Music theory as we usually understand it was built at the end of the Baroque period.
It was (and still is) very effective to describe music that is based on a linear progression through a bunch of chords towards a final resolving tonic chord. In the journey, the various chords take on different functions in relationship to the tonic chord, hence the name “functional harmony”.

But groove-based music (Latin, pop, rock, Celtic, …) is not linear. Instead, it is typically based on loops of repeated chords, often four.
Functional harmony is much less effective in describing this sort of music, and is often unable to provide totally convincing or even meaningful answers.

An example of such a loop is Brian’s recent “August Challenge” progression: [C Am Bb F].
The various replies in the forum clearly show that there is more about this progression than meets the eye.

In my own reply, I have already indicated several ways you can analyze this progression, my personal favorite being modal: C Mixolydian: [I vi bVII IV].
Others insist that it must be F Major: [V iii IV I].

In fact, those four chords passing by at a relatively quick pace create ambiguity, and the root movement A -> Bb between Am and Bb is particularly puzzling.

Philip Tagg is a music theorist who proposes a completely different approach, called “Everyday Tonality” because it is meant to describe the contemporary loop-based music we hear most often.
In his framework, the harmonic chord functions are replaced by metric functions, i.e. a function that depends on the position of the chord in the sequence. This metric function overrides any harmonic function the chord may have. In fact, the chords don’t need to have dedicated harmonic functions in the sense of functional harmony. As long as they don’t clash with the melody, the chords can be anything.
Tagg proposes the following terminology:
Tonic chord -> Outgoing chord -> Medial chord -> Incoming chord, and back to the Tonic chord.
The “strong” slots are the first and third ones; slots two and four are weak.

So, according to this approach:
C is the Tonic chord
Am is the Outgoing chord
Bb is the Medial chord
F is the Incoming chord.

BUT…

In Tagg’s approach, the Medial chord is allowed to assume a secondary tonic role in his own right, since it also occupies a relatively strong slot.
So, in reality, the loop is bi-tonal: C and Bb are the two tonal centers. When playing the loop, we are constantly displaced from one tonal center to the other.
Mind you: this is NOT modulation from C to Bb and back to C; it’s simply something that functional harmony cannot really make sense of.

Please also note that in this framework F cannot be tonic: it occupies too weak a slot for that. And C being a tonic chord, C Mixolydian is a better analysis than F Major.
But things change dramatically if you change the loop and make it [C Am F Bb]!

Anyways. Functional harmony is not necessarily the only way to describe music.

I hope you found this interesting.
Regards,
JM