Part-writing Chords: Supertonic I
This Hub is the fourth in a series on part-writing—the essential skill in learning music theory in the Classical style. Unless you have already either worked through those Hubs or learned the basics they cover, you should go back and do that work before tackling this Hub. To help you decide, here’s a quick summary of the content covered:
PW Hub #1: Part-writing Chords: Tonic and Dominant I
- Lead sheet
- “Spacing” of voices
- Parallel and contrary motion of voices
- Concept of “voice leading”
- “Root position,” “voicing,” and “line”
- Polarized roles of tonic and dominant chords in Classical harmony
- Resolution of “leading tone”
- “Open” versus “close” chord spacing
- Chordal “doubling”
- “Common tone”
PW Hub #2: Part-writing Chords: Tonic and Dominant I (Exercises)
- Vocal ranges
- Rule for determining sharp keys from key signature
- Rule for determining flat keys from key signature
- Chords with missing thirds
PW Hub #3: Part-writing Chords: The Subdominant Chord I
- Root motion by fifth
- Root motion by second
- Parallel motion [perfect or imperfect intervals]
- Similar motion; similar fifths and octaves
- Incomplete triads [omitted fifths]
- Tripled root voicing
If you’re comfortable with all of that, let’s proceed!
First, let’s note a milestone: with the supertonic—AKA the ii chord—we are for the first time dealing with a chord that is not one of the ’primary triads.’ As discussed in another Hub (link), the ‘primary triads’ are the Tonic, Dominant, and Subdominant chords—I, V, and IV chords. Clearly the supertonic—built upon the second scale degree and symbolized as the ‘ii chord’—must be “secondary.” Before adding any more detail, here’s what the supertonic looks like in the scale of C major:
- Understand Chords: Chords In Keys (Part Two of a Series)
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As discussed in the Hub Chords in Keys (see link in sidebar for more detail, above right), the “primary chords” are those most commonly used in traditional harmony—the “three chords” of the saying that ‘country music is three chords and the truth.’ In major keys, they also comprise all three major triads to be found within the confines of that key. The supertonic, by contrast, will be a minor triad. (We’ll give minor keys a whole discussion of their own later on, since the minor keys involve an additional layer of complications.)
Let’s start by looking at the part-writing involved in what is probably the most common single chord progression involving ii: ii to V. This progression, common enough in Classical harmony, is particularly favored in traditional Jazz.
For example, the chordal structure of the verse of the Duke Ellington standard Satin Doll can be seen as consisting of systematic transpositions of ii-V progressions. (The ii-V progression normally culminates in the tonic triad, I, but Ellington avoids this until the very end of the melody.) Here is a simplified (albeit fancily-formatted) diagram of the verse harmony, omitting the last tonic:
But we’re here to part-write ii-V, not to multiply examples of its use. How can it best be written?
There’s an easy model: the I-IV progression studied in the last Hub in this series. Since the supertonic is one scale step above the tonic, and the dominant is one scale step above the subdominant, one should be able to simply shift the I-IV up a scale step to arrive at a well-written ii-V. Here’s how this would look (and sound) in C major:
Note the soprano; in each measure it stays constant— as we saw in preceding Hubs, this is called “keeping the common tone,” and it’s good part-writing practice. So is the stepwise motion in the alto and tenor voices. The bass, of course, traces the roots of the chords, dropping the fifth from “D” to “G”—emphasizing for us that this progression is an example of what we called “root motion by fifth.”
Let’s try a practice example of this progression. Here’s a ii-V bass line; to what key does it belong?
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If you said “B major,” good! If not, you may want to quickly refer back to PW Hub #2, linked above, for the rules for key identification.
Following the model progression above, add voices, starting with the soprano and proceeding downward to the alto, then the tenor.
(As always in this series of Hubs, I recommend that you actually write out each example on paper; it will really aid retention of this information. A link for free manuscript is given here for convenience.)
That example was in what we called “open spacing;” let’s try an example in “close spacing,” using the same bass and soprano lines. What is the key?
The answer is “Ab major.” Now see if you can fill in the inner voices in correct ‘close spacing.’
As shown, close spacing has voices taking adjacent chord tones—for instance, the next possible chord tone down from the soprano’s “Bb“ is the alto’s “F.” There is no possible chord tone between the two voices, and the same is true for alto and tenor.
Let’s try one more example before moving on. We saw for the I-IV progression that it is not always necessary, or even possible, to keep the common tone. For example, we looked at a version of this progression that used a “3-1” soprano line—one in which the soprano skipped downward from scale degree 3 to scale degree 1. Since scale degree 1 is the only tone which could serve as common tone, we can’t keep it in the same voice and still use this soprano line. (Not using complete triads, at least! But we’ll review that wrinkle in due time.)
