You would have a hard time getting the needle to track. The groves in the vinyl as made by peaks in the father. The needle will just fall off these peaks. If the groves are too close together then the needle might track between two of the peaks. You will essentially be playing the left side of one grove on the right channel and the right channel on the next grove on the left channel. But assuming you have a special inverted “needle” that could track the peak like the grove of a vinyl record then it would sound just the same. The phase of the sound is inverted but that is not something that the human ear can pick up. This would be like swapping around the two wires on your speaker.
You couldn’t play it.
The needle rides in the grooves and gets the signal from variations in the sides of those grooves causing vibration. Inverting the groove doesn’t just invert the signal, it removes the groove altogether and turns it into a ridge, which the stylus cannot track because now the channels are on opposite sides of the ridge and the now adjacent ridge is actually from the next groove over so they aren’t related at all so you’re trying to read two inverted signals that have nothing to do with each other.
Edit: there’s a physical component to the configuration that you can’t just invert like you could if it was a purely digital medium. The physical properties of the medium itself drive the electrical signal.
It wouldn’t work. The needle would fall off the ridges into the space between, which isn’t shaped like a groove in the way a turntable expects. A snag in the wrong spot might even damage the needle.
You could make a specialized player for father stamps, using optical scanning or some similar technology. Such a device would be useful for quality control, so I wouldn’t be too surprised if the record companies had made some, though I have no way to confirm that. If they did, then someone could listen to the father stamp before using it to press discs, to ensure there were no defects that could be passed on to the batch.
The other answers explaining how your grooves would be ridges is part of the story. If we are talking about a stereo record opposed to mono, then two channels of sound are stored in the groove. One is created by left-right vibration on the center line of the groove. If the recording were only on this channel the needle would vibrate left and right but not at all up and down. On the other channel the vibration is created by changing the width of the groove. As the groove width varies the needle vibrates up and down as it sits deeper into a wider groove.
So now we imagine that the needle runs a half groove out of sync. There would be no rhyme or reason to the groove width or centerline. Both the width and centerline of both grooves you are touching would impact both vertical and horizontal vibration.
Long story short, you would simply get noise not a distorted or off time version of the recording.
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