Part-writing Chords: Mediant and Submediant I

The mediant and sub-mediant chords—triads built upon the third and sixth scale degrees, respectively—are less frequently used than the triads previously considered in this series of Hubs. (This is especially true of the mediant.) It’s partly for this reason that these two chords can be used to broaden and freshen harmonic color.

Before looking at some normal uses of these two triads, though, the reader may wish to check whether it would be helpful to work through some of the previous Hubs in this series—the knowledge contained in them is assumed in the rest of this Hub. Below are lists of the topics that are covered in each of the preceding Hubs.

Part-writing Hub #1

  • 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”

Part-writing Hub #2

  • Vocal ranges
  • Rule for determining sharp keys from key signature
  • Rule for determining flat keys from key signature
  • Chords with missing thirds

Part-writing Hub #3

  • 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

Part-writing Hub #4

  • Primary and secondary triads
  • “Doc Snow rule of doubling”—better known in association with Walter Piston!
  • “Hybrid spacing”
  • IV normally precedes ii in Classical style
  • Chord substitution
  • Deceptive cadence
  • Voice overlap

If any of this seems unfamiliar or confusing, it would probably be best to spend some time working through (or at least reviewing) the relevant material.

As always, I strongly suggest answering the questions physically, on actual music manuscript paper, as you proceed through this Hub. As usual, I’m providing a link to free manuscript paper that you can print out.

In the previous Hub we considered the concept of chord substitution, noting that since third-related diatonic triads—as, for example, ii and IV—share two of three chord members, they will thereby exhibit some sonic similarity. Supertonic and subdominant—ii and IV—are especially vivid examples of this tendency, since in normal usage both chord tend to lead to a dominant triad—the “V” chord. That is what music theorists mean when they say that both ii and IV “function” as preparations for the dominant.

(In fact, this notion of chordal “function” is widespread and influential; theorists recognize chords of all sorts as possessing “tonic,” “dominant” and “dominant preparation” “functions.” But that is a discussion for a later Hub.)

First, let’s look at the mediant and submediant in the context of the major scale:

Example 1
Example 1

As shown, the mediant is the iii chord. Its name seems to recognize the fact that its root lies midway between tonic and dominant in the scale:

Ex. 2
Ex. 2

Correspondingly, the submediant, vi, has a root lying midway between that of the tonic and the subdominant.

Ex. 3
Ex. 3

The mediant and submediant can also be placed in a more specifically harmonic context, though. We noted in the last Hub how tonally strong, and how common, the progressions ii-V-I can be. This is so because of the powerfully stabilizing root motion by fifth it exemplifies:

Ex. 4
Ex. 4

This motion can be further extended ‘backwards’ to incorporate the submediant and mediant chord, too:

Ex. 5
Ex. 5

Notice the striking sound of the mediant—but also the purposeful flow of the harmony, dominated as it is by the tonally strong root motion by descending fifth. These harmonies seem to drive toward the tonic with great energy and purpose, moving systematically from the most 'distant' diatonic chord, the mediant, to the tonic.

Notice, too, that the second and third chords—iii and vi—form a unit that is replicated down one scale step by the fourth and fifth chords—ii and V. This type of transposed repetition is termed a ‘sequence’ and it’s a useful musical technique.

Let’s try writing variations of that progression. Identify the key and scale degrees in the soprano below:

Question 1
Question 1

It’s in Ab, and the scale degrees in the soprano are 5-5-6-4-5-3.

Using the example above as a model, add a bass line.

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Now add alto and tenor voices in turn.

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Here’s another twist on the same chord progression. Name the key and scale degrees in the soprano below. Also, which of the lines in the previous question does this soprano resemble?

Question 2
Question 2

The key is D major, the scale degrees are 1-7-1-6-7-1, and the line is very close to the tenor line in the preceding question; only the last note is changed. Why does that last note need to change?

While you ponder that, add a bass line.

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You may have thought that the line needs to change because the C# at the end of the first full measure is the leading tone, and when ‘exposed’ in the soprano or bass, instead of ‘hidden’ in the alto or tenor, it needs to resolve to the tonic. If so—congratulations! That’s exactly right.

Now add alto and tenor.

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Another harmonic context for vi and iii occurs when, rather than appearing ‘as themselves’ in a ‘falling fifths’ progression like those we have just been examining, the mediant or submediant appears as a substitute for some other chord.

