Part-writing Inverted Chords: Primary Triads In First Inversion
“Great title, Doc,” you say, with possibly just a tinge of sarcasm. “But what in the world is an inverted chord? How can a term like that even make sense?”
Admittedly, it can be a bit mind-boggling to try to imagine how a chord—which is, after all, just a particular sort of sound—can be turned bottom-uppermost. But in music theory “inverted” and “inversion” have specific technical meanings—yes, sadly, more than one. But let’s look at the meaning appropriate to this context.
In previous Hubs on part-writing—see the sidebar link below the picture for a summary—we have seen that triads are built upwards from a tone which we call the “root.” Above the root we find two other “chord tones”: the third and the fifth. And in each case, the root of the triad has also been the chord tone found in the bass—hence the term “root position.”
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- Part-writing Chords: Summary I
"Part-writing Inverted Chords" Hubs presumes basic part-writing skills. Here's a 'syllabus' and a summary of what's needed--and a guide to where you might want to start if the present Hub feels a little too advanced.
An inverted chord is one in which the root is not the bass tone. In this series of Hubs we will be considering (and working with) triads in which the third of the chord appears as the bass tone instead. Such chords are referred to as “first inversion triads.”
The primary triads in any key are usually considered to be the triads built upon scale degrees 1, 4, and 5. For example, here are the primary triads of C major, each given first in root position and then in first inversion.
Note that it doesn’t matter what the precise voicing of the upper tones of the chord is for purposes of determining the ‘position’ of the chord: if the bass is the root, then it is a root position chord, and if the third is the root, then it is a first inversion chord.
Before we come to grips with specific first inversion triads, though, let’s consider the advantages and disadvantages of first inversion chord for a moment. After all, they represent a new complication for us: why is it worthwhile to ‘invert’ chords in the first place?
There are two principal reasons. First, using inverted chords allows the bass much more freedom than it could ever have if limited to chordal roots. It can become a more equal and more interesting counterpoint to the soprano than otherwise—it can be, in short, much more melodic.
Second, and even more important, inverted triads are harmonically less clear and forceful than root position triads. Phrased in the negative as it was, this may not sound like a good thing. But ‘dialing back’ the harmonic strength of some chords allows others to shine the more—and the differentiation creates new musical meaning. In the first PW Hub, we looked at three different lead sheet realizations of “Auld Lang Syne.” Here are the first and third:
The “clunkiness” of version 1 compared with version 2 is partly due to the exclusive use of root position triads. Both of the factors mentioned—the added linear interest in the bass, and the added harmonic differentiation—are important in making version 2 sound more sophisticated, expressive and persuasive.
Now let’s turn from the ‘why’ of using inversions to the ‘how.’ Consider the following progression:
Here we see a first inversion I chord resulting from the bass movement from root to third—a phenomenon sometimes called “bass arpeggiation.” The tonic function is prolonged for two beats as a result.
Contrast this with a progression we practiced writing in the ‘Part-writing Mediant and Submediant’ Hub:
The second chord of the two differs by just a single tone, found in the tenor. But the alteration of the “C” to the “B” changes the whole sound of the example. Now tonic function occurs only on beat 1 of the first bar, and the tonal ‘distance’ of the mediant triad—arguably the greatest of all the diatonic triads—makes for a piquant harmonic color, unexpected and (in two different senses) cool.
(And by the way, any slight similarity you to the end-phrase of the “Mickey Mouse Club Theme Song” you might find is strictly coincidental and unintended. As a former fan, I would never, ever, parody it.)
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Some listeners may prefer one, some the other. But there is no doubt that the first version, using the inverted tonic triad, represents a much more common harmonic idiom. (Indeed, it’s partly the ‘freshness’ of the less-common alternative that appeals.) So let’s practice using it ourselves.
As always in these Hubs, I strongly recommend that you physically write out these examples on paper. The physical engagement this promotes will really help the information stick with you. If you have no manuscript paper handy, just download and print some using the sidebar link.
As usual in these Hubs, begin by identifying the key and the scale degrees of the soprano line.
It’s a 3-1-1-7-1 line—just like that in the examples—in the key of Eb. Now write the appropriate bass line, following the model progression given above. You will need to make one adjustment—what is it, and why is it needed?
