Diatonic harmonic function of chord inversions

I'm trying to make my way through the classical harmony, and I'm making good progress, but since my last composition lesson there's been something which is not entirely clear to me.

So my teacher is a good creative advisor, but when it comes to actually teaching theory... he can do better. He told me that when making these harmony exercises with a given bassline, you have to determine what the function - tonic, subdominant, dominant - of the chord on that note should be. The way I understood it, is that you only want a tonic in root position at the beginning and the end (an exercise is usually 8 bars long) and inbetween should be a succession of subdominant and dominant functioning chords. You want to group chords within the same function as much as possible, so if I'd analyze a bassline that way, I would get something like this:

Now what isn't entirely clear to me is the way that the function of chords change when you invert them.

So for example, I has the function of a tonic, but I-6/4 has the function of a dominant, as in the cadential 6/4 chord. VI and VI-6 can have the function of a tonic, but VI-6/4 is more like a subdominant chord. So obviously chords that have the root of I, IV or V as bass take over that function, but what exactly gives a chord a T/SD/D function/feel?

I think I got most of this covered, but I'm just making sure if I'm understanding this correctly :)

Edit: This is the way I have currently harmonized this bassline:

Just saying that I've only had chord degrees I to VI and the dominant-seventh chord yet, so that's all I can use now. :)

Your understanding is close. One way to look at things is that the function of a chord is determined by its use. The figured bass approach treats a chord as primarily being intervals above a bass while the (more modern) Rameauian (I just wanted use all the vowels in a row) treats chords a permutations of a chord with the root in the bass. Both approaches are correct but they look at things from different points of view. In some cases one POV may seem a better explanation. In the cadential 64, the upper notes act like they are intervals moving over a bass (one gets a sequence of parallel thirds in the upper two voices) while in an arpeggio, a 64 sounds like a rearrangement of the chord notes.

I think of inversions as providing a method of writing smooth bass lines without changing chord roots. This generally works with first inversion chords. A progression like C-G-C is fine with the bass jumping around (and taking care of voice leading in the rest of the phrase) as is C-G63-C where the bass is just a passing tone between two root position chords. The second is smoother if that is what one wants. One can even get nice root movement by sixths using the Pachelbel Canon progression (or something similar) with C-G6-a-e6-F-C6-d; this is part of the "rule of the octave" studies predating Pachelbel. However, in various compositions of that time (and I cannot remember any specific one) there were other possibilities, C-G6-a-C64-F-C6-d6-G which cycles nicely back to the beginning. The e6 of the first example is replaced by a "passing" C64 in the second. Depending on the melody and the rest of the phrase, one of these may be preferred.

• Okay okay I get what you mean and it's a good thing to hear that I'm digging the right way, but for the "what exactly gives a chord a T/SD/D function/feel?" part, do you have anything to add on there? Besides, I have been thinking about reading Schoenberg's Harmonielehre to expand my knowledge on the physics behind harmony. Would you recommend any books regarding harmony? Commented Jan 7, 2018 at 18:54
• Afaik a chords relative characteristics lies in it's notes harmonic intervals, it's distance to other chords and notes in common with other chords. The T, S and/or D have the largest tonic interval (4th/5th) possible within a diatonic scale, combined a bit of voice leading, since they share one note in common. These chords are combining dramatic shift and familiarity, unlike two neighbouring chords that has different tonality and lacks common voice leading note. Also unlike the chords with tonic intervals of a 2nd or 6th, who are harmonically familiar, but lacks dramatic tonal distance.
– Erik
Commented Jan 7, 2018 at 19:47
• @ttw "bass is just a passing tone": a passing tone is a non-chord tone between two notes that are a third apart. A "neighboring tone" is a non-chord tone a step away from two notes that are the same note. With respect, your example is neither, because all the tones are chord tones. If the B in the G6 chord weren't part of a chord, it would be a neighboring tone rather than a passing tone. Here's a decent explanation of non-harmonic tones. Commented Jan 7, 2018 at 21:35

While it's perhaps reasonable to say that chords change their "function" when you invert them, I think that is because inverted chords are progressively less "stable" or "rooted" than their root position counterparts. As such, they are less "foundational" in terms of establishing key. As such, they have different functions to some extent. However, I wouldn't think of these as hard-and-fast rules.

The reason, then, that you start the piece with the tonic in root position is that doing so establishes the tonality better than if you use a different chord or a tonic chord in a different inversion. (Again, you don't have to, if you want the tonality to be ambiguous for musical reasons; for an example you need look no further than the opening of Beethoven's 5th symphony, which appears to start in Eb and doesn't clearly establish C minor tonality until several bars in.) Once you have established the key, the function of the use of chords in different inversions is to establish "good" voice leading. ("Good" in quotes because again these are not hard-and-fast rules; whatever works, works.)

Look for stepwise voice movement (as ttw says "if that is what one wants," but stepwise movement in voices provides balance and clarity -- not always what one wants, but something typically to depart from rather than ignore). When you have a leap, attempt to make the next note move in the opposite direction by step. Attempt to have the chords stick pretty much to the same register (keep the notes at close to the same pitch). The bass in your exercise is applying rules of stepwise voice movement: it has mostly steps, has no more than one skip at a time, and prefers stepping back into the skip rather than stepping away from it.

Now, I wouldn't personally say that I64 has the function of a dominant. Rather, I would say that it is a version of the tonic chord that leads nicely to a V7, since they both share the same bass note. That's the reason that it's used in a cadence, not because it has some sort of intrinsic dominant identity. What dominant identity that it may have derives from the context of the dominant cadence in which it occurs in this instance. If it were in an entirely different place, it wouldn't necessarily have a "dominant feel."

With the idea of good voice leading in mind, I would suggest you might do the first five chords like this: I, IV, I6, V64, I. The point is that the nice stepwise motion in the bass derives from the use of different inversions, and it is that stepwise motion that is the driver of what inversion to use.

(By the way, if, for the V64, you substitute a V43/6, i.e. C-D-F#-A, followed by a g minor chord in first inversion, you get a beautiful modulation to the relative minor with the same nice stepwise bass line. I thought you might find that interesting.)

• I've used your comment together with a new plan of approach to harmonize the melody. Posted the result in the original post! Would you mind looking at it and give feedback? :) Commented Jan 7, 2018 at 23:14
• That sounds nice. You have good stepwise motion in the voices. Consider changing the D in your VI chord to an Enat. This becomes a secondary chord, in this case the vii o6 of V (seven diminished six of V), written viio6/V. (If I were allowed to, I would also consider changing the bass to C, making it a V7/V.) The secondary chord makes for a compelling vector to the dominant to emphasize it at your half cadence. I would also remove the ties from the repeated notes, at least for the most part. The repeated notes work fine IMO. Commented Jan 11, 2018 at 3:54