Which substitutions are possible? That is, which triads are a third away from (and therefore share two tones with) the mediant and submediant? The answers will be obvious to some readers, and perhaps puzzling for others. If you are not one of the first group, don’t give up right away. Write out on paper the lower two notes and the upper two notes of the vi chord:

Example 6
Example 6

Now do the same for the iii chord. For each pair of notes, there will be one tone which will form a ‘new’ triad. Work through the four possibilities. You should end up with something very similar to this:

Ex. 7

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Ex. 7a  (Same as Ex. 6)Ex. 7bEx. 7cEx. 7d
Ex. 7a  (Same as Ex. 6)
Ex. 7a (Same as Ex. 6)
Ex. 7b
Ex. 7b
Ex. 7c
Ex. 7c
Ex. 7d
Ex. 7d

So, vi can potentially substitute for I—as mentioned in the last Hub of this series, this commonly happens in the context of the “Deceptive Cadence”—or for IV. It isn’t hard to find examples of vi leading to V, which could be thought of as vi substituting for IV, although it isn’t usually viewed in that way.

The mediant triad, similarly, could substitute for either I or V. If you think about it, that is a remarkable thing, since, in the context of Classical practice, tonic and dominant functions form the opposite poles of tonal harmony. Possibly this very ambiguity helps explain why one sees relatively few examples of the iii triad. Yet there are usages which suggest precisely these mediant substitutions, as we’ll see.

Beginning with the submediant, here are two versions of the progression I-vi-V-I. As mentioned a moment ago, one way to think of this would be that the vi chord substitutes for the IV chord we would expect to lead to V. Like the IV chord, vi has a potential pitfall when leading to V: since the root motion is by second, objectionable parallel fifths or octaves could easily arise. This danger must be avoided by making sure that the upper voices—or at least those involving root and fifth of the V chord—must move in contrary motion to the bass. Here are two examples:

Ex. 8
Ex. 8

In the first version, the inner voices, which contain the root and fifth, move contrary to the bass. The soprano moves in parallel thirds with the bass. In the second, all three upper voices move contrary to the bass; this is the more common version, and allows smoother motion in the upper voices.

Try this progression in another key. As usual, start by identifying key and scale degrees. To which voice—and which version—of Example 7 does the given soprano correspond?

Question 1
Question 1

The 3-3-5-3 soprano in F major corresponds to the 3-3-5-3 alto in Example 7b, so use that example as a model to help you add bass, alto and tenor voices.

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Let’s try the “deceptive cadence” progression, in which vi substitutes for I. I’ll throw you in at the deep end by first giving a version using the subdominant: I-IV-V-vi. (The obvious alternative, I-ii-V-vi, would not fit with the soprano’s “G.”)

The problem that this creates is that you now have two successive root motions by second; each requires careful use of contrary motion with the bass in order to avoid troublesome parallel perfect intervals. See if you can navigate this challenge successfully; identify key and scale degrees, then add the appropriate bass.

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Question 4
Question 4
Question 4

As you can see, the soprano and bass move in contrary motion only for the first of the two motions by second, moving instead in parallel thirds for the V-vi progression. Add alto, then tenor.

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Question 4
Question 4
Question 4

Now let’s try a version using the ii chord. This soprano could be harmonized with either ii or IV, but we’ll avoid the double motion by second we saw in the last question. However, as you consider your bass line, be careful—this melody poses other pitfalls. See if you can avoid them.

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Question 5
Question 5
Question 5

This bass line is forced by the downward skip in the soprano from the “A” to the “F#,” because a downward leap in the bass—“F#” to “B”—would create objectionable similar fifths. Therefore, the bass must leap upward to the “B” instead—and that means that it must start low in order to avoid ‘squeezing’ the inner voices at the end of the progression.

Once the bass line is correct, though, writing the inner parts is fairly easy. Write alto first, then tenor—either order works fine in general, but the alto is given first below!

Q5c-d

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Question 5
Question 5
Question 5

The alto and tenor must move contrary to the bass in the I-ii, as always. The doubled “A” in the ii chord is normal—remember the “Doc Snow doubling rule” that the primary tones within a key are the first choices to be doubled!

Unfortunately, that doubling also means we can’t keep a common tone when moving from the ii to the V—but the resulting tenor is doubly OK, even though it arrives by similar motion at an octave to the bass. First, that ‘similar octave’ does not involve two outer voices, which it must in order to be a problem. Second, it is approached by step in the tenor, and to be a problem it must be approached by skip or leap in the soprano.

