Thursday, August 15, 2013

Harmonic Secrets

To most people, harmony is a mysterious thing. Even to some composers! Just to set the mood, here is a piece intended to be harmonically mysterious, Les Baricades Mistérieuses by François Couperin le grande played by Scott Ross:

Just to give you an idea of the extraordinary reactions this piece can provoke, here is a website entirely devoted to the piece and its influence. That is just for interest, I don't advocate any of the material or claims on that website, which get rather too ephemeral. But it would be interesting to have a look at the music. It's only two pages, so I'll put up the whole thing:

The time signature nowadays would be written 2/2 or the half-circle with a slash that is often called "cut time" but that is really an archaic medieval modal time signature meaning tempus imperfectus or duple time. The key is B flat. It sounds almost as if it starts in the middle, which is a nice effect. Composers can go one of two ways to avoid the opening of a piece sounding too standard: they can compose an introduction, often in a slower tempo, or they can, as novelists sometimes do, give the effect of coming in in the middle of the story, which Couperin chooses.

The harmonic effect here is one that comes from counterpoint, often called "voice-leading". You might remember from my post of a few days ago I cited a book that I called a "bible of music theory", Aldwell and Schachter's Harmony and Voice-Leading? Well, it is pieces like the Couperin that are responsible for why the phrase "voice-leading" is in the title. Harmony actually, both historically and currently, comes from counterpoint, from voice-leading. The phrase "voice-leading", by the way, just refers to the way the voices move from harmony to harmony (from one chord to the next). But harmony itself is built from different voices. One of the problems with harmony nowadays is that a lot of composers and listeners have forgotten this. In the strummed chord progressions of popular music, the contrapuntal nature of harmony is nearly extinguished.

But the whole effect of Couperin's Les Baricades Mistérieuses depends on the voice-leading. The kind of texture he is creating uses two different kinds of effects. In one, a voice is held over from a previous harmony and resolves down into the next harmony after the bass note is sounded. There is an example in the very beginning where the top voice sounds a D, the third of the tonic B flat, and this is held over the sounding of the F in the bass, the root of the dominant F chord. It then resolves down by step to the C, the fifth of the dominant. In modern harmony courses, this is called a suspension, specifically a 6-5 because those are the intervals over the new bass note. In French baroque music this is often indicated with an ornamental sign and is called a coulé. Also at the beginning, but in the alto voice, is another suspension, from B flat to A, a 4-3 suspension in modern terms. Then, going into the next measure, after the repeat sign, the A now resolves up into the B flat when the harmony returns to the tonic. For some odd reason, modern harmony books, even Aldwell and Schachter, focus almost entirely on the suspension that resolves down. But Couperin makes considerable use of the reverse: a dissonance that resolves up, usually the leading tone resolving to the tonic, what we might call a 7-8 resolution. Theorists seem to want to regard this as an anomaly, but Baroque composers seem quite comfortable with it. The term for this kind of ornament is port de voix or "carry the voice". In the next measure we see a 9-8 suspension, a 4-3, and going into the next measure again, a 7-6.

The lovely and mysterious effect that Couperin creates here is through the inventive and layered use of suspensions of both kinds, the standard one that resolves down and the less-common one that resolves up. I say "layered" because he often has two different suspensions resolving at different times in the same measure. It creates a kind of filigree of harmony. All this depends on a contrapuntal device however! This piece is not a simple succession of chords, it is a harmonic web of different voices that resolve according to long-standing rules of counterpoint. The most important: dissonances resolve by step, whether up or down. Probably the reason for this is that when the note resolves by step, we know exactly where it came from, i.e. which voice it is. Bach sometimes breaks this rule by resolving a leading tone down an octave, for example, but he always does it in a context where it is clear what note is being resolved where.

One final comment, another kind of layer here is that while one voice is resolving by being delayed by an eighth-note, another might be resolving after a quarter-note delay. There are different levels of layers!

