Part-writing Inverted Chords: Mediant, Submediant & Leading Tone Triads

This is the third of a series of Hubs describing the characteristics, patterns and part-writing usage for triads in first inversion. If you've missed the first two in the series, you can catch up using the links in the sidebar below.

Or perhaps you really haven't delved into part-writing before. In that case, starting a bit earlier in the sequence is almost surely a good idea. Or you may just come to feel, as you proceed, that this Hub is a bit too advanced for your current knowledge.

In cases such as those, you can use the sidebar, too--it contains a link to a summary Hub describing the content and suggested sequence of the preceding series. You can use it to access discussion and practice exercises on part-writing any root position triad. (As a convenience, it also lays out the 'rules' for part-writing, which are presented in a progressive manner throughout the first series of part-writing Hubs.)

Use it to pick a more compatible starting point, or just to make a quick self-placement check, or as a review tool!

Zambian violinist "Caitlin" plays inverted; we don't know about her chords.
Zambian violinist "Caitlin" plays inverted; we don't know about her chords.

In this Hub, we'll consider the first inversions of the triads built upon the 3rd, 6th and 7th scale degrees--the iii (III), vi (VI) and viio triads. First, the vi triad in its context in the major scale:

Now a typical voicing of this triad:

Ex 2
Ex 2

Note that the third, C, is present in both soprano and bass. This 'doubling' of the third is normal for any secondary triad--the third of a secondary triad, after all, will be the primary tone present in the triad.

(The leading tone triad is a slight exception; in its case the fifth is the primary tone, but the third is still the usual tone to double. But that third is scale degree 2, which is also a strong and stable scale degree. One could jokingly call it an "honorary primary tone.")

One possible use of the first inversion submediant is to connect tonic and supertonic. As we've seen previously, the tonic-supertonic connection (like the subdominant-to-dominant connection) involves root motion by second, and this can be prone to creating objectionable parallel perfect intervals.

One way of connecting them is via an intermediary vi6, as shown in the example below.

Ex 3
Ex 3

VEx1

The possible parallel fifth between soprano and bass (beats 1 and 3) is avoided by moving the soprano first, creating the vi6, then by moving the other voices into the ii triad. (Note that there still could easily have been parallel octaves--they are avoided in this example by the tenor's contrary skip downward to the A.)

Compare a couple of other possibilities in harmonizing the same soprano:

Exa 4 & 4a
Exa 4 & 4a

Now try using the chord progression of Example 3 in a practice question.

(For newcomers to this series: I strongly recommend doing all exercises on paper. You can check your work by clicking through the thumbnails; I give the 'answers' voice by voice, normally in the order bass, alto and tenor. But you'll benefit far more if you force yourself to work through the questions, rather than just reading through them. If you need paper, the sidebar links to a site where you can download manuscript paper to print at home.)

What are the key and scale degree numbers of the following soprano?

Q 1
Q 1

The soprano traces a 5-6-6-7-1 line in F, exactly as Example 3 did in the key of C major.

Now add the corresponding voices.

(By the way, if you are a newcomer jumping into this series, most folks do not work one voice at a time. It's strongly recommended that you lay out the bass first, as this is the voice defining the harmony. Then work out alto and tenor at the same time, on paper; you can make minor adjustments to the bass in the process, if necessary.)

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Update Note

An alert reader spotted errors in this original version of this question. The question and discussion (below) have been corrected, but the original notation can still be seen in the video example, so that anyone interested in following the changes can do so. The discussion is in the comments capsule at the bottom of the Hub.

The original version can also be used as a 'find the errors' exercise. For those who want to try it, there are two problems there to be spotted.

Note, however, that the *audio* portion of video example was already correct.

It's better not to follow the model exactly, because the resulting tenor would be at the bottom of its possible range. But you can use the same 3-3-4-2-3 alto line as in the model. In this version, I give a 1-3-2-7-1 tenor line, resulting in an incomplete tonic triad. (From a doubling perspective, a 1-1-2-7-1 line would be better, but the difference in sound will not be dramatic, and the line is more interesting.)

