Musical Form, Part 2

Yesterday I put up a post about musical form that mostly talked about how melody can be used to structure a piece. This merely scratched the surface, of course as there are many, many ways that I didn't mention such as the way a melody can be transformed in the course of a piece so that it not only provides a unifying element, but also helps to push the piece forward. The 19th century particularly explored this idea.

But I'm not going to talk about melody today, instead, I'm going to merely scratch the surface of how harmony is used in musical form. Everyone knows what you mean when you use the word melody but harmony is a word with complex meanings. Like 'melody', it comes from the ancient Greek: ἁρμονία (harmonía) which meant joining or fitting together. We use it in a very general way to mean the vertical aspect of music: everything relating to notes sounding together. But there are more specific meanings as well. If you take a course in university in the music department called "harmony" it is going to be about the system of tonal 'grammar' that was used in Western music between 1600 and 1900. This system looked at different chords as being functional, i.e. they were part of a web of tension and release that was used to structure the flow of music. For example, a lot of recent music is based on drones, long-held notes and chords, and for that reason is not 'harmony' in the strict sense as there is no harmonic function. Here is a recent song by Paul Simon that is almost completely without harmonic function. The verses are all one unchanging riff and, therefore, harmony. The contrasting chorus mainly contrasts by dropping the riff and there is a hint, no more, of a harmonic change. But it is minimal. A theorist would say that moving to neighboring harmonies and then back is actually just extending the tonic.

To see how harmony works you could do no better than to look at some music by J. S. Bach who is admired as being probably the greatest master of harmony. Here is a very simple piece by him, the first minuet from the Partita No. 3 for solo violin. Just click to enlarge.

This piece is in E major, which means, in terms of functional harmony, that it is going to begin with an E major harmony and end with one. Later on Beethoven created quite a stir when he began pieces with something other than the tonic--usually the dominant. Ah yes, 'tonic'. The tonic chord or harmony is the one built on the key note, in this case E. By "built on" I am referring to how chords are constructed. You build a chord by taking every other note in the scale. For example, the E major scale goes E, F#, G#, A, B, C#, D# and E. A tonic harmony, starting with E, would be E, G# and B. Every other note. Simple. Here is the E major scale and three important harmonies derived from it: the tonic, on the keynote, the subdominant, on the 4th note, A, and the dominant, on the 5th note, B:

The basic layout of this minuet and virtually every other dance movement from the Baroque era is Tonic -- Dominant -- Tonic. But there are thousands of ways of going from tonic to dominant and back! One more thing before we go to the piece: as you will realize if you look back at that scale, you can build a chord on every note of the scale. The three chords I picked out and labelled, tonic, subdominant and dominant, are the main members of little families of chords. I say that because every chord has related chords that it shares notes with. The closest relationship is when two notes are shared. For example, the tonic, E, G# and B, shares two notes with the mediant: G#, B and D#. These two chords are related. Similarly, the subdominant, A, C# and E, shares two notes with the submediant, C#, E and G#. Mediant and submediant are labels for other notes of the scale. You want the whole list? OK:

1. tonic
2. supertonic
3. mediant
4. subdominant
5. dominant
6. submediant
7. leading tone

All right, now let's look at the beginning of the minuet. Click to enlarge:

The first two measures are just as Bach wrote them. The next two are my simplification of the first two showing just the harmonies. It starts with the tonic, of course, and the next chord is the dominant. Actually, just part of the dominant, without the lowest note. Then we get that lowest note, B, but over it is a G# so what that harmony actually is, is the mediant. Then the next measure is the submediant. Yes, lots of stuff in just a couple of measures. I won't go through every measure because I just want to give you a taste of how harmony works. But to round things off, let's look at the ending. Click to enlarge:

The supertonic is part of the subdominant 'family' as it shares two notes and the mediant is part of the tonic 'family'. So the basic harmony of the last two measures is subdominant, tonic, dominant, tonic. Bach uses other family members to make it more interesting and smooth the movement of the voices. Now let's listen to the whole piece. Here is Arthur Grumiaux playing both minuets (they usually come in pairs).

