Basic Harmony - Illustration: Puff

.
As I was writing the previous post, I saw how difficult it was to explain matters of notation and terminology in addition to the elements of harmony purely by visual means.  (It's amazing that this was how it was done, for the most part, for many, many years, in many many places.  As a result, the few musicians who survived this training were more mathematicians than musicians.  The rest of them were taught at the keyboard, or in other words, using musical examples at every step.)

What I'm going to do is to illustrate as many of the basic ideas of harmony I have already begun to explain using this one example of Puff, the Magic Dragon.

First of all, here's (1) the basic tune, with (2) the chords below it, and (3) a simple bass line under everything else.  Luckily, it fits on a single page.  For this first little movie clip, I spent most of the time implementing the "bouncing ball" method, to keep your eye on the point of the score that's sounding.  Already, there is a compromise: I have to choose a key, that is, a set of notes that we are going to use, and these sets are named for the starting note of the scale, in this case C.  In C major, the chords used are I (C major chord), II (D minor chord), III (E minor chord), IV (F major chord), V (G major chord), VI (A minor chord), and VII (B diminished chord, which doesn't get used in this song).  All the chords (except VII) are used in this song, so I haven't bothered to give you a picture showing them all.  Here it is.  (Reduce the volume of your speakers, just in case):

(As you see, moving the arrow along is so much work that I gave up after the first few lines.)

I'm going to do two slight changes immediately, because it sounds so dull:
First, I'm going to change the II chord that appears here to the #II chord, which means that it is really a chord imported from another key (in this case, chord V of G major).  It is very common to "travel to" other keys in the course of a piece, and this song briefly visits G major just here, and returns right away to C.
Secondly, I'm going to change the notes of the bass line to introduce a little rhythmic variation, since we're not going to have any percussion playing along.  (I'm going to hold back from "strumming" the chords, until I have them the way I want them.)  There is a little hiccup in the bass right at the second measure, and I guess I'll remove that presently.  Anyway, here it is:


(It's now a clarinet playing the melody, but I forgot to indicate that in the score.)

The next step is important.  Many of my friends to whom I've explained most of this took a little while to get this into their heads.

One of the traditional values of harmony is to make the separate lines of the chords as smooth as possible, in other words, to have as few skips as possible, and even those as small as possible.  This comes from the aspect of harmony that is called counterpoint--the skill of writing chords so that each part is a melody that is independent and pleasing in its own right.  We use the word 'part' here imagining that the chord is actually sounded by three people (or three instruments) each playing one of the notes.  One instrument plays (or is imagined to play) the top note in each chord, the next instrument plays the middle note, and a third instrument plays the lowest note.

The first two chords are I and III, and at present we have the three parts of the harmony all skipping up two notes from one chord to the next.  So what we have is

1 - 3 - 5

3 - 5 - 7.

When you read this, each line is one chord, and going down the first column you have the notes "sung" by the lowest part, down the second column the middle part, and along the third column, the highest part.

With the understanding that 1 and 8 are essentially the same note (octaves), and 2 and 9 are 'identical', and so forth, an alternative is

3 - 5 - 8

3 - 5 - 7,

making use of the fact that 8 is just as good as 1.  This is so smooth that only one of the three parts moves at all!  (We have to build in an occasional skip just to make sure that the parts don't wander higher and higher, or lower and lower, out of their voice ranges entirely.)

Let's include the third and fourth chords in our study of smooth parts.  The first four chords are I, III, IV, I.  The smoothest choices I can think of are below.  Another important classical principle is to avoid parallel octaves and fifths, that is if the 'interval' between two parts in one chord are either 8 (octave) or 5 (fifth), we want to avoid the same interval in the very next chord.  (Of course, a guitar playing so-called "power chords" blithely violate this principle, but good counterpoint is not high on the list of considerations in popular music, and that's appropriate. Sometimes, there is reasonably good counterpoint in pop/Rock; e.g. "You're going to lose that girl" by the Beatles.)  This has an impact on what we do between III and IV.

3 - 5 - 8

3 - 5 - 7

1 - 4 - 6

1 - 3 - 5.

Well, we have unavoidable 'drifted' downwards; but in the next few chords we can drift back up again.  But the important thing is that, even when we rearrange the notes of our triads to obtain smoothness, we use the same three notes.

The next clips shows the parts completed smoothly all the way to the end.  To emphasize how smooth the parts are, we've used "choir Ahs" as the sound for the chords, while a clarinet is playing the melody.  I also couldn't resist adding what the software calls 'swing' to the music, where the rhythm is jazzed up slightly.  With this effect, we almost don't need to make the chords repeat, that is, we don't need a strumming effect.