Part-writing Seventh Chords: The Half-diminished Seventh Chords

If you are looking to part-write half-diminished seventh chords, this is the right place. But be aware that quite a lot of previous knowledge is assumed. In fact, this is the second Hub in the *third* series dealing with part-writing, so we are quite a ways along!—in fact, if this were a typical music school first-year theory course, we'd be getting toward the end of the course.

See the preceding Hub, linked below, for more details, if you're unsure whether this Hub is right for you.

And, by the way, if case you're wondering about the rockers pictured below, they are Dave and Rick, of the band Seventh Son, performing what appears to be a first inversion F# triad. (That's if you assume standard tuning. Got a better idea for a 'seventh' icon? All suggestions gratefully accepted!

In the previous Hub, we considered the part-writing issues involved in using the dominant seventh chord—notably, the need to resolve the leading tone and especially the seventh of the chord. Those principles will stand us in good stead as we work our way through this Hub, so you may wish to review. If so, the link is in the sidebar.

This Hub will take a slightly different approach from previous ones. Rather than considering a single specific functional chord, such as V⁷, we’ll look at a single chordal sonority, the so-called ‘half-diminished seventh.’ It occurs in two different tonal contexts, each with different tonal functions and slightly different voice-leading issues. Consider example 1, below:

As you can see, the identical seventh chord appears in the scales of C major and A minor. In the former, it’s vii^Ø7, and has a dominant function, frequently substituting for V⁷. In the latter it is a ii^Ø7 chord and serves as a dominant preparation, leading the listener to expect a following dominant or dominant seventh chord.

(By the way, the circle-and-slash is a common abbreviation for 'half-diminished'. A half diminished seventh chord is so called because it consists of a diminished triad with a minor seventh. That's in contrast to the diminished seventh chord, which has a diminished seventh instead. The half-diminished seventh is often called a 'minor seven flat five' chord in popular music contexts.)

In terms of voice leading, the main difference is that vii^Ø7 has a leading tone, which may require resolution, while ii^Ø7 does not. Compare two short progressions:

In the first, we see vii^Ø7 embodying a dominant function in C major, creating an imperfect authentic cadence to the tonic. It’s in root position, which means that the bass tone is a leading tone, and therefore must resolve upward by step to the tonic. (As we saw in the last Hub, this is mandatory for leading tones in bass or soprano, but not in alto or tenor, where the lack of resolution is less apparent to the ear.)

In the second progression, the identical voicing acts as a dominant preparation chord, leading to a perfect authentic cadence via the dominant seventh chord. The ‘B’ in the root is no longer a leading tone, and need not resolve. (The ‘G#’ in the soprano is, and does!)

In both cases, though, the chordal seventh—the ‘A’, given in the soprano—follows its normal resolution, falling stepwise. That’s mandatory.

A couple of questions may (or may not) have occurred to you. First, what about the doubled third in the tonic chord at the end of 2a? Is that kosher, given the ‘Doc Snow doubling rule’ that it is the primary tones in a key (scale degrees 1, 4 and 5) which are normally doubled?

The answer is yes. While the doubled third in a tonic chord is generally considered ‘option C,’ it does remain a viable option. In fact, it’s the required option in this case: if the alto ‘D’ were to fall to a ‘C’, parallel fifths would be created with the soprano, while on the other hand taking the tenor ‘F’ upward to ‘G’ would create a less-than-desirable unequal ‘diminished-to-perfect’ fifth progression. (The dissonant diminished fifth, ‘B-F’, also tends to resolve inward—another expectation that tends to be respected in part-writing.)

Secondly, what about the root position itself? In a previous Hub, we saw that diminished triads rarely appear in root position; the overwhelming number are instead written in first inversion. (Traditionally dissonances involving the bass tone were carefully managed, and in a first inversion diminished triad, all upper tones are consonant with the bass.)

One would think the addition of a chordal seventh would simply increase the dissonance, and strengthen the tendency to avoid the root position. However, that is not what happens. First inversion is easily the most common position for vii^Ø7 and ii^Ø7, but the root position is used more often than is the case for the plain diminished triad. An interesting (if not very typical example) is found in #7 of Bach’s 371 Chorale Harmonizations:

The seventh resolves ‘tactically’ via the tenor’s descent, which transforms the chord from vii^Ø7 to vii^o. (This analysis takes D to be the key locally; the key signature reflects the A major tonality of the chorale as a whole.)

Here’s a second example from the ‘371’. In #307, this vii^Ø7 occurs as a passing chord, connecting a vi to a I. (Three consecutive root position chords in stepwise motion is not something you run into every day in common practice ‘Classical’ music, but here Bach makes it seem deceptively normal. The seventh is crucial to avoiding parallel octaves.)