The minuet we have been looking at is less than a minute of music without the repeats! But in that minute Bach has a wide range of harmonies, all carefully calibrated to move us toward the dominant, which is where the first half ends, and then move us back to the tonic. This is one way of using harmony to structure musical form. From about 1600 to 1900, this was the predominant way of putting a piece of music together.

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What is Musical Form?

Over a year ago I wrote a post on Form in Music that inspired some brilliant comments about the role of rhythm in jazz. It also inspired an email from a friend who said he didn't understand any of it! That post was intended to be the first of several on musical form, but I didn't follow up. My learned anonymous commentor made some excellent points and it is well worth going back and reading the whole post and the comments.

What I want to do here is restart the discussion by looking at form from an entirely different angle. In the previous post I talked about the basic structure of songs as that is something many people are familiar with. Today I want to take a different tack. There are three fundamental aspects of music: melody, harmony and rhythm. Every piece of music is a structure in which any one, two or all three are present--even John Cage's 4'33 which has a structure consisting only of rhythm, i.e. time. The form of a piece of music, that is, the articulation of it in time, is created by using any one, two, or all three of these aspects. That is so abstract that you are probably either scratching your head or rolling your eyes! Let me make it more concrete.

Let us imagine a simple musical context: a drumming circle. In Montréal when I lived there a group of drummers used to meet on Sunday afternoons in the park and drum together. Someone would start a simple beat then others would add various subdivisions and syncopations of the beat until a satisfactorily dense texture was created. This might go on until everyone was tired of it and then stop. Or, if it started to flag, someone might try and start an entirely new pulse, thereby launching a new section. If this just goes on until it peters out, then you have the form A (the first beat) followed by B (the second beat). If everyone then went back to the first beat then the form would be ABA. This is the very simplest musical form. Do something, then do something else, and if you are clever, then you return to the first thing again.

But the very first kinds of written down music in the West are both more complex than this but also even simpler. One of the earliest kinds of music in the West consisted of singing the psalms. Singing made the text a more sacred utterance. One person would first sing a few notes to establish the pitch, this is an "intonation", then the rest join in on a "reciting tone", just a repeated note. This reciting tone can go on as long as needed for the text. It can be punctuated if needed to indicate a division in the text. This punctuation was called a "fluxus". Then you return to the reciting tone. To end, there is another few notes that fall in pitch, called a "cadence" which means falling or "cadere" in Latin. Don't mix this up with the cadence in common practice harmony, which refers to a structure of two or more harmonies.

I suppose that what I have just described is very roughly ABA, but it is really a kind of musical prose, where the form is very loose and while originally there is just enough melody to encourage people to sing a text, the tendency over time is to add more and more decoration. Here is an example of this kind of psalm setting, one of the early favorite texts "Justus ut palma" from Psalm 91:

This kind of form is so loose that it is almost impossible to describe. A lot of music composition consists in giving form to what was originally formless. So a meandering melody like this, only organized in terms of a reciting tone and a final tone, composers are going to replace with a melody with a clearer structure. I'm not going to work my way through music history here, instead, I'm just going to jump to a different kind of melody that is very organized. Here is the original subject from the Art of Fugue that Bach will transform in various ways:

This subject is both very simple and highly organized. It is the very opposite of the loose, meandering kind of melody found in Gregorian Chant. The first two measures state the tonic harmony, D minor, as simply as possible. Then the next measure states the dominant harmony. The last measure allows for ambiguity as it can be harmonized in different ways, but it returns to the tonic at the beginning of measure five. Notice that there are two measures of arpeggiation followed by two measures of a scale. Notice also that the rhythm speeds up over the four measures. This extremely simple, highly organized theme will serve as the material with which Bach will construct a whole series of fugues, fourteen in all, and four canons. Here is a performance of the first fugue, which uses the theme exactly as I have given it above:

You will notice that as each voice enters, it does so with the same theme. This is one way of structuring a piece of music with melody. Though, of course, as soon as you have more than one voice, then the harmonic structure becomes hugely important as well. But let's leave that aside for the moment and just note how this simple melody ties the whole piece together. You can look at the structure of fugues in various ways, but the most salient aspect is that theme: it is what generates the structure, that is, the form.