Here’s what this looks like in the key of Db, as given in the last Hub:
Try rewriting this one in the key of A major; the soprano is given to get you started, but for extra points write it yourself, without looking at the prompt.
But that isn’t the only context in which we will find the supertonic chord. Another common progression involves not root motion by fifth, but by second: the supertonic quite frequently follows the tonic chord, in a I-ii progression. Here’s an example--what’s the key?
This I-ii progression is in D major. Compare it to the IV-V progression in A major:
Notice that it’s identical on paper, except for the key signature. The voice-leading is identical, and the only tone that differs is the second tone in the soprano: “G” in example 7, “G#” in 8. Now listen to the two back-to-back:
The change of the second triad from major to minor certainly makes a marked difference!
(By the way, it’s worth remarking that in Classical harmony it is much more common to hear I-ii than the reverse--writing a ii-I progression on a part-writing assignment will usually result in a lowered grade! This can be confusing for music students coming from the popular tradition, where the ii-I progression is perfectly fine. Without going into the reasons for this difference, let’s just note that it’s important as part of the harmonic style that makes Classical music sound the way that it does.)
Returning to the voice-leading shown Example 7, it shows the standard method for part-writing progressions involving root motion by second: the bass moves contrary to the upper three voices. This automatically prevents the objectionable parallel fifths or octaves that we learned about in the last Hub.
Let’s try it in a different key. First, identify the key and scale degrees of the given soprano:
This is a “5-4” line in the key of Eb, similar to the soprano line given in Example 7. Add the appropriate bass, alto and tenor.
There is an alternate voice-leading as well. Sometimes a melody creates parallel thirds with the bass if it is harmonized with the I-ii progression. This can work if done carefully:
Here the remaining voices move in contrary motion to the soprano and bass, avoiding the objectionable parallel fifths and octaves that so easily occur with root motions of a second. As always, the voices could be exchanged: the parallel motion need not be between soprano and bass; that is just the most common scenario.
Note one other thing about this version of the I-ii progression: the doubling of the ii chord. We saw in the preceding Hubs on part-writing that for primary triads, it is most often the root that is doubled. Next most frequent is the fifth, then the third. (We also saw that sometimes it is helpful to write an incomplete triad with tripled root and no fifth—but the third should never be omitted.)
In this version, the ii chord has a doubled third. This wouldn’t be a problem even for a primary triad; but for a secondary triad it is actually the most common voicing. It makes sense in a way: if you think of it in terms of scale degrees (not chord members) doubled, then it is quite simple: the primary scale degrees—1, 4 and 5—are most frequently doubled, regardless of whether they form the root, third or fifth of a particular triad. (Call it the “Doc Snow rule of doubling.”)
Try a twist on this voice-leading. What is the key and scale degree sequence of the soprano below? And to which voice of Example 10 does it correspond?
The answers are E major, “1-6,” and “tenor.” Using Example 10 as a model, add bass, alto and tenor voices.
Notice the spacing that is forced here: neither close nor open. Call it a ‘hybrid’ spacing, if you want! It is not a problem in itself—although since the alto and tenor are at their maximum allowable separation, care would be required in connecting the next chord.
So far we’ve considered the possibilities that arise when connecting the supertonic to the dominant and to the tonic. But what of connecting it to the remaining primary triad, the subdominant? Here are the two triads in their simplest form:
The two triads clearly share two chord tones: “F” and “A,” the root and third of the subdominant, form the third and fifth of the supertonic. This will also be true of any two third-related chords within a key. And fortunately, it makes connecting third-related chords quite simple in principle, since there are two common tones one can exploit:
The repeated tones make for a very smooth and safe chord connection—though it would be easy enough to create objectionable parallel fifths by taking the soprano down to “A”:
Note the 'hollow' sound given by the over-emphasized fifth.
Instead, double the root, and be sure to approach the octave “D”s—or whatever pitches form the roots of the ii chord—in contrary motion.
Let’s continue our exploration of root motion by third with another practical example of IV-ii. As usual, let’s start by identifying key and scale degrees of the given voice:
We’re in F Major, and our soprano consists of a common-tone line, “4-4.” Now add bass, alto and tenor.
By the way, in Classical style the normal sequence is “IV-ii”—not the reverse. Again, the reasons for this will be discussed later—there will be a Hub about normal Classical chord sequencing. For now, just know that there is a reason why our examples always present IV before ii.
Let’s try one more example of IV-ii. Key and scale degrees?
This soprano is a “1-2” line in A major. Now add bass, alto and tenor. Use close spacing.
The IV-ii progression brings up one last point. Third-related diatonic chords with their shared double common tones also tend to sound somewhat similar. For this reason, third-related chords are often substituted for each other. The possibilities in C major are shown below—or most of them, at least.