As shown, the bass needs to leap downward to allow room for the inner voices between alto and tenor—by beat 4, the bass and soprano are occupying adjacent chord tones, if this adjustment is not made. And bass and soprano must be in contrary motion if we are to avoid parallel perfect intervals, particularly in moving from the IV to the V. (As we’ve seen in previous Hubs, in connecting IV and V, all upper voices should ‘by default’ move contrary to the bass in this chord connection.)
The bass could have begun on the low Eb, of course, but that would have been a semi-tone below our specified vocal range. It would be a relatively small infraction, in the scale of things, but the version given is ‘completely legal.’
Now add alto and tenor voices.
Starting with a close position chord is necessary, since there isn’t ‘room’ for inner voices otherwise. The descending contour we need (as discussed just above) gives us the 1-1-6-5-5 alto line shown. (Note that the unison doubling of the Eb on beat 2 is both legal and common; some students have a tendency to think that there is something wrong with it, but not so.) The tenor line follows in straightforward fashion.
One last point. Compare the doubling of the I6 in Question 1 with its doubling in Example 1. What do you notice? (Here is Example 1, for convenience.)
If you said that Example 1 featured a doubled third, you are right—give yourself a brownie point. But if you said that it featured a doubled third in blatant defiance of Doc Snow’s Doubling Rule (which says you should double scale degrees 1, 4, and 5, the primary tones in the key), then take 10 Brownie points.
I bring this up, not only because I love to drag in the name of that rule every chance I get—even though the idea should really be credited to Walter Piston—but because there is a very strong tendency not to double the third when writing primary triads in first inversion. This doubling practice will be followed throughout the rest of this Hub.
Try another practice question. What is the key and what are the soprano scale degrees?
In G, this is a 5-5-4-2-3 line. Add a bass line.
It’s slightly better to write the low “G” at the end than the upper “G”. But don’t worry about it if you wrote the latter; the musical harm will be slight.
Now fill in the inner voices, beginning with an open position chord. It’s better in this case to start with the tenor, rather than the alto. (In reality, the strict line-by-line approach of these Hubs is somewhat artificial, forced by format requirements. One of the advantages of working the examples on paper is that you can work out all voices together. Sometimes a perfectly legal choice in one voice forces an error in another!)
Note that the tenor line—3-1-1-7-1—is the same line (transposed, of course) as the soprano line of the preceding example. The tenor and soprano voices have in effect ‘swapped lines.’ The alto can be seen (in transposition) in the alto of Question 1.
Bass arpeggiations can be applied to other chords, too. Here is an example in which the subdominant is treated in this way.
There is actually a musical problem with this example. Did you feel something was subtly ‘off’ as you listened? Listen again. Can you tell where the problem lies? Compare the comparable ‘substituted’ version.
Again, a small change makes a relatively big difference. Many listeners will feel the second version ‘lies better’—it seems to flow naturally where something in the first does not.
Different listeners will have different levels of sensitivity to this issue, but there is an irregularity in what is called the “harmonic rhythm” of the first example. As explained below, such syncopations are usually avoided in traditional practice; chord changes tend to fall on the beat, and especially on relatively strong beats, such as 'one' and 'three.'
(By the way, note how the the incomplete triad voicing in the first chord allows the common tones to be kept in the same voice over the following two chords.)
Harmonic rhythm and bass arpeggiations
"Harmonic rhythm" may sound self-contradictory: How can rhythm be harmonic? But this term recognizes that harmony can (and does) create rhythm, since each chord in a passage of music lasts a particular amount of time, and the sequence of durations defined by chord changes will possess a definite rhythm.
Consider Example 3 above: Each chord change creates a rhythmic attack. But since a change of chord position is not a change of harmony, there is no ‘harmonic attack’ on the third beat of the example. Therefore, beat two and beat three form a single harmonic unit. So the harmonic rhythm of the first example would be written as shown below:
By contrast, the harmonic rhythm of the second example is identical with its surface rhythm: every beat has a chord change.
But why is this subtly wrong? The answer lies in the normal metric structure of four-four, or ‘common time.’ The first beat of the bar, often called the ‘downbeat,’ is considered to be accented, and beat three receives a secondary metric accent. But relatively long note values convey a sense of accent, too—so the long harmonic-rhythmic unit, the IV6-IV, creates a sense of accent on beat two. This ‘agogic accent’ (as accents created by length are termed) is in conflict with the meter, creating the sense of unease we have been discussing.
