic. They fill the bar without changing the sentence, which is why analysis reads them as ornament, not structure.
Two bars, four chords, and the structure is still I, ii, V. The diminished chord is the harmonic rhythm filling the space.
Writing and playing
Whoever arranges decides the harmonic rhythm as they decide the tempo: on purpose. Taking chords out of a crowded chart is the fastest way to calm a song; putting passing chords into a sparse one is the fastest way to give it movement. And whoever accompanies needs to know where the chords change before knowing which they are: the wrong change in the right place bothers people less than the right change in the wrong place.
What to take from here
Harmonic rhythm is how fast the chords change, independent of the tempo and of the melody's rhythm. It accelerates before cadences, and that acceleration is one of the clearest signals a phrase is ending; it distinguishes genres that use the same chords; and the chords it adds when tightening are passing ones, ornament over a structure that did not change.