Part-writing Seventh Chords: The Dominant Seventh Chord
This Hub is the first in a series dealing with the part-writing issues—the ‘tricks and traps’—involved in using seventh chords. But the series is the third of three sets (so far) on part-writing! So it’s not too surprising that the present Hub assumes a fair amount of knowledge: proficiency in reading music in treble and bass clefs, knowledge of the basic rules of part-writing, and skill in using at least tonic and dominant triads in root position and inversion.
It may help in assessing this question to have a look at the summaries of the Series I & II Hubs. Those summaries can be accessed by clicking the links in the sidebar at the right.
Summary Hub Links
- Part-writing Chords: Summary I
A 'syllabus' and summary for Doc Snow's innovative Hubs on the essential musical skill of part-writing. Sequence, content and links--plus a summary of part-writing 'rules.'
- Part-writing Chords: Summary II
The second 'syllabus' and summary for Doc Snow's Hubs on part-writing. Sequence, content and links.
But you don’t necessarily need to have worked through all those Hubs in order to use this one—many theory courses introduce the dominant seventh chord quite early in the curriculum. And for good reason: it’s a very common chord in common practice music—much more so than, say, mediant triads.
Accordingly, this Hub can follow on from Hubs such the “Tonic and Dominant” Hubs in Series I, or from the “Primary chords in first inversion” Hub in Series II. It also reviews most of the basic 'part-writing rules' which describe the musical procedures now referred to as the 'Common Practice.'
Those Hubs are also linked at right, for those who may want to review them, or who may want to work through them before proceeding with this one. The first two deal with tonic and dominant triads in root position; the third reviews all primary triads in first inversion.
Also relevant would be the overview of seventh chords in general, which can be found as part of my series, “Understanding chords.” It, too, is linked in the sidebar to the right.
The dominant seventh chord, like other sevenths, can be seen as arising from a passing tone. (While I’m giving links to relevant Hubs, I suppose I might as well give the one for non-chord tones, of which passing tones are an important sub-category. See the sidebar.) As shown in the musical example below, a dominant to tonic chord progression can support a ‘5-4-3’ soprano line—that is, a line descending from the fifth scale degree to the third—‘so’ to ‘mi.’ The “F” can be viewed as a passing tone.
But prolonging that “F” creates a clear example of a dominant seventh chord—root, fifth, and seventh. Note the Roman numeral analysis below the staff—the root of each chord is given by the numeral; the major quality of the fundamental triad involved is given by the uppercase (“V” instead of “v”); and the superscript “7” indicates the presence of a chordal seventh. We’ll take note of the Roman analysis aspects of seventh chords as we work through this Hub.
This origin—or at least ‘origin story’—gives a rationale for the first rule regarding seventh chords: chordal sevenths normally resolve downward by step. (There are a few exceptions, which we’ll deal with in due course.)
Inverting the upper two voices, as shown in Example 2, brings to light another important feature in dealing with the dominant seventh chord.
Many listeners will find something wrong with the sound of this progression--or would, in an acoustic performance, as opposed to a computer realization--and will prefer this version:
As discussed in the some of the Hubs previously mentioned, it’s obligatory in normal ‘Common Practice” style to resolve leading tones when they occur in one of the ‘outer voices’—that is, the soprano or the bass—where they are heard most prominently. (It’s acceptable not to resolve them in alto or tenor voices, where the resulting melodic awkwardness may annoy the performers but will not be so apparent to the listener—which is why the alto line Example 1a is OK.)
The normal solution, as shown above in Example 2b, involves adjusting the doubling of the tonic triad. Note how the triad now has a tripled root—the “C”s in bass, tenor and soprano—and a single third in the alto, but no fifth. This ‘incomplete’ triad does not lose its characteristic quality because the fifth is a relatively neutral chord member, contributing little to the sound of the triad, and because the harmonic meaning of the progression is so unequivocal to our musical intuition. We hear what we expect to hear.
It turns out that the use of an incomplete chord is mandatory in the V7-I progression, if we wish to, or need to, resolve the leading tone. The tonic triad may be incomplete, as in Ex. 2b, or the dominant chord may be incomplete, as shown below:
Once again, it is the fifth which is normally omitted.
Let’s work through an example. As always in these Hubs, it’s best to work them out on paper for maximum retention of the concepts and to build skill in using them. Here’s a link where manuscript paper may be printed out, if you happen not to have any handy.
