I'm wondering if chords usually move down by fifths.
A ponderous question. It is simple in presentation but difficult to answer depending on the OP's background. In order to properly answer this question it needs to be properly unpacked:
- First, I take it that the OP intends to ask if chord roots usually move by fifths. Supposing this is true, we need to understand that while seemingly broad, the answer is actually quite specific:
- Composers only began thinking about music in terms of constructing vertical harmonies around the time of Renaissance / Early Baroque. Harmonius vertical relationships were a reactionary bi-product of horizontal thinking. Composers then developed these relationships over several hundred years until the introduction of pan-tonal (i.e. non-functional) harmonic languages in the early 20th century. Yes, there are many, many examples of earlier composers using non-functional harmony, but that fall outside the realm of this answer.
The vast majority of music written after early 20th century branches out in myriad directions. While hard data is nearly impossible to quantify, the extreme prevalence of pantonality during the mid-20th century, the emergence of minimalism, and technology's role in giving voices to non-traditionally educated musicians means that if incorporating progressions at all, it is less likely those progressions will be functional, let alone functional in the way the OP describes.
Further, it is important to acknowledge that the OP must only be referring to music written in the Western European Classical tradition. Many, many, many other types of music around the world do not incorporate functional harmony as we describe it, among many other things.
So now that we've unpacked the context let's look at the actual question:
I'm wondering if chord [progressions written in the Western European Classical musical tradition between the years 1600–1930] usually [contain root movement] of mov[ing] down by fifths.
And here's the answer: it depends
You see, progressions stem from cadences. Cadences have different types of strength. Not all are the same, and different cadences are used for different reasons. This is the result of building and releasing tension. In the Western European Classical musical tradition, an Authentic Cadence is the strongest (with a PAC being the strongest of the two). The interval from tonic to dominant is the fifth.
If we cycle backwards, we run into what's known as the pre-dominant. The root note for the IV chord is known as the "sub-dominant" as it is a fifth below the tonic.
Thus if we look at the following progression:
We see that while the roots of both intermediary chords are in fact, a perfect-fifth away from tonic, the root movement between them is actually only a major-second. In other words, it does not move "down by fifths".
Why are these chords so popular?
As the OP stated, the perfect-fifth is the most harmonically-pure interval after the octave and perfect unison. The above chords are therefore, with respect to their interval, the best suited to give the strongest progression.
Now, what about the ii6/5?
This chord is wonderful as gives the impression of IV-V, while giving descending root-movement of perfect-fifths. While this progression is very popular (especially during the Baroque period, in which the clearest examples of root movement by descending fifths may be found), it does not and cannot constitute the majority of written music.
Alright smart guy, so what about the other chords?
Sure, ii may be substituted for IV, as I described above. Other chord substitutions are weaker: iii for I or V, for example, vi for I or IV. Substituting vii for V gives you a leading-tone chord, which has root movement by minor-second and doesn't fit the "descending by fifth" theory. Let's put some of these substitutions in context:
(root movement by 3rd then 5th)
(2nd then 5th)
(2nd then 5th)
As you can see, substitutions do not intrinsically beget root movement that fits your model.
But all of this is merely looking at how root-movement by fifth is possibly used, not whether or not composers employ them more than any other progression. The fact of the matter is that unless an individual has compiled data for the entirety of written music, it is impossible to answer with 100% accuracy. That said, we need to think about what is the "most likely".
The fact is composers use a variety of chord progression (and regressions) to suit their needs. Theory is developed to try and explain how it is that they make the music that they make. Theory comes after music, not before, and it is just that, a theory. Simply wanting something to be true doesn't in fact make it so.
So root movement by fifths? During one period of human history in the context of one musical tradition, it was a widely-used musical device.