In a more mechanical way, the contemporary composer Steve Reich has done something very similar: use a single theme to generate the structure of a piece. He does it by creating a short theme for piano and then, with two pianos playing that theme together, one "slides" ahead rhythmically bit by bit, a process he calls "phasing". Here is what that sounds like:

UPDATE: Here is a complete version of the piece:

In between the basic subdivisions, i.e. when the notes don't "line up", there is considerable rhythmic tension that is released when the two pianos slip back into alignment,  though, a different alignment! The piece ends when the whole set of alignments has been traversed and the two pianos are back in the original relationship.

What is interesting about this is that he uses only a simple rhythmic device to generate the whole piece from that original theme.

There is a lot more to say about how musical form can be created, but I'll save it for next time!

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Musical Genres and Musical Forms

These are fascinating and revealing topics, but ones that are not susceptible to analysis leading to a clear conclusion. But I won't let that stop me! Please accept these remarks as informal musings. Hey, it's a blog!

Here is the Wikipedia article on musical genres. Musical forms are a little clearer. Here is the Wikipedia article. For the sake of simplicity, I'm going to go with these definitions: musical forms are those structural aspects that we usually parse out with letters. A piece in ABA form has an opening idea or theme, then it goes to a different one, then returns to the first one. Musical genres, on the other hand, are described in more concrete ways as the feeling of a specific genre, such as a waltz, is defined by the meter (3/4) and tempo. A concerto, which may or may not use the classical forms typical of a concerto, is defined by the opposition or contrast between a solo instrument such as the violin, and a larger body of instruments, such as an orchestra. There are innumerable genres and sub-genres and composers may blend them together to achieve unique effects. Chopin's Nocturne in G minor has been described as combining a mazurka rhythm with the nocturne and also using religioso passages.

Here is an easy way to distinguish form from genre. The baroque suite was comprised of a number of different dances sometimes preceded by a prelude. The form of these dances was usually the same: AABB or two distinct sections, each repeated. Harmonically the first section begins with tonic harmony and the second section ends with tonic harmony making for a tidy conclusion. In a major key, the first section usually ends with dominant harmony and the second section works its way back to the tonic. In a minor key, the first section often modulates to the relative major--the major key that has the same number of sharps or flats as the minor tonic. So if the form is basically the same for all these dances, what distinguishes one from the other? The answer is genre. Let's look at Bach's Cello Suite No. 1 for an example. Here is the courante, which is in two sections, each repeated and the first section ends with a cadence on the dominant. It is also in 3/4 meter.

Immediately following this is the sarabande which is in the same key, G major, the same meter, 3/4, also in two sections of which the first cadences on the dominant.

So the two movements share the same form. Why do they sound so different? The answer is that a courante is a different genre than a sarabande. The courante, a dance that divides into two sub-genres, is quicker than a sarabande. The two types are the French and the Italian. This is an Italian type that is the quicker of the two and is rhythmically lively with running passages. The sarabande, a Spanish dance, is much slower and, in contrast to the courante, stresses the second beat. Immediately after the sarabande are a pair of dances with, again, the same form: two sections, the first ending on the dominant and also in 3/4. These are the two minuets. The tempo is slower than the courante and the rhythms are simpler and more graceful. The first minuet, AABB with the first section ending on the dominant, is followed by the second minuet, which is in the parallel minor--the minor key with the same tonic as the major of the first minuet (G major, then G minor). Then, the first minuet returns, but this time without the repeats.
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All three dances are roughly in the same form with the same key, same modulations, same sectional layout and same time signature. But they sound so different from one another that they can immediately follow one another in the suite without the listener becoming bored. The reason is that they are of very different genres. The dance genres are responsible for the different tempos and the internal rhythmic structure.