But let’s do an exercise. As always in these Hubs, I strongly recommend that you work the examples out on paper yourself before checking the solution given. If you don’t have music manuscript paper, it’s easy to print some out. (There’s manuscript paper available for free printing at the link given in the sidebar.)

It’s minor pain to be disciplined about always doing the work on paper yourself, but well worth the trouble; you’ll understand the issues more deeply, and retain the knowledge better, if you do.

Consider the melody below. Start, as always, by identifying the key and scale degrees first.

This is the same 1-6-6-5 line given the soprano in Example 2a, transposed to F major. (If this melody were in D minor, the other key featuring this key signature, it would surely have had a C# in m. 2.)

Next, write the corresponding bassline:

That’s the same bass line, of course—1-2-7-1. (It would also be fine to write it an octave lower than shown; that’s not too low for the basses to sing.)

Now supply alto and tenor.

Now, let’s use the same model progression again. It will fit with the soprano below; identify the given line's key and scale degrees, then add the bass line.

We’re in D, and the soprano line is 5-4-4-2. Using close spacing, add alto and tenor parts.

(If you’re new to these Hubs and don’t know that term “close spacing”, it refers to chord voicings in which the upper voices occupy adjacent chord tones. For instance, in this case that means that your alto should start on ‘F#’, since that is the next chord tone below the soprano’s ‘A’. For more on the concept, see the Hub linked in the sidebar.)

There’s a slight twist in this version; see if you can spot what’s different from the model.

If you didn’t already spot the difference in this version, notice the doubling in the final chord: there’s no more doubled third in the final tonic! How did that happen? Does that mean that there are parallel fifths in this example?

Well, no. In this version, the 1-6-6-5 line originally appearing in the soprano of the model is now the tenor line, safely below the alto’s 3-2-2-1. If the lines were reversed, we would have parallel fifths, with ‘E-B’ in the second last chord paralleled by ‘D-A’ in the final chord. (That’s exactly what you’d get if you wrote ‘open’ instead of ‘close’ spacings—hence the direction above to go with close spacing.) Instead, we have parallel fourths, which are perfectly acceptable.

Here's what it sounds like:

Now let’s turn to the minor-mode model progression. Recall that its half-diminished seventh is on scale degree 2, is symbolized as ii^Ø7, and functions as preparation for the dominant. For convenience, here’s the model progression again:

Identify the key and scale degrees of the melody below, and add the corresponding bass line:

There’s one salient logical option for the bass, as shown—it would be possible to write part of the bass in the lowest portion of its range, but why? And simply transposing the model up would lead to a bass and soprano only a third apart on the third beat, so there would be no 'room' for alto or tenor voices.

If this bass line is adopted, it enforces the use of close spacing, in contrast to the open spacing of the model progression. Now complete the inner voices.

Notice how the alto and tenor voices ‘flip’ with the spacing change; that's a common thing, and can sometimes be a quick solution to part-writing problems. Here's how it sounds:

Let’s try another version of this progession. Here’s the melody. What are the key and scale degrees?

Since this is supposed to be the minor-mode progression, the key must be F# minor, which would make the scale degrees 5-4-4-3. (But note that the line could equally well be harmonized with the major-mode progression, in which case it would have been a 3-2-2-1 line in A major.) Add the bass line, modifying it to begin in the lower octave, and end in the upper.

Now add alto and tenor, using open spacing.

Note the ‘voice overlap’ involving the last two notes of tenor and bass: the tenor ‘E#’ is lower than the bass ‘F#’ that comes next. As discussed way back in “Part-writing The Supertonic”, such a voice overlap:

...makes the voices harder to follow, and thus results in a slightly less transparent texture. Where possible, voice overlaps are better avoided.

However, that’s not a hard and fast ‘rule,’ and if you look, you’ll find voice overlaps similar to this one at quite a few authentic cadences. Perhaps the strength and familiarity of the cadence pattern override any lack of textural transparency the overlap causes.

In this case, I wanted to use the upward-sweeping bass line to demonstrate how a small change—just the final tone shifted up the octave—can make a big difference. And given that bass line, the only straightforward way to avoid the overlap would be to use close spacing, which would have taken the tenor up to F#. That’s possible, certainly, but would create quite a different vocal sound for the texture as a whole.

Such are the tradeoffs that one makes.

Just for fun, here’s the close-spaced version, so you can judge for yourself. (But note that the piano version is less affected by the register shift than a vocal performance would be.)

As mentioned above, the root position use of the half-diminished seventh is not as common as its use in first inversion. So let’s introduce ii^Ø65, the first inversion incarnation of our chord. (As discussed in the previous Hub, the ‘six-five’ is the ‘figured bass’ notation indicating a first-inversion seventh chord.)