We did not run into this problem in the bass arpeggiations of the tonic, because those arpeggiations all began on beat one, which is a strong beat. Therefore they reinforced the meter, rather than conflicting with it. This can be seen readily if we write out the harmonic rhythm:
The moral: we need to take a bit of care with the harmonic rhythm when writing bass arpeggiations. They should generally start on metrically ‘strong’, not ‘weak,’ beats.
For purposes of our practice exercises we'll deal with this discrepancy by changing the meter to suit the harmonices we want to practice. We'll end with a "half cadence" to the dominant chord, like this:
Now let’s try a practice example using the same bass line. Here’s a somewhat challenging soprano line. What is the key, and what scale degrees are involved?
In A major, we have a leaping 5-4-1-7 line. Add the appropriate bass line.
The most obvious possibility; the whole line can’t be taken an octave lower since this would exceed the bass range, but the first note could be an octave lower. The limited space available for inner voices in chords one and four means that close position chords are required. Combined with the need for contrary motion in approaching the V chord, this will force a violation of one of our ‘rules.’ Which is it?
Add the voices to find out.
The rule we had to damage a bit was the ‘voice overlap’ rule: the alto on beat three is above the preceding soprano note. But there is really no choice given the context, and the melodic emphasis of the soprano leap means that there is little chance of confusing the ear.
Here’s one with a different soprano. Identify it as usual.
The key is Bb, and the line is 3-4-4-2. Add the appropriate lines, using open position chords.
Here is an example of bass arpeggiation applied to the dominant.
Since the arpeggiation begins on a (moderately) strong beat, the harmonic rhythm will not be undercut. This arpeggiation could equally well begin with the inversion, as we did in the subdominant example. It would look and sound like this:
Actually, it works better--there is a problem with the first version. It's not the easiest to spot, since it's not an issue mentioned in this Hub--but look it over and see if you can pick it out. Here it is again. Click on the second thumbnail to pull up the answer.
Here’s a practice version of this progression. Identify the soprano as usual, then add the parts—you’ll find that there is one possible octave for the bass, and one possible chord position with which to begin.
A couple of cautions: remember that the dominant chord has the leading tone for its third, and this tone is never to be doubled. Also, if in another context you must write your own soprano or bass line, remember that the leading tone must be resolved in those parts—though the alto and tenor parts may leap away from the leading tone, if necessary.
Note that this example displays another of the virtues of inverted triads: they are ‘user-friendly’ for part-writing in that there are no fifths above the bass. (They may still exist between upper parts.) This reduces the chances of parallel perfect fifths quite noticeably.
Let’s try one last practice question before turning to the using inverted primary triads in minor keys. What is the key and what are the scale degrees for this line?
We’ve got a 5-1-7-2-1 line, in D major. Add the corresponding bass line, then inner voices. Use close spacing throughout.
The bass line could be an octave lower. The other parts lie toward the upper side of their vocal ranges, which would make this short exercise sound quite bright if performed vocally, an effect which would be augmented further with the bass in the upper octave as well. (For example, Handel’s Hallelujah! chorus has many similar choral voicings.)
Turning to minor keys, the tonic arpeggiation is a convenient place to start. For one thing, it is the simplest case, in that there is only one form of the tonic chord in minor, whereas all other triads have two possible forms (though not all are commonly used.) There are no real complications in simply transferring the voice-leading we used in our first example:
Note again that the doubling of the third in the I6 triad is not standard; doubling the root is much preferred. (In this case, the doubling arises from the desire to make a direct comparison with the mediant, as we did at the beginning of this Hub.)
But the main student pitfall in part-writing this progression is the danger of forgetting to raise the leading-tone in the dominant triad.
Let’s start with an easy question—and one in which the doubling issue just discussed does not occur! Identify the key and scale degrees of the soprano.
The key is A minor, and we have a 3-1-1-7-1 soprano—one in which the leading tone is already raised for you! Add the corresponding bass line, ending in the upper octave.
Add inner voices, beginning with a close position chord.
Here’s another one. You know what to do! (But start with an open position chord.)
Did you remember the raised leading tone before it popped up? If so, feel a little smug! If not, well, then you see what I mean by harping on the whole leading tone thing.
Let’s move on to the more involved case of the subdominant arpeggiation. In minor, the subdominant can take two forms: scale degree 6 can be raised or not. If raised, then the subdominant will be major, and if not, then the subdominant will be minor. This is shown below.