Chord substitution is most often thought of in the context of jazz: musicians like pianist George Shearing famously used (and still use) chord substitutions to create fresh-sounding versions of standard tunes that had become overly familiar to many listeners. But it can work just as well in other popular styles, and can be seen at work in Classical practice, too.
For instance, the familiar “deceptive cadence” substitutes the submediant triad for the tonic. Here’s how it sounds. (We’ll hear the expected cadence to I first, followed by the ‘surprising’ substituted vi.)
Other substitutions are common in Classical style, too. For example, the viio triad often acts like a dominant harmony of sorts. And--most relevant for this Hub--ii and IV act nearly interchangeably for most purposes: despite the differing chord qualities of these two triads, many listeners find it challenging to reliably tell the two apart when placed in a musical context. How obvious to you is the difference between the following harmonic progressions? Which features ii, and which IV?
As we’ll see in a future Hub, there are variations that can bring them yet closer in sound. But the overall musical effect of the two versions is already quite similar, even for those who readily hear the difference between the ii and the IV.
Which was which, you ask? OK, here’s the notation for the two progressions:
So why worry about the difference between ii and IV in cases like this? Well, even small differences can be expressively important sometimes. And technically there can be advantages one way or the other.
For example, some would criticize the voice-leading of the second version in Example 18. Using the ii chord forced the use of the upper “A” in the bass in the third chord, the V, since using the lower octave would create objectionable ‘similar fifths,’ as discussed in PW Hub #3:
The soprano’s “E” forms a fifth with the bass “A,” and the soprano approaches that fifth by skip, not step. These conditions are the precise ones characterizing the forbidden similar fifths.
But avoiding this similar fifth by using the upper “A” instead creates problems of its own. Now the bass “A” is higher than the following tenor “F#”—a fault called “voice overlap.” It makes the voices harder to follow, and thus results in a slightly less transparent texture. Where possible, voice overlaps are better avoided. So, in this case, it might be better to use the IV than the ii.
(It’s true that this level of attention to voice-leading detail can seem a bit fussy, especially to Twenty-first century ears accustomed to much, much stranger things. But it’s part of how Classical style attains its refined texture.)
On the other hand, consider Example 20, which shows a “1-6-7-1” soprano harmonized in two ways. The first version uses ii to harmonize the “6,” while the second uses a IV in the same place. (You may remember that we discussed above how tricky this latter voice-leading scenario can become.)
The first version is quite straightforward, with clear lines in all parts. True, we’ve used what we called the ‘hybrid’ spacing for the supertonic chord on beat two, but that is OK, even if it doesn’t blend quite as smoothly as the standard close and open spacings. (And we could have opted for standard open spacing, and doubled the root of the supertonic chord instead of the third, had we wished.)
The second, while workable, shows a bit more ‘stretching.’ Notice the doubling of the IV chord; we have a doubled root and a doubled third—an incomplete chord voicing we have not seen before. It is an acceptable, but not preferred, voicing. The alternative—also acceptable but not wonderful—would be to use leaps in the tenor, like this:
So, on balance, it’s a little easier to use the ii chord in this situation than it is to use IV. (By the way, it’s worth pointing out that this is partly because the chord progression IV-V-vi involves two consecutive root motions of a second—the trickiest root motion to deal with. Using the supertonic converts the first of these connections to root motion by fifth instead.)
Once again, we’ve managed to wade through a lot of information together, so let’s sum up for now. We have looked at how the supertonic can connect to each of the three primary chords I, IV, and V, and in doing so we also completed the cycle of possible root motions. It’s useful to put this in the form of a table:
We also learned that in contrast to the primary triads, for which the root is the preferred tone to double, the supertonic most often has the third doubled. That is actually part of the larger rule I immodestly call “Doc Snow’s rule of doubling.”*
Let me (equally immodestly) highlight that rule by putting it in the by-now familiar fancy format:
We learned a couple of new chord voicings during that discussion, too: the ‘hybrid spacing,’ and the incomplete triad with doubled root AND doubled third. (Note that the latter is not workable for a V chord, as it involves the forbidden doubling of the leading tone!)
Lastly, we learned the very important idea of chord substitution and studied the important set of chord substitutions involving diatonic third-related chords (such as I and vi, or IV and ii.) In connection with the latter, we noted some reasons why ii or IV might be preferred in a particular situation.
It’s a lot of information—enough that we have scanted the need to practice using the chords we’ve been examining. But that will be the material of a forthcoming Hub in this series!
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*I was joking--albeit a bit self-satisfiedly--when I proposed the "Doc Snow" name for this rule. But reader 'chasmac' points out that it was also taught by one of the grand old men of American music in the twentieth century, Walter Piston. So if we're going to name this rule after a person, it would be better called the "Walter Piston doubling rule."
Sic transit gloria mundi. . .
Other Hubs by Doc Snow
- Part-writing Chords: Summary I
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- Part-writing Inverted Chords: Primary Triads In First Inversion
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