Answer: For anyone in our TV audience who hasn't taken music theory in school, a 4-3 suspension is a case in which a triad appears with a fourth in the place of what should be its third, and the fourth then slides down to where it ought to be. The note forming the fourth is held over from a previous sonority in which it was a legitimate chord member, and then the harmony changes around it, and it seems out of place for a moment until it moves down a step. The suspension is a very effective contrapuntal device, somehow very emotional, and chains of suspensions are often found in baroque and classical music.

Here's an example of a 4-3 suspension, from Bach. The G in the last measure was the seventh of the previous chord, becomes the 4th above the D bass (plus an octave, but that doesn't count; it's still called a 4-3) and then relaxes to the F#, the third of the final D major triad.

I know everyone out there is anxious to write a suspension now, so here are step-by-step instructions for one type of 4-3 suspension.

(1) Find a place in your music in which a chord is followed by one whose root is a fourth below any of the first chord's tones. A V7-I is a very popular choice, since the 7 of the V chord is a fourth above the root of the tonic triad. That's what we saw above, though there are of course other ways to do it, like a IV-I or a ii-vi.

For example, let's add a 4/3 suspension to one of Bach's chorales, without his knowing it. Here's a phrase ending from Nun Komm, Der Heiden Heiland (measure 1 of this example):

(2) The two chords forming the cadence are V7, i in B minor. The 7 of the V chord is E, a fourth above the root of the i chord, and it happens that this is written in such a way that the E is followed in the same voice by D, the third of the minor triad. So this is easy: in our first revision (measure 2) we just repeat that E at the beginning of the B minor chord, and then move it to D where it belongs. Though there is no tie, this is a kind of suspension, with a more pronounced effect.

(3) In the third version (measure 3) we add a tie to make that suspension the smoother held-over type.

What about writing melody alone? The same principle applies but now the harmony is just implied, or perhaps is elsewhere in accompaniment. In Vivaldi's famous Largo from Winter of the Four Seasons, there's a 4-3 suspension in the melody in the second measure, and it is key to the effect of the tune:

Once again the composer simply let the melody repeat the 7th of the V chord above the I harmony, where it didn't belong, and then let it fall into its proper place by dropping a step. You could do that yourself in any tune in which you have a V7-I chord change and the melody singing the seventh of the V chord, as above.

To sum up: find two chords in which the first one contains a pitch that is a fourth above the root of the second chord. Hold that note over into the second chord and then move it downward by step to form a third with the second chord's root. And remember this: avoid sounding the third in the second chord except in the voice that is doing the suspension. That would "give away the ending" as well as adding another dissonance. So your chord of resolution will initially have no third - it has to wait for it.