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What exactly is the procedure for harmonizing a bass line? In my class, the teacher introduced inversions of chords, which are not hard to understand per se, but I can't wrap my head around how can I use them when harmonizing a bass line.

If I have to use strictly triads in root position, I could give each note its degree just by looking at the note. But I understand there are some degrees that can't pass to others, like a chord from the dominant group (V, vii°) to a chord from the subdominant group (IV, ii). So I know that I can use inversions to solve this issue.

Other than that, what do I have to look for to understand when I could use an inversion?

For example, I have this exercise done in the class:

enter image description here

I know what I'm asking is probably a hassle to explain completely, but my book is pretty hard to understand - at least for me. If anyone could help me, or at least give me some direction to some resource to study from, you'd have my eternal thanks.

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A single bassline can be harmonized in a number of different ways. Assuming you are working only with diatonic triads (three note chords that require no accidentals), you'll typically have three options for your harmony for each note. In the key of G major, those options look like this:

  • G: I, vi6, IV64
  • A: ii, vii°6, V64
  • B: iii, I6, vi64
  • C: IV, ii6, vii°64
  • D: V, iii6, I64
  • E: vi, IV6, ii64
  • F#: vii°, V6, iii64

I realize this probably looks a little daunting right now, but it becomes easier as you practice. To show you how we can apply this, let's look at the last four measures of your exercise. We have the following bassline: D, E, C, D, G, C, G. I usually find it easiest to work backwards when harmonizing, so let me walk you through that process:

First of all, we already know the last chord has to be a I chords in root position, so let's look at the second to last chord. We know we need a cadence here, either plagal or dominant. The only chord we can use that gives us a valid cadence is a IV, a C in root position. So, our last two chords are basically decided for us. From here on, we have to start making some decisions...

This is where we start to get out of the realm of right and wrong answers. You could, for instance, harmonize all six of these chords in root position and not break any rules (V, vi, IV, V, I, IV, I). That would probably sound alright, although not particularly creative; besides, we want learn about how to use inversions, so let's be a little more daring here. For instance, we could instead harmonize this passage as iii6, vi, ii, V, vi6 - IV64, IV, I.

Now I could have just picked those chords randomly from my available options, but I actually didn't; there's a method to the madness! First of all, you'll notice that iii, vi, ii, V is a sequence of descending fifths in the root of the chords. Whenever you can harmonize with chords where the root descends by a fifth, it will sound very satisfying (you'll learn more about this when you talk about secondary dominants.) Second, you'll see that I choose to take the V to a iv6 instead of a I, borrowing from the structure of a deceptive cadence. My other option was to move directly to the IV64, but, as you pointed out, it is unusual in this style of harmony to move from a dominant chord to a subdominant chord, so I eliminated that option. Lastly, I choose to switch from a vi6 to a IV64 on the third to last note in order to set up the final cadence. I didn't have to do this, but it makes things a little more interesting to not always line up the harmony one-for-one with the bass line.

One more thing to consider: second inversion (64) chords can be a little tricky and should be used with care. Typically, second inversion chords are only used in particular ways. Let's talk very briefly about three common ways you will probably encounter in basic harmonization: passing, neighbor, and cadential. A passing second inversion occurs when you have stepwise bass movement, for instance: I, V64, I6. A neighbor second inversion occurs when the bass line stays on the same note while the harmony shifts, for instance: I, IV64, I. A cadential second inversion occurs when you use the following very common cadential figure: I64, V, I. This is by no means an exhaustive list, but it's good to keep an eye out for these opportunities to use second inversion chords when scanning your bass line.

In short, for all the notes between the cadences, you have some freedom as to how you'd like to structure the harmony, and your options only grow as you learn more and more theory. The good news is that with practice all of these patterns become internalized and you can quickly assess your options and make a decision. Until then, however, the best method is to write out all three options for each chord and then work backwards from the cadences, eliminating the options that won't work and choosing your harmony from the remaining options based on your own aesthetic judgement.


Some Additional notes as per your comments

Can a cadence be set up anywhere in a phrase? For example, how you set up the deceptive cadence between the two measures?

A cadence is specifically at the end of the phrase. When I wrote about using a deceptive cadence, I meant that I was simply alluding to that type of cadence in my chord choices. It's not actually considered a cadence unless it falls at the end of a phrase.

My book tells me to not use triads built on the III and VII grades of the scale in Major and Minor and the II in the Minor mode for now. Do you know why?

Triads build on the seventh scale degree in major and the second scale degree in minor turn out to be diminished triads (vii° and ii°), which I suppose you haven't learned how to resolve yet. I'm not sure why you're being asked not to use iii in major though. It's pretty common to procede a vi with a iii, but I suppose they want to teach you how to handle voicing that specific case before you start using that chord. Chords on the third scale degree can be tricky in harmonic minor, as you end up with an augmented chord (III+), but you probably haven't reached that yet.

