The ‘unit 9’ of this lesson’s heading refers to a chapter in the widely acclaimed Harmony and Voice Leading, a univer-sity-level textbook by Edward Aldwell and Carl Schachter. The chapter deals with chords that lead to the dominant – IV, ii and ii6 – while continuing to use the I, I6, V, V7, V6, V6/5, V4/3, V4/2 and vii6 chords of previous chapters.

I had asked Gustave to compose a number of short passages that would explore and illustrate the chord usage and voice-leading described in the chapter. Unit 9, Preliminary Exercises traces the growth in Gustave’s technique, as he worked his way through the complexities of this aspect of musical composition.

Lesson Format

Email lessons can be highly interactive, as this example amply illustrates: it includes ‘layers’ that refer back to earlier exchanges – layers that my students and I distinguish via text color and font style.

For graphic simplicity, I’ve reduced these to two layers, here: my comments are always in Verdana (grey for material from previous exchanges, and black for more current expla-
nations), and “Gustave’s” are in Times New Roman (same color, regardless of layer).

Classical Harmony

using “Harmony and Voice Leading”,

by Aldwell & Schachter

unit 9, preliminary exercises

Hi, Gustave;

It’s nice to see how well you’re assimilating the stylistically correct usage of these new chords – good work!

I’ve pointed out a few ways to make your basslines more ‘linear’ – these usually involve a more specific choice of dominant harmony (eg, V6/5, V4/3, or vii6 instead of V), which I’ve detailed.

Let’s take a look at your latest work:

Unit 9, Preliminary Exercises, Ex. A

  1. Good work, Gustave. The only comment I have is that you can achieve a more ‘contrapuntal’ bass line by using a V6/5, vii6, or V4/3 here, instead of the root position V7. Such a change would yield a smoother bass line, and save the power of your root position V7 for the cadence. The soprano’s 4th degree could easily be harmonized via the vii6, which as you know contains the 7th, 2nd and 4th degrees. Taking your starting voicing, I would write:
  2. as in:
  3. However, I think the best harmonization would be via a V4/3:
  4. See what I mean?

Are you implying that, whenever possible, V7  - or inversions of V7 -  are better choices than vii for expanding I?

Not necessarily – they are all good. I personally like the fuller sound of V4/3 than vii6, but so much depends on context: there are times when the (relatively) weaker sound of the vii6 is better – eg, so as to be less obtrusive. At other times, one wants the more clearly “dominant” function of the V4/3 (or other inversions of V7).

Unit 9, Preliminary Exercises, Ex. A, in minor

Good! The V4/3 or vii6 could also work, if you wanted to ‘step’ up to the bass' D, rather than leap.

Such as:

Your use of V4/3 is perfect, and your use of vii6 is pretty good too. For the vii6, however, I would rather see the alto sing (from the beginning): E ↓ D ↑ E than have her skip down to the B, then up to the E again. There is a problem of too large an interval between the alto and soprano when the alto sings the B, but this isn’t the main reason why I’d change it – I think it’s simply smoother to have the alto sing E ↓ D ↑ E. Now, of course, this new alto creates an irregular resolution of the G#-D diminished 5th – which should properly contract into A-C (a minor 3rd). However, the bass has been moving through scale degrees 1 – 2 – 3, and thus ‘covers’ the note to which the diminished 5th should resolve. This is one of the exceptions that Aldwell went over in the chapter on vii6 – see 7-17 and the paragraph that precedes that illustration as well. Aldwell says “As part of the diminished 5th, the 4th degree will normally move up to the 5th degree only if the bass moves up to the 3rd degree in parallel 10ths, thereby bringing in the tone of resolution in another voice but very prominently (Example 7-17). This voice leading occurs frequently.” Now, I realize that in the example that you and I are dealing with, the bass isn’t moving up to the 3rd degree in completely parallel 10ths — those parallel 10ths occur only in part:

. . . but other text books aren’t so strict about the parallel 10ths — their main concern is that the bass moves from a root position tonic triad, through the vii6, to the first inversion tonic triad, so that the bass moves into the 3rd degree, to which the 4th degree (in the upper voice) would have properly moved. Aldwell himself writes a “summary”, at the bottom of the same page, in which he writes “If the dissonance is a diminished 5th, it must resolve unless vii6 moves to I6”, which sums this up nicely. I should also mention that my new alto uses two 4th degrees, with one of them — the soprano — resolving properly, and the other — the alto — not.

Unit 9, Preliminary Exercises, Ex. B, in G minor

  1. Your ii chord is missing its fifth, and is therefore ‘incomplete’. Had it been ‘complete’, it would have been incorrect, as ii chords in minor are diminished, and should therefore always be in first inversion.
  2. Such as:
  3. A good try, Gustave, but while you’ve given the ii chord its fifth (Eb), you have somehow omitted its root (A). Since your resulting chord has two C’s and two Eb’s, we must regard it as being a iv chord (Cm) with no fifth, rather than a ii chord with no root.
  4. As well, your alto’s move from Eb (bar 2, beat 1) to D overlaps the tenor’s previous Eb.
  5. Here’s one possible solution:
  6. as in:
  7. The use of V6/5 in bar one eliminates the ‘jumpy bass’. The new voice leading allows smooth, unobtrusive melodic motion in the inner voices. Notice that in bar 2, I had the tenor skip up to the chordal 7th — but this is precisely the only skip I’d noticed in Aldwell (ie, from 2nd degree up to 4th degree).