You may have written a “C#” in the alto for the very last chord. This is not the worst mistake ever, but the “E” is a better choice, since “E” is the primary tone found in the triad. The “Doc Snow doubling rule” strikes again!

Let’s try some examples (arguably) involving mediant substitutions, too. Here’s an example in which iii can be seen as substituting for I: I-iii-IV-V-I. Once again, this involves consecutive root motions by second. As usual, contrary motion between upper voices and bass prevents problems.

Example 9
Example 9

Note the descending scale in the soprano, and how the leading tone is harmonized by the iii. The leading tone normally ‘wants’ to resolve upward, especially when placed in an outer voice. But you do find descending scale segments like this one—and often it is the iii triad which is chosen to harmonize the leading tone instead of the more usual V chord. (This tends to ‘soften’ the leading tone’s characteristic tendency.) From this perspective, you might think that the iii is really substituting for V, not I—but remember that V-IV is a very rare progression in Classical harmonic style; I-IV is much more ‘plausible.’

Try this progression in another key. Identify that key and the soprano scale degrees as usual.

Question 6
Question 6

It’s F#, and the scale degrees are (of course!) 1-7-6-5-5—it’s the same soprano. Adding bass and inner voices should be no problem.

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Question 6
Question 6
Question 6

Here’s another variation on the theme: ii can substitute for IV in the preceding progression. Harmonize this soprano with I-iii-ii-V-I.

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Question 7
Question 7
Question 7

We’ll conclude with a couple of progressions which don’t so clearly reflect the concept of substitution. First is a straightforward progression using root movement by fifth. What are the key and scale degrees of the soprano below?

Question 8
Question 8

The line is 1-1-6-7-1, in the key of Bb. Harmonize it with the progression I-vi-ii-V-I.

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Question 8
Question 8
Question 8

Now consider this soprano:

Question 9
Question 9

Although it is in Bb, like Question 8, the “Bb” on beat 3 means that using a iii chord there is unworkable, as the chord does not contain that tone. So, an extra credit question, not too hard: what other chord might you use on beat 3?

If (after a suitable pause for thought) you reasoned that ii and IV are frequent substitutes for one another, that the Bb would form the fifth of a IV chord, and that therefore the harmonization might well be I-vi-IV-V-I—well, then congratulations: “Good work!”

Now complete the harmonization in our usual manner.

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Question 9 (with bass)
Question 9 (with bass)
Question 9 (with bass)

This progression is quite common in many styles. It can readily be found in Classical repertoire, and was a favored set of ‘changes’ for a great many doo-wop hits from the 50s and early 60s—in fact, in that context, the progression deserves the label of “cliché”. Here’s an invented (but very typical) example:

Ex. 10

Let’s finish this Hub with an “exam question,” a longer, tougher challenge. Here’s the soprano:

Question 10
Question 10

It’s in D, as you can probably readily see by now. How could one go about harmonizing this?

It’s designed to allow you to use the examples already given in this Hub. Notice, to begin with, that the first measure closely follows the pattern of Example 10 (repeated here so you don’t have to scroll back up to look at it.)

Example 10 (repeated)
Example 10 (repeated)
Example 10a--reduction of Ex 10
Example 10a--reduction of Ex 10

So the harmonization would closely reflect what was done in that example.

What about measure 2? Well, first I’m going to mandate that beat 1 be a vi chord, forming an example of the “deceptive cadence” progression, as shown in Questions 4 and 5 above. (It’s an unusual example, admittedly—usually the soprano in a deceptive cadence is either 7-1 or 2-1.)

Further—for reasons too lengthy to go into here—we don’t want to use another vi chord on beat 2 of measure 2—in fact, we don’t want to repeat the same chord consecutively in these exercises at all. So what chord should we use on beat 2?

Let me put forward as model a progression discussed in PW Hub #4:

I-IV-ii-V example

Example 11
Example 11

The progression is I-IV-ii-V-I. Notice the sequence IV-ii in particular: as we have discussed, these chords can substitute for each other, but they can also occur in succession. In Classical practice, though, the sequence is usually IV-ii, not the reverse, since the ii triad tends to 'drive' toward the dominant chord more strongly.

Can you use this to advantage in the question we are working on? (Hint, hint!)