Let's listen to that again, this time trying to hear all the suspensions. Here is a version on piano played bCziffra György:


Rickard said...

Harmony is quite mysterious indeed. There are many things I don't really understand and some that I prefer not to think about (avoiding to learn too much theory, I don't think overthinking things instead of following what sounds good would be so helpful right now). One thing I've been wondering about is "why 4-part harmony?". It seems like 4-part harmony is something usually desired but I don't know why. Things sound perfectly fine with just 3 parts sometimes or even just 2 parts. Another thing is the concept of passing tones and neighbouring tones. I prefer not to think about these and it goes pretty well anyways. Another thing (would be useful to know) is how to know what belongs to a chord and what doesn't. Obviously, a block chord or arpeggio says alot but what if it's more vague, maybe a web of voices, maybe with 6ths, 7ths, 9ths etc. which could be interpreted as part of a chord. Modulation is another thing I haven't gotten a good understanding of yet. I suppose that it can be achieved in countless ways.

Rickard said...

Oh, another thing: cadences. In analyses of pieces it seems like composers typically use cadences every x bars but I find it somewhat mysterious too. What counts as a cadence (are full chords really required for example)? Are cadences needed so often, so regularly? And so on.

Nathan Shirley said...

AKA Georges Cziffra.

Bryan Townsend said...

Some very good questions there! Yes, a lot of performers (and perhaps composers) talk about how "analysis is paralysis". You can certainly over-think things. As Glenn Gould said once, certain questions are "centipedal". He tells the story of the centipede who was standing around, minding his own business when someone asked him, "when you go to walk, which foot do you start with?" This question so perplexed him that he couldn't move and ultimately fell over into the ditch and died!

But on the other hand, all the things you mention are actually things that every music student learns so I don't think by learning them you would be in any danger of "over-thinking".

Why 4-part harmony? Harmony actually started out, back in Notre Dame in Paris in the 12th century, in two parts. Look up "organum" for some examples. This very soon became three part harmony as that added a lot of substance.

Three parts were typical for a long time as it enabled you to sound the root, third and fifth of a triad, which you couldn't do with two part harmony.

But as the very concept of harmony developed, there arose the idea of four parts because with four parts you could have the root, third, fifth and seventh. That seventh became used more and more and in fact, became very important in creating full cadences.

Passing and neighboring tones are very important. If you sit down to do a harmonic analysis of a piece of music you will quickly discover that some notes don't quite fit! I. e. they are not part of the harmony. Passing notes are ones that move between a chord tone to another chord tone, but pass through a non-chord tone on the way. They are present in virtually every piece of music! Neighboring tones are quite similar as they are next to and resolve to a chord tone. Yet another kind of non-chord tone is the escape tone.

Modulation is something I will save for a whole post, and thanks for the suggestion!

Cadences typically occur at the end of phrases and phrases are typically four or eight measures depending on the tempo and note-values. Cadences give the music structure and organization. Music without structure or organization is usually very bad music! Not to mention very hard to listen to. The problem for modernist composers was largely how to structure music without cadences. Some succeeded, some didn't...

Yes, in Hungarian the family name comes first.

Rickard said...

Ah, I see, 4-part to include the 7th. Yes I realise passing tones, neighboring tones are important but what I was trying to say is that I avoid thinking about them specifically. I try to find things that sound good and suiting and indeed lots of passing notes etc. arise. I don't think so much about cadences either but they happen when I compose (although maybe in just two or three parts if that counts (it seems like cadences can be harmonic, melodic and/or rhythmic (according to Wikipedia))).

Bryan Townsend said...

The wealthiest musician in history, according to all accounts, composes completely by intuition and doesn't even read music! (That's Paul McCartney) So if you choose to ignore everything about passing notes and neighbor tones, this is perfectly ok. The only thing that really counts is the final result.

But if you ever feel that you just don't know how to structure a piece, especially a longer piece, then perhaps some study of the role of the cadence might help.