One of the things that was largely lost in the move towards musical modernism was this repertoire of genres that composers could make use of. They are still available, of course, but composers have usually avoided them in the last hundred years.

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Beginnings

I wrote a post about endings, so I should write one about beginnings. How a piece starts is important, because in the world of digital media, it is all too easy to turn it off and go on to something else. This isn't true in the concert hall, but we probably listen to more recorded than live music these days. A while back I did a post called "The One-Minute Test" in which I listened to the openings of several different pieces. The test was, if something didn't grab me in the first minute, that's it.

Sometimes a composer comes up with a brilliant opening:

That's one of the best. Or this:

Of course, that was a bit of a miscalculation, because if you start with something that dramatic, it is hard to follow. Better to start with something ambiguous and there are few beginnings more ambiguous than this one:

Sometimes it is best to just jump right in:

What about pop musicians? True, they are working within simpler forms, but on the other hand, they are in most danger of the listener switching off. Here is an interesting pop intro:

But the absolute best pop intro I have ever heard is this one:

Unfortunately, like the Richard Strauss, the song doesn't quite live up to the intro. Here is a famously good song beginning:

In fact, the Beatles were masters of how to begin a song (sometimes with a little help from their friends, especially George Martin). He suggested starting this one with the chorus:

That one did pretty well... I just read that for a while during the heights of Beatlemania, 60% of ALL singles sold in the US were by the Beatles, who at the time had the #1, #2, #3, #4 and #5 top singles. The next one is an exceptional intro, even for them. Just listen to the chords John is playing--pretty much as chromatic and ambiguous as the opening of the Mozart quartet above:

Lately a lot of the pop songs I have heard have all fallen into the rut of having four or eight bars of treading water before much actually happens:

Sure, you can start with just eight bars of the accompaniment, but it's not exactly creative now is it? Here's another one:

I think that there should be something either intriguing or attention-getting up front. Like this:

Or you could just start with something magnificent:

Or riveting:

Well, that really wasn't fair, was it?

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Form in Music

This is such a huge topic, much too big for even a series of blog posts, that all I will do is just give a tiny introduction. We are all probably familiar with some of the basic ideas of musical form. The most familiar we find in popular song. Here is a song in the very simple form of a verse ending with a refrain. The verse here consists of two two-bar phrases that return with new words each time. The refrain is another pair of two-bar phrases with different music and with two voices in harmony. After a two-bar chordal introduction and two bars where the sitar introduces the melody, the song simply alternates between verse and refrain.

A slightly more complex form is a verse-chorus arrangement where one section of music returns with new words each time--the verse--while a contrasting section returns with the same words. This section, called the chorus because it usually has backing vocals (but not in the case of the example below), usually has the same words each time and typically contains the title of the song. This is from the movie Help:

Another contrasting section, called a 'bridge' or 'middle-eight' can appear as well. Here is where strong harmonic contrast can appear. In the next song, the bridge starts with the words "Life is very short...". The verse is the beginning music and ends with the repeated refrain "We can work it out".

In instrumental music you don't have the option of repeating music with different words so other devices become important. Common to both vocal and instrumental music are the basic ideas of repetition and contrast. Some music is repeated and in between different music is used for contrast. The contrast can be melodic, harmonic and rhythmic. Notice the shift into triplets for a waltz feel in the bridge of "We Can Work It Out". In larger instrumental forms harmony becomes more and more a structural device that can be used both for contrast and unity over larger stretches of time. Starting in one key, then modulating to a different key or keys is how you can construct a piece several minutes long. That's something for another post!

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