Should I incur in errors while harmonizing, like parallel/hidden 5ths and 8ves, would the best solution be changing the whole chord, or are they solvable without doing that?

In most cases, you can avoid parallel and hidden 5ths and 8ves by revoicing the chord, rather than changing the harmony, although there are some cases where you may just need to change your harmony to get out of a jam.

  • I can't thank you enough! You clarified most of my doubts. I have some questions left if you don't mind: > Can a cadence be set up anywhere in a phrase? For example, how you set up the deceptive cadence between the two measures. > My book tells me to not use triads built on the III and VII grades of the scale in Major and Minor and the II in the Minor mode for now. Do you know why? > Should I incur in errors while harmonizing, like parallel/hidden 5ths and 8ves, would the best solution be changing the whole chord, or are they solvable without doing that? Thanks again! – Dodicin Nov 28 '14 at 18:00
  • Good questions. I'll edit my answer to include responses to these questions, as my reponse won't fit in a comment. – Casey Rule Nov 28 '14 at 18:15
  • Thanks once more for the help. I've skimmed through the following chapters of my book, and found out that the peculiarities of the III would be its attraction to the IV and the matter with its leading tone that could ascend or descend, talking then about how this matter goes to make up the phrygian cadence. And yes, I didn't quite understand the matter. – Dodicin Nov 28 '14 at 18:58
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Casey Rule gave a fine answer, I just want to point out a few things about harmonizing in general and you should be aware of while trying to harmonize a bass line.

  1. iii chords are quite rare in a major key, in fact in all my classical theory studies I don't remember analyzing anything that used any type of iii chord in a major key.
  2. While vii° is a viable option, it is quite rare to see it outside of first inversion (vii°6) and if you use it, you will be going to a I chord most of the time because how the diminished 5th likes to resolve.
  3. As Casey points out, second inversion chord are considered dissonant and need to be approached carefully. He listed a few way and there are more, but the best way to look at it is only use a second inversion chord if it is a primary chord (I, IV, or V) and is either at the cadence, approached by step to and from, or part of an arpeggio.
  4. Moving the chords by 3rd or 4th is typically more desired then moving by 2nd so seek to use chords that are not next to each other and if you do move by 2nd try not to string a bunch of them in a row.
  5. Casey already cover this well, but learn and understand cadences. While most of the harmony can vary and be looked at different ways, cadences are very important and there are really only a few ways to approach them.

Besides that, do what sounds right. If given only a bass line, there are many different ways to harmonize the same bass line. I would suggest to keep it simple as you start and listen to how the progression sounds. You can always take a simple progression and re-harmonize it later.

  • Thanks for the helpful insight. As for the fourth point, should I favor intervals of 3ds and 4ths between the chords in their root position (not considering the root in an inversion)? I believe my book says the same by calling the intervals of 4th and 5th principal, while calling skips by 2nd strong and by 3rd weak (Noting also how to avoid creating a harmonic syncopation with the latter one). So, I should try to use mainly principal and weak intervals? (Hopefully the terms are not much different in English) – Dodicin Nov 28 '14 at 18:14
  • @Dodicin Yes in fact most of the time, the inversions are to smooth out the bass. I'm not use to that terminology, but it sounds like what I'm talking about in the fourth point. – Dom Nov 30 '14 at 0:34
  • @Dom - What do you mean iii is rare? I've gone through iii quite often. And the seventh chord iii7 is so common in anime music. – Maika Sakuranomiya Jun 19 at 12:06
  • @MaikaSakuranomiya I was talking in a classical context. In analysis, it may have come up a handful of times in practical pieces. – Dom Jun 19 at 13:08
  • I've also seen iii7 in classical pieces as well. I've seen the iii triad pretty often especially in Baroque period music, for example, in the I-IV-vii*-iii-vi-ii-V-I progression. iii7 is not really as common, but I've seen it sometimes. – Maika Sakuranomiya Jun 19 at 13:10
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When you harmonize a passage for four parts what you have to get your head around is that you are writing a melody within the confines of the given chord progressions.

There is somewhat leeway in regards to root position and first inversion but you want to use these inversions in a way as to make the melody you are writing appealing.

So this means smooth transition between chords. A pleasant line and good form needs to be part of this melody.

When it comes to second inversion chords they are only used in very specific cases. These include.

  • Passing Six Four
  • Cadential Six Four.

On the other hand where triads in second inversion only comes in specific cases the quadtat(Dominant 7ths) has a great more freedom in regards to its inversion.

When you use chords with sevenths you can easily use them in second and third inversion as long as it makes sense in the melody you are writing.

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