Is the I-IV-viio-I progression never usable?

Question

This question arose while studying the circle of fifths. Along with the cadence, I learned the progressions below.

1. viio - iii - vi - ii - V - I
2. I - IV - I
3. I - V - I
4. I - IV - V - I

But if 'I - IV - V - I' can be possible why can't a 'I - IV - viio - I'? Or is it possible that it is just not in the description?

And In that case, the circle of fifths is not fully achieved. But if don't mind the circle of fifth. can't we just proceed with that?

Answer 1

The I-IV-vii^o-I progression is possible, but is omitted from the examples, because they are focused on cadences by perfect fifth. In all of the cases above, the final I chord is approached by either descending or ascending fifth.

Answer 2

All those progressions are likely to sound good. And actually, you can make pretty much any progression sound phenomenal in the right context.

I don't see any problem with I - IV - viio - I. It's actually a quite common progression in popular music, and it will sound great. It just doesn't follow the circle of fifths (Actually is kind of does if you think if the viio as a V7 in first inversion). But anyway you should think of the circle of fifths as a tool for writing progressions, not a dogmatic rule.

Answer 3

I think it helps to not think about the "circle of fifths" progression but instead think of "roots by descending fifth" progression. The ideas are more or less the same, but the latter wording focuses more on relative root progression rather than a specific chord template.

When you look at your several progressions you will see that all of them are based on root progression by descending fifth. The four progressions feature...

• viio - iii - vi - ii - V - I, all descending fifths
• I - IV - I, first change is descending fifth
• I - V - I, second change is descending fifth
• I - IV - V - I, a descending fifth progression harmonically sequenced up a fifth

Root progression by descending fifth is considered a strong progression. Other strong progressions are roots by descending fourth and roots by ascending step. Notice that all your examples are entirely combinations of those three strong progression types.

Other progression being considered weak should not be misunderstood to mean bad or not allowed. Strong progressions have a connection to rhythm, the bar line, and cadences, and so the handling of strong/weak progressions has structural importance for phrasing and form.

But if 'I - IV - V - I' can be possible why can't a 'I - IV - viio - I'?

Any chord progression is possible, but you might explain them different ways. I'm not sure why you say the second progression is possible despite with these chords, in your words, "the circle of fifths is not fully achieved". I mean only that I don't know why you recognize these chords can work regardless of whether they conform to the circle of fifths. But, probably the most common way to explain it would be through chord function.

In functional harmony chord functions are: tonic, dominant, and pre-dominant. You can read up on the details of functional harmony, but the main point for your question is dominant function can be achieved with either V or viio. In other words the two progressions - I IV V I and I IV viio I - are functionally the same. The are both tonic pre-dominant dominant tonic.

The viio chord will often be in first inversion viio6, but that is more of a voice leading issue and doesn't change what happens functionally.

But if don't mind the circle of fifth.

You really should not think of harmony being derived from the circle of fifths progression.

Instead think of...

• relative root progressions
• chord and scale degree functions
• chords are the result of voice leading

From comments...

thanks but (IV-V) in 'I - IV - V - I' is not fifth too so why that is can?

As I mentioned above this is a descending fifth progression harmonically sequenced. I IV is a descending fifth, V I is a descending fifth. As a harmonic sequence you just take I IV and raise it a perfect fifth and repeat the progression. You can also think of it "grammatically." Using functional labels it's just tonic > pre-dominant > dominant > tonic the epitome of functional harmony. But, you can also think of it "grammatically" as a departure from the tonic I IV, which is a sort of "opening", like an antecedent, and a return to the tonic V I, which is sort of "closing", like a postcedent.

...but (IV-V)...

That is root progression by ascending step. Root progression by descending fifth is not the only usable progression. The basic run down of common root progressions are:

• descending fifth, ex. V I, a "closing"
• descending fourth, ex. I V, an "opening"
• descending thirds, ex. I vi IV ii viio V, a movement from tonic through predominant/subdominant to the dominant
• ascending step, ex. IV V, a movement from subdominant to dominant, of V vi, a "desceptive progression

You should also be aware of how important the bass line is apart from the chords and chord roots and the sort of harmonic "equivalence" some progressions have. Ex. IV V I and ii6 V I where the root progression are different, but the bass parts are the same. In common use those two progressions are effectively the same.

Also be aware that some relative root progressions are commonly found in specific regions of a key. Like roots by ascending step in IV V or V vi as very common, but ii iii being less common, but you could "explain" ii iii "working" with good voice leading an using the modal/secondary chords as a sort of functional pre-dominant depending on the specifics. In other words the position of roots in a key can often be more important than the interval/direction of the root progression.