Here’s a progression using ii^Ø65, modeled on a passage from Bach’s chorale setting #295:

As you can see and hear, it’s similar in overall sound to the root position version, and yet the lines created are distinctly different. The bass is a classic 1-4-5-1, very strong tonally; the tenor features a passing seventh as part of the dominant; and the alto is equally classic, involving a deliberately unresolved leading tone to enable a complete tonic triad as the final sonority.

Here’s a challenge: can you deal with a slightly adapted version of this model? What line of the model does this soprano most closely resemble?

The ‘new’ key is A minor, so the soprano’s 1-1-7-1 is closest to the 1-1-7-5 alto in the model. Of course, the leading tone must resolve when it is in an outer voice, forcing the change to the last tone.

Complete the texture, using the identical (but appropriately transposed) bass line from the model.

The main result is that you are forced to end with an incomplete tonic with tripled root. That’s perfectly OK.

Here’s another line from the same model. Identify key and scale degrees as usual, and complete the texture, using a high-to-low version of the bass line.

Note the consistent open spacing throughout—and yes, the first chord is open-spaced, too; the interval between bass and tenor doesn’t count in reckoning such things.

Turning to vii^Ø65, here’s another Bach-derived example, this one adapted from #11:

In this simplified and adapted version, vii^Ø65 is used as part of a bass arpeggiation that connects vi and iii. It’s an unusual example, admittedly. That’s because in situations where vii^Ø65 might be appropriate, other choices are generally less unwieldy. (Notably, the triad without the seventh—vii^Ø6.) There’s always the possibility of parallel fifths involving the perfect fifth between third and seventh, complicated by the imperatives to resolve seventh and possibly leading tone.

Still, you might think that examples like this one would be a bit more plentiful than my casual survey seemed to indicate:

Using Example 6 as model, harmonize the following soprano in close spacing:

The doubled third in the final tonic triad is less than usual, especially in a first inversion voicing. But the alternative would be an unresolved seventh.

The second-inversion voicings of either ii^Ø43 or vii^Ø43 did not turn up in my quick survey at all. You’d expect to see them in a late 19^th-century composer like Wagner, though, and sure enough, a quick glance at the Prelude to Tristan turns up this contrapuntal elaboration of a second-inversion half-diminished seventh:

Did you find the half-diminished seventh? It's on the fourth eighth-note, where the soprano arrives at 'F#'.

That chord would probably be analyzed in A as the chromatic chord “vii^Ø43 of V”, though it doesn't resolve directly to that chord. (This passage, by the way, is known to musicology as the ‘leitmotif’ for the Love Potion. Don’t ask.) Wagnerian style is rife with half- and wholly-diminished seventh chords, chromatic voice-leading, and indirect or unexpected resolutions.

For a (made-up) example a little closer to choral style, consider this:

Here, a ii^Ø43 accommodates a linear bass line preparing the dominant seventh. Note how the common tones link the two seventh chords smoothly.

Try applying that model to this soprano using open spacing—and ending, this time, with a complete tonic:

The 5-4-4-3 soprano ‘buries’ the leading tone, allowing it to remain unresolved in the alto. It would also have been possible to swap alto and tenor lines, creating a close-spaced version.

A somewhat similar strategy produces this example of vii^Ø43:

Like Example 8, this would probably not have been acceptable to the 18^th-century ear; there is a certain harshness resulting from the 4ths between bass and an upper voice (the alto, in this case.) In the 21^st century, it will mostly pass unnoticed. (Listen to the solution below when you've worked it out, and see what you think.)

Try that model in another key:

One last example. This third-inversion half-diminished seventh, ii^Ø42, is drawn from #15 of Bach’s 371 Harmonized Chorales:

Note the similarity in essential voice leading to Example 8 above. Note, too, that the dissonant seventh in the bass is treated like a suspension—prepared by “A” in the preceding tonic chord and resolved downward by step to the “G#”, in characteristic fashion.

Now apply that as model to this soprano. Careful, I’ve made this a bit tricky!

The trick was that the given soprano is a 'mash-up' of the soprano and tenor voices of the model, spliced together at the eighth notes. The other voices remain unchanged, with the result that the final chord is incomplete, with both root and third doubled. (Yes, that can be done on occasion, though it is less common than our more familiar doubling options! It must be admitted, though, that it would be pretty darn rare at a final cadence.)

Note that the soprano and alto look like parallel fifths, but actually aren't. While the 'G-D' dyad on the first beat appears to be followed by a parallel 'A-E', that "E" is actually "Eb", making the fifths unequal. Even the strict theorists who disapprove of the 'd5-P5' unequal fifths would sign off on the 'P5-d5' fifths here.

And that is probably enough for one Hub. Thanks for working through this one. Next time, we'll take a look at more seventh chords which prepare dominants.

Stay tuned… heh!