So, with models to apply, can you figure out the chords to use which will let you write a bass line for that soprano? I’ll give the answer in two phases. (You may or may not need to be walked through the process in detail, so I would suggest that you try working out the answer on your own. Then—and only if needed—you can refer to the following explanation.)

Question 10 melody (repeated)
Question 10 melody (repeated)

First, the chords. For measure 1, applying the model suggested would give a I-iii-IV-V chord progression. For measure 2, vi was given on beat 1, harmonizing scale degree 3. We can be sure that a V chord is required to harmonize the scale degree 7, on beat 4 of measure 2, and that we will end with a I chord.

So our problem comes down to two chords—those found on beats 2 and 3. We need to get from vi to V. What two chords connect those two? Well, the example given as a hint above contains the sequence IV-ii-V. Can we logically move from vi to IV? Of course! We just did so, in our “doo-wop cliché” example, after all. So measures 2-3 can be harmonized vi-IV-ii-V-I.

Example 12--Melody with chord symols
Example 12--Melody with chord symols

Second is the challenge of writing the actual bass line. In this key, there’s an obvious choice of octave for the beginning tone, and if we follow the model it will dictate our tones up to the first beat of measure 2. (That’s one of the advantages of thinking linearly, as we have been doing in this series of Hubs.)

In the second measure, it will be best to keep to the same general register as the first measure, even though there are some possible tones in a lower part of the bass range. These will not sound as good, though, because they will force one or more of several things best avoided: we could 1) jump more than an octave; 2) leap or skip several times in the same direction; and we could 3) outline a dissonant interval. All of these are both subtly grating to the ear, and harder to sing than the alternative.

Bass issues 1--bad leap, outlined 9th
Bass issues 1--bad leap, outlined 9th
Bass issues 2--3 consecutive skips/leaps, outlined 9th
Bass issues 2--3 consecutive skips/leaps, outlined 9th

Putting all these considerations together gives us the bass line below. (If you already got it, then—again!—“Good work!” If not, well, this was meant to be a challenge, so don’t feel discouraged.) Now add alto and tenor parts:

Q10b-d

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Question 10 (with bass line)
Question 10 (with bass line)
Question 10 (with bass line)

And that’s it! Here ends the first part of our consideration of part-writing. We’ve looked at how to part-write all major-key diatonic triads in root position, examining normal harmonic patterns and the pitfalls they may sometimes contain.

Compulsive score-keepers may notice that we haven’t looked at the viio triad yet—that’s because it is not normally used in root position! (We will consider it when we deal with triads in inversion.)

Others will notice that minor key usage still needs to be dealt with as well. That will be the topic of the next Hub in this series.

More by this Author


13 comments

Doc Snow profile image

Doc Snow 4 years ago from Atlanta metropolitan area, GA, USA Author

Thanks for working through this Hub on the mediant and sub-mediant!

I hope it was helpful for you. Let me know if you have questions, comments, requests or feedback, and I'll see what I can do about it!


tsmog profile image

tsmog 4 years ago from Escondido, CA

Totally, awesome. Amazed. And, Thankful. A mix of emotions reading and interactively participating, while tasting through learning appreciation. A most highly recommended hub and series. Awesome!


Doc Snow profile image

Doc Snow 4 years ago from Atlanta metropolitan area, GA, USA Author

Wow--I think that betters just "useful!"

I'm delighted that this Hub pleased you so well. Thanks for your kind words!


tsmog profile image

tsmog 4 years ago from Escondido, CA

Doc, I appreciate music and know the connection with spatial intelligence and math. I have a nephew who loves guitar and does well. Reading this hub I think I may understand better and be able to communicate better with him too and my bro who plays with him. I plan as time allows to read & interact with the others.


Doc Snow profile image

Doc Snow 4 years ago from Atlanta metropolitan area, GA, USA Author

Cool. Let me know if there's some aspect of theory (or some other aspect of music) you'd be interested in hearing more about--like most Hubbers I've always got the antennae out for things to write about.

As I expect you know! ;-)

And I don't mean to spam my own comment thread, but I'm just wondering if this Hub would be of interest as well?

http://hubpages.com/entertainment/Strange-Days-Aga...

It's a little different--kind of a blend of theory, history and appreciation--plus some memoirs.