By the way, though the ‘answers’ are presented one line at a time, usually in the order “Bass, Alto, Tenor,” composers typically work out their voice leading simultaneously, or by beginning with the bass and working back and forth among all voices. Working on paper first lets you do the same—though I suggest you do begin with the bass, then work out the alto and tenor parts; the bass is most important in defining the harmony, so setting it first is helpful. You can always adjust the octave placement of bass tones if needed as you add the inner parts.
Start by determining the key and scale degrees of the given soprano:
The “C#” implies that this is D minor, not F major—the other key that would fit this key signature. The soprano line would then be 7-1—the same line as in Example 2b and 2c. Start by writing the bass line.
Q 1a-bClick thumbnail to view full-size
Let’s use 2b as a model, and write an incomplete triad as we add alto and tenor.
Q 1b-dClick thumbnail to view full-size
By the way, note what happens if we simply make the triad complete: parallel perfect fifths—the single most stereotypical mistake one can make in traditional part-writing practice.
Let’s make the questions a little more interesting by extending sequence to three chords. Here’s an example using a ‘neighbor note’ figure as soprano line.
Using Ex 4 as model, complete the 4-part texture under this 1-7-1 line:
Q 2a-dClick thumbnail to view full-size
Easy enough, assuming no trouble in identifying the key of F major. We can also use a ‘passing note’ figure for our soprano, like this:
Again, the example can be used as model. But this time an adjustment will be desirable. Because the soprano lines in the last few examples have been relatively high in the vocal range for that voice, it’s been natural to spread the voices relatively widely in order not to take the lower voices too high—note how shifting the alto and tenor upwards to the next available chord tones would have meant alto and tenor parts that are too high.
As indicated in the example, the ‘spread out’ voicing of the chord (in which the upper voices occupy non-adjacent chord tones) is termed ‘open.’ Conversely, the second voicing, featuring voices on adjacent chord tones, is termed ‘close.’
In Question 3, the soprano lies relatively low. If we were to use open spacing once again, the tenor and bass lines would be too low. So use ‘close spacing’ as you complete the Question. (Hint: you can use the same lines as in the example; just swap them into different voices.)
Q 3a-dClick thumbnail to view full-size
As shown, the bass line must remain the same, while the 5-4-3 line shifts from alto to tenor and the 1-7-5 line does the opposite (and is moreover shifted upwards by an octave.)
(Note that the interval between upper voices—soprano and alto, and alto and tenor—should not normally exceed an octave.)
Here’s another question along the same lines. Begin by identifying key and scale degrees:
Did you see the key as major or minor? If major, it’s a 3-2-1 line in A; if minor, then it’s 5-4-3 in F#. Either is perfectly legitimate. But let’s do the major version first.
Q 4a-dClick thumbnail to view full-size
If you followed the model, you wrote close-spaced chords, ending with a complete tonic triad, as shown. (The corresponding open-spaced version would work just as well in this case, providing a slightly darker-sounding harmonization in real-world performance.)
Now try it in minor—but this time, let’s use open spacing, and end with an incomplete tonic.
Q 5a-dClick thumbnail to view full-size
Note the soprano and alto voice-leading: the timid might worry about the possibility of (forbidden!) parallel fifths, since here the voices are separated by fifths, and move the same direction and by the same interval.
But that’s not quite the case, upon closer examination; the soprano actually moves by whole step while the alto proceeds by half step. As a result, the fifths are ‘unequal’—the first is perfect, but the second is diminished. These “P-D” fifths are not generally considered problematic—though some authorities proscribe the reverse (“D-P”) sequence.
Now let’s consider what happens when we invert the dominant seventh. The ‘neighbor note’ version we saw way back in Example 4 makes a nice model for this, if we move the soprano line into the bass, as shown:
There a couple of interesting things about this. First, note that, although the leading tone is resolved—it must be, since the bass is an outer voice—both the dominant seventh and the tonic are complete! This can happen in the resolution of the first-inversion dominant seventh because the fifth can be supplied by a 5-5-5 line (here occurring in the tenor) that is impractical in the resolution of V7.
The 5-5-5 line does involve what has been termed “Option B” doubling of the initial tonic, which has the fifth of the chord in both alto and tenor. Luckily, option B is quite acceptable, and is not at all infrequent.
Note, too, the Roman numeral analysis—or more properly, the ‘figured bass’ numerals accompanying the Roman “V.” The “six-five” indicates a first-inversion seventh chord in first inversion, and derives from figured bass notation. This notation was common in the Baroque era, and acted somewhat as chord symbols do today, affording an accompanying keyboardist or lutenist a compact notation for playing improvised chordal accompaniments. The basic idea is that the numbers represent intervals above the bass note: the tenor “A” is a sixth above the bass, while the alto “G” is a fifth (plus an octave) above it. (The chordal fifth, the “E” in the soprano, is assumed by convention.)
