Saturday, August 31, 2013

The Joy and Mystery of the Subdominant!

This is a follow-up to the last post. The tonic and dominant have clear and obvious functions: the tonic is the point of rest and resolution; the dominant is the point of tension. A lot of music just goes back and forth between the tonic and dominant. But just what is it that the subdominant does? It takes us from the tonic to the dominant; it prepares the dominant; it is the transition from tonic to dominant. Well, that doesn't sound too exciting, does it? But as a matter of fact, the subdominant area is where most of the really interesting stuff happens and where the most exotic harmonies are found.

The subdominant area actually has two functions. Apart from preparing the dominant it is typically found in the coda of a sonata or other piece. After a great deal of fuss and energy spent going from the tonic to the dominant, a lot of pieces have a section near the end where the tension is relaxed by having a passage in the subdominant.

But the main subdominant function is to get us to the dominant in interesting ways. The tonic is a fixed, known quantity and so is the dominant. But the subdominant has proven to be a wonderfully flexible area that has attracted much of the harmonic ingenuity composers have come up with. The subdominant function or area can be the subdominant chord or the supertonic chord as they share two notes. But it can also be something more exotic, something that goes to the dominant in a more intense way. Two of the most interesting harmonies that serve this function are the Neapolitan sixth and the augmented sixth chords.

The Neapolitan sixth chord is a major chord built on the flattened supertonic. In harmonic analysis it is written as either bII6 or N6. In C major it would be a D flat chord. It is usually found in first inversion, which is why it is called a sixth chord. In C it would be spelled F A flat D flat. How is this a subdominant function? For one thing, the bass note is F, which is the subdominant. Also, it has the subdominant function as it characteristically moves to the dominant: it is a "pre-dominant" harmony. The Neapolitan sixth is most often found in the minor mode and it gives a momentary "Phrygian" feel to the harmony because of the flat second degree. What makes it different is that the flat second degree, rather than resolving down to the tonic, as it would if it were truly Phrygian, it goes instead to the leading tone (part of the dominant chord) and then to the tonic. Here is how it looks in D minor, first how it moves to the dominant and then in a full cadence.


The effect of the Neapolitan is to greatly intensify a cadence. Here is how it sounds in an example from Mendelssohn. This is from the Songs Without Words, op 102, no 4. The key is G minor, so the Neapolitan Sixth is spelled C E flat A flat. It occurs in the second half of the fifth measure, at the 17 second mark in this clip:


Here is the score:


The progression is quite typical of the Neapolitan: it goes to the dominant which cadences to the tonic. Bach, of course, created a much more complex and interesting context for the Neapolitan, using it in a passage that first suggests a deceptive cadence, then moves to the Neapolitan and finally a V to I, but not a perfect authentic cadence as both chords are in inversion. Pretty fancy!


I quoted this in a whole post about the deceptive cadence.

There is a lot more interesting stuff that can go on in the subdominant area, but I will save it for another post. What I am calling the "subdominant area" is that whole group of chords, including the subdominant, the supertonic and the Neapolitan, that all serve a subdominant function and lead to the dominant.

8 comments:

Virgil T. Morant said...

I read an article not long ago by authors who had surveyed a massive amount of rock and roll music and noted that the plagal cadence was very widely and often used. Another use of the subdominant that, while it has a longer standing history than rock and roll, surely is done to notably different effect when it's coming from a rock band than when it's coming from a chamber orchestra.

Bryan Townsend said...

There is a lot of research still to be done on rock and roll. The Beatles are particularly known for having used a "double plagal cadence" or Bb to F to C. And the plagal cadence has been used by Debussy and others in modern music. But the plagal cadence is still a bit of an oddity...

Rickard Dahl said...

The dominant/subdominant split is an interesting way to view the chord functions in the western diatonic modes. I didn't think about it earlier but the same split of dominant/subdominant functionality occurs the same way (same degrees are dominant, same are subdominant) in all the western diatonic modes. For example the 2nd degree chord of all the church modes share two tones with the subdominant chord (fourth degree). In "Modal Musical Composition" Stephen M. Cormier writes that the dominant and subdominant areas of a mode should be in balance to maintain stability. As an ionian example he mentions that the 4th degree can become a threat to the tonic if given too much prominence. Is the subdominant/dominant balance something often considered in traditional tonal harmony?

Anyways, about voice leading: Is good voice leading typically seen as a result of movement between chord tones or do non-chord tones play a role? It might sound like an odd question but maybe an example would be good. So lets say we have a A minor chord going to an E minor chord and lets say there is a case of the A going to E for some reason, can it be considered smooth the A moves by the way of using passing tones either up or down, lets say A, G, F, E? Or is it considered unsmooth by default because the chord tones go from A to E (maybe not the biggest jump but still)?

Bryan Townsend said...

Those are a couple of really meaty questions!! I might take this up in a blog post. But for now, just a brief response. No, a balance between subdominant and dominant is NOT considered good in traditional harmony. The reason is this: as I was saying in the post, the tonic has a clear and important function. It is the resolution. The dominant also has a clear and important function: it is the opposite pole, the point of tension. The role of the subdominant and related chords is to get us to the dominant, to prepare the dominant. It is the area where the most ingenuity can be exercised, which makes it interesting. But a piece that tried to balance the subdominant and dominant areas would be in danger of being too bland and dull.

If you look at a lot of Bach chorales and similar examples of voice-leading, you will see that the upper voices, especially the middle ones, tend to move by step. The melody might have more leaps. But the bass voice, while it can move by step, just as often moves by skip. The characteristic movement of the bass is from V to I, both in root position. This is movement by 4th or 5th.

Rickard Dahl said...

I see. I don't know remember what he said about it in detail, maybe I misunderstood what he meant. Either way you're probably right, could possibly sound dull or bland, which I think might be the case of most music approached from a theoretical aspect rather than following what is aesthetically pleasing. I don't really follow theory books so much anyways, I see them more as a collection of ideas of how things can (but don't have to) be done.

Bryan Townsend said...

Exactly!! I think composers are usually on the lookout for a good idea they can steal.

Maury said...

I think you had the key to the comment about the dominant and subdominant balance but then ignored it, namely that one or the other can become a threat to the mode. This is the context in MMC of that remark as I understand it. In the case of Mixolydian for example the subdominant is a major triad while the dominant is minor. The subdominant because of its tonal strength has to be balanced effectively both with the minor dominant and also with methods that negate the tendency for the Mixolydian subdominant to become the (Ionian) tonic. It should be remembered that if modality is to be observed even with Ionian and Aeolian then presumably the usual tonal methods and formulas won't be used in the same way, e.g. harmonic and melodic minor scales, diminished seventh chords. What the author emphasizes and I think we all know too is that the diatonic modes are harmonically weaker than the artificial scales we call major and minor. Therefore more attention has to be paid to maintaining a mode's integrity.

Bryan Townsend said...

Thanks for bringing this out. I don't know the Cormier book and am less familiar with purely modal composition than I would like to be, so maybe I will pick it up. Yes, I understand what you are saying: all those things, like the alterations to to the minor scales to create leading tones, i.e. a major dominant chord, are often unavailable in modal composition. So you have to be careful that you don't lose the sense of where the tonic really is. I suspect this is an artifact of the fact that we have had hundreds of years of tonal music affecting our ears!