2. Soprano overlaps alto.Yes.

Unit 9, Preliminary Exercises, Ex. D

A bassline of something like:

. . . would be a treatment more in keeping with what Aldwell shows: it gives a sense of forward direction (via a ‘contrapuntal’ bassline), and moves from I6 to ii6 – which is much smoother than I – ii. Please try the exercise again, using this bassline.

Here are two versions – which is better?

I’ll let you decide: are there any voice-leading problems in either of them?

Yes: in bar two of the first version, the bass sings a descending minor 7th, which is a bad idea, even if that leap is followed by motion in the opposite direction!

Exactly correct!

Aldwell asks why this exercise (Ex. D) wouldn’t be suitable in a minor key. Do you know why?

Is it because one would have to use a root position ii° chord, which, being diminished, should be avoided in minor?

Excellent point, Gustave — one shouldn’t use a root position ii chord in minor. However, the problem lies elsewhere: in Ex. D, the soprano’s last three notes are:

The second to last note is obviously harmonized by the V or V7 chord, and the third to last note will have to be harmonized by the ii6 chord:

Here’s where the problem arises: should one double the ii6 chord’s bass (ie, its third, which is the preferred doubling, in minor), there will be no way of moving to the raised leading tone within the subsequent V or V7 chord. Here are bars 2 & 3 of Ex. D, transposed to the key of C minor:

Notice that there is no leading tone in the V7 chord!

As in:

That’s it!   But watch that skip of a minor 7th in the bass.

The only way to get it would have been to have the alto move up from the Ab to a B natural, giving us a forbidden augmented 2nd -----

Exactly! That’s the problem.

. . . or, have the tenor skip down from the F to a B natural, which would produce a very dissonant leap that is not allowed (so far) within an inner voice.

Yes, that’s completely correct, Gustave — that dissonant tenor leap isn’t allowed in this style.

Notice where you ‘resolve’ that B natural, though, Gustave — it would be better to have it lead to the tonic, and have the the alto move down to the 3rd degree. (And, of course, make the bass move up a 2nd rather than down a 7th.)

There is a solution, though: double the ii6’s root (D) rather than its third:

Here the tenor can safely skip down from the D to the B natural. However, the doubled root for the ii6 isn’t great.

Very good, Gustave. Just remember to also resolve your tenor’s B natural to the tonic, the alto’s G to a final Eb, and to move your bass up to G, rather than down to it.

Unit 9, Preliminary Exercises, Ex. E

But I still wonder what’s wrong in the bass, here?

First, jumping back to a i after the ii6 is a little awkward – having the ii6 proceed to a i6 might be more satisfying.

The main issue, though, is that it’s usually better to expand the i via dominant, rather than supertonic, harmony. Applying that principle in this instance, we can use a vii6 instead of the ii6, to produce the progression:
i → vii6→i6 | ii6 V7 |

Also, notice that at beat 4, bar 1, your alto overlaps the tenor.

For example:

Yes, this is the proper bassline, and a better chord progression.

Let’s look at the few remaining voice-leading problems:

Bar 1, beats 3 & 4:   rather than have your alto skip up to G, then down again to Eb, why not simply move it from C to D? The resulting dim5 (F#C) to p5 (GD) is fine, since the dim5 of a vii6 can move up to a p5 if the bass moves to the 3rd degree.

Bar 2, beat 1:   you were very close, but you gave the tenor a G rather than an A, which produced an ACEbG, or iiø7 — which we aren’t using yet.

Bar 2, beat 3:  the tenor skips up from the tonic to the chordal 7th – so far, the only skip to the chordal 7th we’ve seen has been Aldwell’s skip from the 2nd degree up to the 4th degree.

Bar 3, beat 1:  the alto overlaps the tenor’s previous note. Her descent, from D to Bb, also clashes with the tenor’s resolution from C (the chordal 7th of V7) to Bb, creating that stylistically prohibited situaton in which two voices move by similar motion from a second to a unison. Both problems are easily solved by having the alto remain on D:

Rather than re-do any of these, Gustave, I think it will suffice if you just study my suggestions, and try them out in a few different keys (at the piano, as well as on paper) — you’ll then be ready to move on to Aldwell’s own exercises. I’ll email some specific assignments toward the end of the week.

As usual, please don’t hesitate to email any questions you may have!

All the best,

Michael Leibson is a composer, music consultant, and music educator, who specializes in jazz and classical harmony. To learn more about him, click here; for information about studying with him, click here; and for copyright information, click here.