The modern stereo record is like a v-shaped channel with undulations on both sides about 45 degrees to the normal. The magnetic (or earlier crystal) pick-up devices of the stereo cartridge are about perpendicular to the sides of the channel, thus 90 degrees to each other, like two pistons with their rods tied together and pivoting on both sides.
In the vertical-lateral world, movement to the left equals rising on the right, i.e., the left piston compresses if the stylus moves laterally to the left or if it rises vertically from the right, and vice versa.
For reasons of compatibility in the early days of LP's, the stereo channels are 180 degrees out of phase, so that if we were to record a pure single tone on both, it would mechanically result in a left to right to left swinging motion. Thus mono records could be played on stereo equipment, because the cartridge would perceive a side to side motion as one side rising and the other side falling.
The Edison record unfortunately, has both sides rising and falling simultaneously, mechanically in phase, but electrically 180 degrees out of phase, because the pick up device has already reversed one channel. So if I reverse it again, I'm in business.
My point is that simply using one channel was good enough, and that rewiring the cartridge does noticeably improve the quality. My understanding of this is that because the groove in the Edison record is much wider than the stereo stylus, there is some mechanical bouncing around side to side, which will cancel out electrically when the two channels are added together.
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