It would also be possible to end on a complete tonic triad, with the alto taking the fifth, C, and the tenor taking the third, A. In that case, the alto would be obliged to ascend to D on beat 3, creating a 3-3-6-5-5 line. (The leap of a fourth in an inner voice is generally considered in the 'better avoided, but still legal' category.)

Yet more challenging is this question.

Q 2
Q 2

The accidentals all but tell us that we are in minor, and thinking about the scale degrees in the soprano line confirms this idea--we have another 5-6-6-7-1 line of sorts. This time, though, the line is chromatically inflected: that is, the sixth scale degree appears first in its lowered form (in accordance with the key signature) and then in its raised form (in accordance with the melodic minor form of the scale.)

We saw something similar in the last Hub, where a descending chromatic line passed through the two forms of scale degree six. That line arose from arpeggiating the supertonic chord; this one arises from the progression of VI6 to ii (root position.)

As in the previous case, it is better to keep the two forms of the sixth scale degree in the same voice; distributing them between two different voices introduces a somewhat jarring effect known as the "false relation."

As hinted above, the indicated harmonization here is i-VI6-ii-V-i. Add the remaining voices.

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Note the unison doublings on beats two (Bb) and four (A) between alto and tenor. Many students tend to feel that there is (or should be) something wrong with such doublings. But in fact they are perfectly OK, as long as they are approached and left in contrary or oblique motion, as is the case here.

Let's add the most tonally distant diatonic triad--the mediant (iii)--into the mix.

Ex 5
Ex 5

Again, the third is doubled.

The mediant is often found in close proximity to the submediant, as in this (root position) example:

Ex 6
Ex 6

Here the mediant is seen performing one of its useful major-mode roles: harmonizing the leading tone while avoiding actual dominant harmonic function. It's a common strategy in harmonizing a descending diatonic soprano line such as the one shown.

The submediant follows, prolonged by a bass arpeggiation which creates a sequential melodic pattern in the bass voice. ("Sequence," when used in music theory, denotes a pattern in one or more voices in which a melodic 'cell' is systematically transposed. In this instance the 'cell' is the ascending third C-E (beats 1-2), which is then transposed down a third, A-C (beats 3-4).)

Try that same progression in a different key.

Q 3
Q 3

It's 1-7-6-6-6-5-5, this time in E minor. Add the voices according to the example.

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How could you adapt the progession in order to fit the soprano below?

Q 4
Q 4

If you took a few moments to look at this melody (and perhaps even sketch out a possible bassline or two) a couple of things probably struck you.

First, since the soprano tones on beats 3 and 4 of the first bar correspond to the bass tones in the model we used in the last two questions, we would create parallel octaves if we failed to adjust the bass somehow. An easy adjustment would be to reverse the order of the bass arpeggiation on beats three and four, simply putting the first inversion triad before the root position triad.

Second, the chord on the downbeat of measure two must change, since the soprano scale degree involved--5--does not fit the supertonic triad. Since it clearly does fit a dominant chord, as does the following tone, let's make beats 1 and 2 form a bass arpeggiation as well.

A chord progression fitting this description would be: I-vi-ii6-ii-V-V6-I. Create a 4-part setting using this melody and chord progression. Begin with an open chord voicing.

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Nice!

Let's vary this a little, to take look at a unique usage of the first-inversion mediant. (It is marked with an exclamation point below.)

Or is that what this particular harmonic idiom really is?

Ex 6
Ex 6

It appears in this example that V is followed by a iii6 triad!

It sounds OK, but seems a bit odd from the perspective of harmonic theory, since V is supposed to be the highest apex of harmonic tension, and normally one does not 'back down' from that tension. Yet here we seem to retreat all the way to the most tonally distant of the diatonic triads.

