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It is Jules Antoine Lissajous of La Belle France whom we have to thank for this interesting way of visualizing stereo information. Basically you can think of an oscilloscope screen with a bright spot in the center. Apply the left channel of a stereo signal to make the spot move horizontally. Apply the right channel of a stereo signal to make the spot move vertically. The result will be a pattern that is both beautiful and informative at the same time (a little like myself, on a good day!)
Unfortunately poor old Jules Antoine died some fifty years before anyone was able to see his imaginings on an oscilloscope screen, although he had devised a way of projecting simple patterns, which we now know as Lissajous figures, on a wall. Now of course, we can use software to view the patterns created - in this case Audiofile Engineering's Spectre. Let's dive straight in with a stereo recording of drums...
Remember that the left channel of the stereo signal makes the trace move horizontally and the right channel makes it move vertically. A mono signal therefore will move both traces equally at a 45 degree angle sloping upward towards the right.
You will see this most clearly on snare and kick drum beats, which are strongly mono in the mix. Where the cymbals splash around the room into the overheads, then there is more difference between the channels and more stereo content. You will see the trace balloon into a fatter ellipse, once again tilted up towards the right, and occasionally into a circle.
This is exactly what you would expect from a stereo signal. What you don't want however is for an ellipse to form slanted in the opposite direction as this would indicate an out of phase signal.
As a comparison, here is a mono recording of drums made with a single mic in front of the kit...
As you can see, there is no stereo information and all there is is a line slanted upwards towards the right. But what if things had gone wrong and the signal was out of phase?
To demonstrate this here is a contrived out of phase recording. It's actually the previous recording duplicated, one channel inverted, then bounced into stereo. It shows the effect very clearly, and you should hear exactly why you never want your audio to be out of phase...
As a final example I have a recording of sampled drums made by a particularly inventive Audio Masterclass student. (If you want to hire him, then let me know and I'll put you in touch, but I don't think that creativity like this will come cheap.)
In this example you can hear and see that the recording is in phase, has a useful amount of stereo content, and at around the 12-second mark you can see tiny mono cymbal hits that have no stereo content at all. Notice that they move the trace horizontally or vertically according to whether they appear in the left or right channel.
The Lissajous display is an excellent way of visualizing a stereo signal, and provides an important 'early warning' against potential phase problems. It's fun too!