The question, then, is which form is appropriate? You may remember that the harmonic minor scale is a good guide to ‘default’ chord forms—and of course, the harmonic form does not have a raised sixth scale degree. Therefore, the ‘default’ subdominant triad in minor keys is minor.
However, the major form does also see some use. Probably the most compelling reason to use it arises in cases where an important line—especially a soprano melody—moves 6-7-1. The 7th scale degree will usually be raised to act as leading tone, and failing to raise the 6th as well would create the ‘illegal’ melodic interval of the augmented second. So the raised seventh can force a raised sixth, which in turn means a major subdominant triad. (More briefly, and perhaps more clearly: melodic lines like 6-7-1 may require the use of the melodic minor scale, rather than the harmonic minor.)
As an example, try this practice question. What are the key and scale degrees of the soprano?
E minor, 5-4-#6-#7.
Try adding the bass-line—but be aware there is a trick to it, one involving a new concept. You might try playing or singing possible bass lines to bring your ear into play in judging their relative merits. (As in the major-key examples above, the subdominant arpeggiation occurs on beats two and three.)
As shown, the “trick” is to use the raised sixth on beat two in the bass, so that it ‘matches’ the soprano’s sixth a beat later. Using the lowered sixth in this position creates a jarring effect called a “false relation.” (However, this effect is sometimes used, as for instance in vocal music text-painting emotional distress.) Compare the ‘default’ version with a version featuring the false relation.
You may prefer either version, but bear in mind that the ‘vanilla version’ is the default.
Now add the inner voices, beginning with a close position chord.
The parallel motion between bass and soprano requires special care to avoid parallel fifths; the alto and tenor must both connect with the dominant chord by contrary motion.
Here's another, using a similar chord progression--key and scale degrees?
G minor, 3-4-6-5. (The soprano "D" couldn't be part of a V chord if this example were in Bb.)
Now add the other parts.
This question used the 'default' minor form of the subdominant.
Let's turn now to bass arpeggiations of the dominant triad. There are again two possible forms, minor and major; by far the more common of the two is the major form, which includes the leading tone. Let's try a question, harmonizing a soprano with the progression i-iv6-V-V6-i. Analyze the soprano, then harmonize.
The 1-1-7-2-3 line in C# minor requires a 1-b6-5-#7-1 bass line to realize the harmonies indicated. Here again, the possibility of a false relation arises; forgetting to raise the leading tone in the bass would have sounded odd indeed:
As discussed in the second of the Minor Key Part-writing Hubs, the minor form of the dominant triad can also be used , though it does not function as a true dominant harmony if this is done. In fact, that is its advantage—by delaying the dominant function, a composer can build harmonic suspense and lengthen phrases. An illustrative example of a minor dominant:
Although the chord on beat 2 is built on the dominant, its minor quality defeats any possibility of dominant function. This 'saves' that function for a definitive arrival on beat 4. (In this example the strategy is applied over a very short span of time, but it is often used over much longer phrases.)
Now try the same progression in a different key and a different soprano. Analyze the soprano as usual, then add the remaining voices. Start with a close position chord.
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- snowonmusic | A music theory blog that's NOT all work!
A music theory blog that's NOT all work! A great place to ask questions about this Hub or about other music topics, to hang out, to talk about odd bits of musical structure, and even to play some musical parlor games!
A somewhat unusual little progression to end our look at part-writing first-inversion triads, perhaps, but fun and colorful!
Let's look back at what we've learned in this Hub: the concepts of first-inversion triads and of bass arpeggiation; how to apply these concepts to the primary triads I, IV and V (or i, iv (IV) and V in minor); the part-writing pitfall of the "false relation (which, in 'real music' can also be a powerful expressive device); and we have practiced useful voice-leading practices to help us avoid the pitfalls.
In the next Hub in this series, we'll look at secondary triads in first inversion.
Other Music-related Hubs by Doc Snow
- 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.'
- How (Not) To Practice Music Efficiently, Part One
The first of a pair of articles on how (not) to practice music, this article sets the record straight on much confusing practice advice you hear. Plus, great pictures of some musical greats!
- Better Faster: Top Ten Music Practice Tips
The shorter version of Doc Snow on practice technique--or how to get better, faster.
- String (or Restring) Your Guitar: How (Not) To Do I...
An illustrated guide to restringing an acoustic guitar. If you've been too intimidated to try this yourself, pluck up your courage and save yourself $15!