Lastly, the harmonic function of idioms like this one is considered quite differently than that of the root position progressions we looked at in the first part of this Hub. The latter were actual, structural chord progressions defined by clear bass motions defining the harmony. Progressions involving the inverted dominant sevenths, on the other hand, are considered to be ‘prolongations’ expressing a single harmonic function (the tonic) by means of embellishing linear chords.
Returning to the line above—“F-E-D”, which is of course 3-2-1 in D minor—can you find a way to use it as a 5-4-3 line in some key? For your convenience in considering this question, the line is given without key signature below:
The answer turns out to be that you cannot. A 5-4-3 line ending on “D” would either begin with an “F#” (if in B minor), or involve an “Eb” (if in Bb major.)
Let’s try a question based upon this model. As usual, start with the identification of key and scale degrees.
Q 6aClick thumbnail to view full-size
This can only be A minor, with a 3-2-1 soprano. Add a bass line, beginning with the upper “A” in the bass staff.
Q 6a-dClick thumbnail to view full-size
As shown, this forces the use of mixed spacing, beginning with a unison “E” in alto and tenor parts—doubled fifths in an open-spaced tonic triad—and ends with a close-spaced tonic triad.
But seventh chords, like triads, have second inversions as well as first inversions. Once again we can rearrange voices a bit to derive a useful model:
Compared with Example 6, the bass and soprano parts have exchanged lines; the alto and tenor remain unchanged. That means that once again we can have a resolved leading tone and complete voicings of both dominant seventh and tonic.
Of course, a new inversion also means a new figured bass symbol—the ‘four-three’ shown. This will be valid for all second-inversion seventh chords, dominant or not.
Try a major-key version of this model:
Q 7a-dClick thumbnail to view full-size
Try another major-key version, harmonizing the same line. But this time, reverse the bass: instead of 3-2-1, let’s try 1-2-3, like this:
Q 8b-dClick thumbnail to view full-size
Did you have any misgivings as you checked out the answers appearing on your screen?
If not, do you see anything that seems a bit ‘off’?
How about this?
Here, the chordal 7th proceeds upward in defiance of its expected resolution! True, the essential part-writing involved is familiar, simple and logical, with scalar parallel thirds accompanying the familiar 5-5-5 and 1-7-1 lines which we have been with for some time now. And it is true that the whole progression is considered to be a linear one in any case—not a structural one. That would logically mean that the seventh was not structural, either, perhaps helping to justify the irregular resolution.
Nonetheless, such progressions have a history of causing theoretical unease—Professor William J. Mitchell, of Columbia University, used to term this usage a ‘pseudo-position’, for instance. The unease is perhaps the greater in that you can find such progressions in works of unimpeachable pedigree:
Ex 10a & b
The first is a reduction from the opening of the second movement of Mozart’s Horn Concerto, K. 447; the second comes from Haydn’s Trio in G, Hoboken XV:5, third movement. Again, one can probably find more such examples in Classical instrumental writing than in Bach chorales—though there is this, from the opening of Chorale 60, “Ich freue mich in dir”:
Sure looks familiar—and it took about two minutes of random searching to find. Hmm...
At any rate, let’s try fitting this progression to a suitable soprano line. What’s the key and scale degrees involved?
OK, that was easy! It has to be the familiar 5-5-5 line, of course, which makes the key Eb. Go ahead and complete the four-part texture.
Q 9a-dClick thumbnail to view full-size
There’s really only one suitable octave for the bass, but either close or open position could have been chosen at the outset. The darker version, beginning with the open position triad, is shown.
Let’s conclude with a quick look at the final inversion of the dominant seventh chord, in which the bass tone is the chordal seventh. Since the bass is an outer voice, that means that it should resolve downward—in other words, V43 should be followed by I6. Here’s an example:
If we are to preserve the tonic-dominant-tonic structure, our obvious choice becomes i6-V42-i6 progression, as shown. It’s a neighbor-note prolongation par excellence.
Try it in A major:
Q 10a-dClick thumbnail to view full-size
A close-position version would have been possible, with alto and soprano beginning and ending on unison “A”s.
This final version shouldn’t prove too challenging:
Q 11a-dClick thumbnail to view full-size
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Well, that is enough for one Hub, and (luckily) enough to cover the essential aspects of part-writing dominant sevenths, if not every refinement. Of course, sevenths don’t only occur in connection with dominants.
But that is a matter for next time, when we tackle the half-diminished seventh chord, in its two normal tonal contexts. Use the 'next' button, below, to check it out!
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