LET'S DEVELOP THE idea of tense melody notes a bit further from article 7. Remember, any note outside of R 3 5 or 7 is tense by my definition, so you can begin to feel the levels of tension that your choice of chord against a particular melody line brings. Remember, there is always a choice of chords, and as you go on the choice becomes mouth-wateringly large!
Here's a simple melody, which we can try and harmonise a few different ways. Play the melody and sing it a few times so you get used to the feel of it:

If it was your task to put chords to that how would you go about it? Before you stumble around trying to pick chords out of the air, you should ask yourself a few questions about what the melody tells you:
1 What key is the melody - from the key signature this indicates G major - E minor is also possible but we haven't discussed minor keys in these articles yet.
2 The melody is diatonic.
3 As this melody ends on the tonic note, there is a fair chance it will end on the tonic chord, if we are considering this short phrase to be an ending.
With just these conclusions we could start to produce our topline and chords like this:

That's all very well, but it doesn't produce answers for the melody notes before the final chord. We need to start asking questions again.
4 Does the melody feel as though it has one or two chords to a bar? Could it work with one or two? Try this:

Why did I pick D7 for the first bar? Simply that the guaranteed way of arriving at tonic is via V7, in this case, D7 - G.
How would I know which chord to introduce in the first part of the opening bar, if I felt that two chord changes were more suitable? Try this:

We now have Am7 - D7 - G, and it produces a very nice effect, making the D in bar 1 tense to the Am7 chord. Sing the tune and play this through until you have worked out a good voicing for the chords on either keyboards or guitar.
That still doesn't answer how I got there, apart from the obvious fact that this is a diatonic tune, and I've used only diatonic chords (ie. chords from the G major set shown below).
What is more, this works equally well.

Again the D melody note at the beginning of bar 1 is tense to the C chord, but it still works well.
So how can we pick chords with such certainty, and be confident they will "fit" the tune we have written? I'll answer that by going back to the problem of melody notes:

This D melody note tells us very little about what might accompany it. I can put dozens of chords under that melody note, and they will fit - at least they will in isolation. There are a vast number of possibilities.

These can be produced randomly, so that the melody notes get progressively more tense. Nevertheless, we do know that it is possible to harmonise any melody note with any bass note and harmony, providing the R 3 7 idea is followed. So where D in these examples is either R 3 5 or 7, the resulting chord is not particularly tense. Where the note is outside of that, the chord becomes correspondingly more tense.
So why do these three chords progress so well:

The answer is in the bass line progression itself. If we've decided that this three note idea could end on G major as tonic, then the most probable chords are Am7 D7 G because of the bassline progression, which moves in a cycle movement. That is to say, each successive bass note is either a 4th up, or a 5th down (this is the same thing) counting letter names. Without doubt, this is the most important idea in any form of tonal music, and has been for four or five hundred years. Taking that argument back to the first example, you can now see the logic of Am7 D7 G, simply working back from the G, by step.
This is so powerful, that we can actually produce other versions of this original five note tune, adding a chord to each note, and working back from the last G chord. This produces this bass line with that melody:

Now, if we simply use the R 3 and 7 idea to voice the chords, assuming that all these bass notes are the roots (the name notes) of the chords, we arrive at:

Practice thinking letter names in 4ths. So if you start C, then carry on F B
b E
b A
b and so on - a cycle of perfect 4ths (a 4th of 5 semitones). It really is amazing how often this is used in all sorts of different music.
This is not the only bass line progression, but it is certainly the most important! I hope you're getting quite excited about this, because next month, I'll open the box on all the most common bass line progressions, and begin to show you how to put them together. In the meantime, pick up the book of songs that you bought last month (didn't you!) and see how many cycles of chords you can find.