But is that what happens, really? Listen again to the example. Does it feel as though the harmonic tension is lost when the V changes to iii6?

Music theorists have said 'no' to that question. They explain this idiom, not as a true mediant chord, but rather as a modified dominant. One term used to describe this is "apparent mediant." The idea is that this chord appears to be a mediant, but really sounds like a (modified) dominant.

Try using this "apparent mediant" idiom to harmonize the following melody.

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Q 5
Q 5
Q 5

The stepwise introduction of scale degree 3 makes this probably a more typical 'apparent mediant' than the one in Example 5, where the mediant was part of descending arpeggio pattern.

Let's look at this idiom in minor mode. If we follow the implications of the idea that the 'apparent mediant' is really an altered dominant, we'll write a 'mediant' triad that is augmented in quality, because it will include the raised leading tone--a necessity for dominant function. This will create an augmented fifth between root and fifth of the 'apparent mediant' triad.

Here's how it looks in C minor:

Ex 7
Ex 7

(This augmented triad does not occur 'naturally' in major mode. But it is technically a diatonic triad in minor. In terms of usage, augmented triads, like diminished ones, have traditionally been used only in first inversion, which 'mellows out' their dissonant qualities somewhat.)

What do you think of this sound?

Many listeners have found it piquantly attractive, precisely because of that mildly dissonant quality--so much so that the 'altered dominant' has become a common chord in jazz, where it tends to be thought of by an enharmonically equivalent respelling notating it as a dominant with a raised fifth. No more 'apparent mediant!' In C minor, for example, this spelling would be G-B-D#.

Try part-writing this minor mode version of the melody using the 'apparent mediant.'

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Q 6
Q 6
Q 6

Just for fun, let's conclude this section on the mediant with a straightforward major-mode bass arpeggiation of the mediant. It may not be a particularly common idiom in general, but what the heck.

You'll need to take some care designing the chord progression to make sure you fit in the bass arpeggiation described. To help out, I'll give both outer voices.

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Q 7
Q 7
Q 7

Moving on, we arrive at the sole remaining secondary triad: the leading tone triad, built on the (raised) seventh scale degree. (For now, we'll disregard the subtonic triad, found in minor mode and built upon the lowered seventh. Its usage in root position was discussed in an earlier Hub.)

The leading tone triad is diminished in quality, like form of the supertonic with lowered seventh. Like it, the leading tone triad normally appears only in first inversion, not root position. But it is quite useful, and fairly common.

The normal doubling is shown below--and is by far the most frequent doubling used.

Ex 8
Ex 8

The most common use is as a linear chord, connecting a root position tonic to a first inversion tonic, as shown:

Ex 10
Ex 10

Note how all voices move by step, two in linear scale segments and two in 'back-and-forth' neighbor note patterns. The voice leading is somewhat similar to the voice-leading patterns we saw in our first Hubs on part-writing the tonic-dominant connection.

For an easy start in part-writing this idiom, re-write the model in G major.

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Q 8
Q 8
Q 8

Now try this one:

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Q 9
Q 9
Q 9

Not too hard, if you picked up the key of C minor readily. (Though there is always the 'trap' of forgetting to raise the leading tone!)

There is a matter of mild controversy, though. Some would disallow the voice-leading of the alto and tenor as shown: those two voices move entirely in parallel fifths!

So what is the controversy? That is just bad, isn't it?

The complicating factor is the fifth in the leading tone triad: it is not a perfect fifth, therefore the fifths are not, by the strictest criterion, parallel. A few writers excuse them on this account; some take the opposite view. Still others--and I was taught this, as a young music student--feel that the first pair of fifths is fine, but that the second pair, which ends with the perfect fifth, is objectionable.

(The logic of this last school of thought is that the problem with parallel fifths is the over-emphasized 'empty fifth' sound which results. This can't happen when the second chord of the pair is actually diminished. But, on the other hand, the diminished fifth is still 'close enough' to 'point up' a succeeding perfect fifth.)

