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

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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:

part-writing-inverted-chords-mediant-submediant-leading-tone-triads

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

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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.)

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.

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.