Guest 2 years ago

Thank you for this Hub as a resource its been very informative. I have been following it for a while and frequent the pages often for theory reference. I am for the most part able to grasp a lot of the concepts except for discerning a logical approach in choosing a suitable tone to double for secondary triads. Whereas you specified, for example in a ii chord, normally the third being a primary tone in relation to the key is the most desirable choice. But the answers to the questions have been known to select either the root or the third arbitrarily. A deceptive cadence for the most part ensures that I am more than likely to double the third in the vi chord. While the ii regardless of position suggests a toss up. I would think that in proceeding the V chord, the ii would have a doubled third as to pay homage to its predominant function but in practice, it seems to be a case by case basis. I did catch the trend of doubling the third of a ii chord when following a I chord, but not in succeeding any other primary triad (the same can be said of the iii chord as well). Is there a strategy I am missing when considering the most desirable possibility when doubling a secondary triad? Thank you once again Doc Snow I really appreciate your work


Doc Snow profile image

Doc Snow 2 years ago from Atlanta metropolitan area, GA, USA Author

That's a great question.

In secondary triads, the rule of thumb is to double the primary tone (i.e., scale degrees 1, 4, or 5). That's exactly as you specify for the supertonic triad. (And, btw, in each of the three minor triads, that's also the third of the chord. For the diminished triad, the normal--in fact, almost invariable--doubled tone is also the third, which is scale degree 2. That scale degree almost gets 'honorary primary tone' status.)

But, like the Pirate's Code, the doubling rule is 'more of a guideline.'

Specific reasons generally lead to the choosing of other tones to double. Let's look at a couple of the examples above.

In Q. 10, there are three secondary triads. Two follow the principle of doubling primary tones (thirds)--the iii triad in m. 1, and the vi triad in m. 2. There is also one that instead doubles the root--the ii triad, also in m. 2.

In that last case, doubling the third would require an awkward leap in the tenor, eliminate the common tone with the succeeding V chord, and likely create an unnecessary voice overlap. The doubled root may also (arguably at least) serve to emphasize the difference between the IV and the ii chord, which could be seen as desirable.

Or take the vi triad on the second beat of Q. 9. There, the root is doubled. Consider the alternatives if we were to insist on a doubled third: that third could only occur in the tenor, which is certainly possible. But then what do we do with the alto? If we take it down to the 'D' for a complete triad, we create parallel 5ths. If not, we have the same doubled root as we had before, but now we have an incomplete voicing with doubled root and doubled third. That's not terrible--I venture to say you can find instances in Bach. But it's not obviously a better doubling than the one we have. Plus, it gives up one of the two common-tone connections between the I and the vi. Better to keep both, and a nice smooth tenor.

So, doubling exists in an equilibrium with other considerations, such as melodic design and relative voice motion (counterpoint)--and the 'others' quite often win out. That's what makes it rather a 'case by case' thing, as you quite reasonably describe it in your question.

Hope that helps!


Guest 2 years ago

Thanks once again Doc Snow, that actually did help my thinking a lot. Any chance you may have a book published in the future? Your approach to explaining part writing is digestible which can't be said for a lot of music theory blogs or sites.


Doc Snow profile image

Doc Snow 2 years ago from Atlanta metropolitan area, GA, USA Author

"Any chance you may have a book published in the future?"

'From your lips to God's ear!'

Thanks much, and I'm glad those examples did help!


Ricardo 2 years ago

I have find your work very helpful BUT there are some errors in what you wrote and in the notation as well. In the last example you said measure 2 beat one is vi however when you wrote it, you wrote (I), I assumed it was typo because the notation is correct. Hope you don't mind me suggesting, If you can proof-read... Let me know If I was mistaken. I learned a lot from your blog. I am bit confused sometimes because of the errors. I have read the supertonic and the mediant topics. I will be visiting the minor functions soon. thanks


Doc Snow profile image

Doc Snow 2 years ago from Atlanta metropolitan area, GA, USA Author

Thanks for catching that. I assure you that I do proof-read everything. But it's difficult to be author, proof-reader and editor, because you don't have 'the fresh eye' when it comes proof-reading time.

Therefore, I'm doubly grateful to reader like you who take the time and trouble to alert me to those errors that do slip through! Thank you, and I'm glad that these Hubs are helpful none the less!


Kristen Howe profile image

Kristen Howe 18 months ago from Northeast Ohio

Great music lesson in this hub! Voted up for useful and interesting, too.


Doc Snow profile image

Doc Snow 18 months ago from Atlanta metropolitan area, GA, USA Author

Thanks very much!

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