If this last point of view is adopted--that is, the view that perfect-diminished is OK, but diminished-perfect is not--then there is a ready cure. In fact, there are a couple:

Ex 11 & 11a
Ex 11 & 11a

In the first version, the 'diminished-to-parallel fifth' is avoided by using an incomplete triad voicing, which provides no fifth; in the second, the tenor takes the fifth via a downward skip, instead of the alto.

Try the progression in this major key, avoiding the potential 'quasi-parallel fifth.' Begin with an open position chord.

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Q 10
Q 10
Q 10

Let's look at another common usage of the leading tone triad. As show below, it can also be placed between a dominant preparation chord (such as IV or ii6) and the dominant which follows. In practice, this comes across almost as a variant of the familiar ii-V-I progression, since only one tone distinguishes the viio6 from the ii:

Ex 12
Ex 12

Quite smooth and successful!

In this version, the leading tone triad is set up by ii6, though there are other possibilities, such as IV. (Possibly relevant here is the fact that in the diatonic version of the circle of fifths, IV naturally precedes viio, so IV and its 'substitute' ii6 are both very plausible 'set-ups' for the leading tone triad.)

Using viio6 to precede a dominant triad works well because the leading tone triad possesses a dominant function, but a weaker one than the dominant triad. The progression therefore flows smoothly from less harmonic tension to more. Accordingly, the leading tone triad easily precedes a dominant--though normally it will not follow it, since that would reverse the normal harmonic flow.

Try writing the progression shown in Example 12 to harmonize this melody.

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Q 11
Q 11
Q 11

And again in minor.

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Q 12
Q 12
Q 12

Note that the alto and tenor move in parallel fifths between beats one and three, but this is not problematic since all fifths but the first are diminished, not perfect!

By way of a 'glorious conclusion' to our Hub, let's work an example of a harmonic sequence. Earlier, we mentioned that sequences are characterized by 'cells' which are systematically transposed. A harmonic sequence usually involves all voices; hence the voice-leading of the cell is replicated in all transpositions.

Let's use the soprano below, which has a sequential structure.

Q 13
Q 13

Note how the middle of the line is characterized by three pairs of repeated notes. These mark the original cell and its transpositions.

A favorite harmonic pattern for creating sequences is the circle of fifths, and a frequent variant of this is to voice alternating chords in first inversion. Let's make the first chord in the cell a root position triad (i), and the second a first inversion (iv6), as shown below.

Now lay out the bass, following the guides given so far.

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Since each pair of repeated notes in the soprano is a step lower, each pair of bass tones must be transposed down a step, too. (By the way, other transpositions are possible and do occur.) The pattern breaks to form a cadence, as shown.

Speaking of the cadence, you may have noted that the dominant function implied at the final cadence of this example is our (newish) friend, the 'apparent mediant.'

Now that you've got a bass laid out, complete the inner voices.

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Did something about this solution feel subtly 'off', rhythmically, at least at the beginning of the video example?

If you felt that it did--and many will not--you were probably sensing the effects of the chord position choices to which I steered you: in this sequence, the first-inversion triads are placed on strong beats (1 and 3), and the root-position triads are on the weak beats. This conflict between harmonic and metric accents results in a subtle feeling of syncopation, which only resolves at at the cadence as harmonic and metric accents come into alignment once again.

Such conflicts can be musically useful, creating feelings of surprise or suspense. But let's assume that in this case, you'd like something more stable and predictable. Reharmonize, reversing the relationship of inverted and root position triads. As always, begin with the bass.

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Q 14
Q 14
Q 14

A quick hint--or perhaps reminder--as you add the inner voices. Since we are in minor, you must watch out for the augmented second which can be created when a voice moves from scale degree six to scale degree seven. Switching the chord positions as we are doing can also switch chord tones in inner voices, creating the potential for augmented seconds where it did not exist before.