Rickard said...

One thing I've thought about but forgot to mention about 4-part harmony: I earlier thought that 4-part was desired to include the octave (doubling) because it's after all the first interval in the harmonic series (and the chords will also sound fuller). Maybe it in fact is one of the reasons it's desired.

Anyways, what I was trying to previously say is that maybe overlearning theory probably isn't a very befenitial way to learn to compose. Maybe a better approach is to learn (some) basic theory, compose some to get a better practical understanding of how things work, learn some more theory if desired, compose more, learn more theory and so on. This ofc while learning to play an instrument, improvising & doing ear training.

I also get the feeling that harmony has lots of rules but also that they can easily be broken without making things sound bad (due to the harmony at least). Besides most harmony books & courses etc. seem to be focus on only tonal (major/minor) harmony but if going outside (even to the close relatives: the Western church modes) many rules don't apply.

Bryan Townsend said...

Sure, in 4-part texture you can double the octave. It is also common to double the third. Doubling the 5th not recommended. But be careful: the basic principle is for the voices to be independent. Doubling the octave reduces this. So do parallel fifths, which is why they are forbidden.

Neither learning a lot of theory nor avoiding it entirely is any guarantee! But you might look into the kind of training that the composers you admire went through. If everyone you admire studied a lot of counterpoint, for example, that might say something!

They are often called "rules", but I think that they are really principles. The thing is to understand the reason for the rule or principle. Also remember that theory books are written by non-creative people usually!

Unknown said...

The other thing to think about with four voiced harmony is (as opposed to two and three) is the ability to voice the harmony across the entire range of pitches i.e. you get:

high (soprano/violin)
middle high (alto/viola)
middle low (tenor/cello)
low (bass/double bass)

With two or three voices you have can't effectively balance the voicing across all the registers and I reckon this is probably the main reason convention settled upon four voices.

Bryan Townsend said...

Very likely! Before the Baroque, when there was a real sorting out of ranges with the polarization of treble (melody) and bass, the separate voices of counterpoint tended to wind around one another indiscriminately.

Rickard said...

Another thing I wonder: I guess most composers (at least in the common practice) studied counterpoint and good voice leading was desired, but how come that in many cases (after the baroque at least although examples could be taken from baroque too) the music doesn't sound so contrapuntal (for example Bach's sounds very contrapuntal, Mozart's not so much for the most part)? Did composers intentionally avoid making different parts sound independent or is the counterpoint just more hidden and maybe more unmelodic? I know it's a pretty wierd question.

Bryan Townsend said...

I think it is safe to say that all composers, at least the ones we have heard of, up until the 20th century, studied counterpoint. If you look at Mozart's music, even where he is not writing fugal textures, I think you will see good voice-leading being practiced: no parallel fifths, sevenths resolving down, leading tones resolving up and no doubling of leading tones. What tends to conceal this in the Classical period and later is the figuration. You can have elaborate keyboard arpeggiation, as just one example, that scatters the voice-leading so that you might not see what is going on unless you collapse the arpeggiations.

If you have a look at Brahms, I think you will find a lot of counterpoint. Also in Chopin, for whom Bach was a big influence.

Actually, quite a good question!

Rickard said...

I see. A more specific thing I wonder: If you have a progression from one chord to a nearby chord a semitone or whole tone away, for instance from a C major chord to D minor chord, can voice leading be smooth or is it considered unsmooth by default?

Bryan Townsend said...

This kind of progression is uncommon for a couple of reasons. First, movement by step risks parallel fifths and secondly, harmonically it is weak. Traditionally movement of the root by fourth or fifth or even third was considered stronger. If you do want to move from C to D minor, it is best if one of the chords is not in root position. For example, move to a D minor chord where the F is in the bass.

You should pick up a copy of Harmony and Voice-Leading by Aldwell and Schachter and work through it. I'll bet you would find it fascinating!