Keep iio6 as it was in the previous example--that is, use the lowered sixth scale degree on beat 2, measure 2--but still avoid the augmented second in connecting to beat 3.

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As shown, an elegant solution is to swap most of the alto and tenor lines, thereby beginning with a close position voicing rather than an open voicing. That enables the tenor to approach the leading tone from above, rather than below, solving the augmented second problem.

And that completes our tour of first inversion triads.

But there's much more to know about part-writing inverted triads--in fact, there's a whole new realm in second-inversion triads. Watch 'Doc Snow space' for a Hub setting up that discussion--it will be coming soon!

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Comments 10 comments

Doc Snow profile image

Doc Snow 3 years ago from Atlanta metropolitan area, GA, USA Author

Thanks for checking out this Hub! Hope you liked it; apparently you read all the way through!

But, any questions? Comments? Suggestions?

In the Hub realm, unlike live acoustic performance, I love to get feedback. Let me know what you think!


david wilson 2 years ago

Great help Doc Snow - loving your series.

A question: in Q13 of this lesson (1st inversions-mediant etc) you identify beat 2 of measure 2 as a diminished vii 1st inversion chord. As there is no 7th degree scale note in the chord can it still be a 7th? And as it is part of the circle of 5ths it looks more like a c# chord (ii diminished). Please help!

Thanks


Doc Snow profile image

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

David, thanks for a great question! And you'll probably like the answer, too: you understand the situation very well, and you are only confused because of a typo. I wrote 'vii' when I should have written 'ii'! (Fixed now, thanks!)

So the chord we're talking about is indeed a C# chord, just as you were thinking--a first-inversion triad, to be precise.

Just to clarify, in classical theory, it's not normally customary to analyze a chord with an absent root. (In jazz theory, it's not unusual at all, for various reasons. But that's another Hub right there.) So, no, without the leading tone, the chord won't be analyzed as vii. (Except, of course, by typo...)

Thanks for the sterling proof-reading, and for sticking with the series! I appreciate your kind words about it very much, and hope you keep enjoying it.


Music Student 20 months ago

Hey Doc Snow, thank you for your series. I make it part of my musicianship discipline to frequent the hub as much as possible. Up until this point in the hub explanations and examples have been very concise. I find myself stumbling in this particular hub when wading through the information. I know that this practice is second nature for you, but for me being a novice I can't seem to organize my process into a methodology to arrive at a correct solution while judging the merits of one approach relative to another. For instance I am cautious in avoiding objectionable movements but can't seem to identify a course of action that would dictate my approach when presented with a soprano line relative to the bass. When placed in root position this process is a lot more forgiving with the soprano voice moving either in parallel imperfect intervals or in contrary motion with the bass. First inversion doesn't award that much clarity, other than moving doubled tones in contrary or oblique motion. And to compound my frustration I noticed a couple of errors in the first example being that the bass on beats 3 and 4 move in parallel octaves with the alto and resolves on an F chord with a missing 3rd. And in example 12, am I wrong but it looks as if the tenor and the alto are moving in parallel 5ths until beat 3, and not in the ideal "perfect-diminished" exemption. I apologize for my nit picking being that I am a fan of the hub but I am at a loss in reconciling the wealth of information you presented in previous entries, where it seems none of my prior assumptions or instincts work in predicting the behavior of the voices. Thank you once again Doc Snow.


Confused Music Student 20 months ago

I just caught that in example 12 the last 5th is diminished between the tenor and alto, but am I wrong about the first 2 5ths in the example as well?


Doc Snow profile image

Doc Snow 20 months ago from Atlanta metropolitan area, GA, USA Author

You mean Question 1. Embarrassingly, you are not wrong--that is indeed a pair of bona fide parallel octaves that I missed somehow. Oh, well, even Corelli missed a few in his timeā€¦

So, excellent catch!

The correction would be to take the alto up to a "D" in unison with the soprano. And yes, that final chord is wrong, too. The tenor should take the "A". That's even *more* embarrassing.

Sorry to let such a shoddy example slip through. I'll have to correct the example when I get some time free (other demands have been keeping me away from expanding on--or correcting!--these Hubs lately.)

(By the way, part of my editing process is to listen to these examples critically, and that's resulted in several corrections. But I've noticed that synth renditions--as you can so conveniently do right out of Finale, which I the notation program I'm using--are much less revealing than actually playing examples on a real piano. Probably the lack of phase differences is part of the reason. Anyway, I'm resolving always to *play* these examples in future. Don't want to confuse future readers, too!)

However--a little to my selfish relief, I must say--you are mistaken about the first two fifths; G-D*b* is also a diminished fifth, breaking up the parallel.

Thanks for really working with these Hubs is such careful detail. I appreciate it; catching the error makes my Hub better, and doing the work so faithfully will pay off for you.


Doc Snow profile image

Doc Snow 20 months ago from Atlanta metropolitan area, GA, USA Author

Weird. I've been investigating this erroneous question, and find a *correct* version in my Finale files for this Hub. It's also a bit better than the fix I mentioned in my initial response.

In this version, the alto line is: A-A-Bb-G (in a unison doubling with tenor)-A. This avoids both the faults 'music student' correctly noted. And, though the notation in the video example shows the incorrect example, the *audio* seems to be the correct version! Certainly, you can (if you've been working on your ear-training!) clearly hear the third in the final tonic triad.

Looks like I spotted the errors back when, but somehow pasted the wrong version into the Hub. Still an embarrassing editorial lapse.

Hope to post the corrected version later today, but we'll see.


Doc Snow profile image

Doc Snow 20 months ago from Atlanta metropolitan area, GA, USA Author

Done. Question 1 is now correct, with a modified discussion of the part-writing issues, and an explanatory note, keying to this part of the comments. As noted, I'm leaving the video notation uncorrected because I don't want to 'disappear' 'music student's' excellent comments, and having some visual reference will make them much easier for future readers to follow. Transparency!

Every error regretted--particularly when confusion is induced and the student's time wasted--and every correction or question appreciated! Hopefully there is at least the pleasure of busting the teacher.

I also want to respond to the larger concern 'music student' expressed above: "[I] can't seem to identify a course of action that would dictate my approach when presented with a soprano line relative to the bass."

I don't know that there is a 'magic bullet' approach to that. Historically, since the Baroque period and the advent of basso continuo, there has been a sort of default in tonal music in which the outer voices have the most impact on the harmonic structure; inner voices, while certainly still important, tend to be regarded as, to some degree, a task of 'filling in'--a bit like coloring a drawing, if you liken the outer voices to the outlines of the drawing.

For practical purposes, it's a useful approach to part-writing because of that range of perceptual importance, and also because there are more part-writing errors that you can commit in bass and soprano--unresolved leading tones and similar fifths and octaves, notably. So it's often helpful to get those voices right first, then 'fill in.' (Playing over those outer voices is a great reality check, too--in a great many cases, errors will stand out that way.)

So that's the work flow that I suggest in these Hubs. But note, too, that it's not inflexible. In particular, as you go you may well find reasons to go back and adjust those first thoughts a bit. (I certainly do that as needed, and I think most of us do.)

So, for example, if you find that the bass you wrote cramps your tenor line, then perhaps the bass should take a lower octave at some point to allow the space the tenor needs. But take time to consider the effects of each change--if possible, by playing and/or singing the results, so you can actually hear what you did, as well as see it. (As much as possible, we want theory to resemble music more than math--even if discussions of this sort tend to emphasize the latter much more.)


Music Student 20 months ago

Thank you very much for taking your time to address my question thoroughly. Each day I grow a little more comfortable with the practice. As always your work and instruction is very appreciated.


Doc Snow profile image

Doc Snow 20 months ago from Atlanta metropolitan area, GA, USA Author

You are most welcome.

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