Hmmm... Responses are all over the place here, and each is correct. But let me see if this will add some clarity to someone who is new to this game. Note to begin: 120 gram, 180 gram, 200 gram actually refer to the weight of the "glob" of vinyl that is dropped onto the press when the record is pressed. The result is a thicker record, but the measure is by weight of the vinyl. 120 gram has been the industry standard.
Elizabeth sets the right context for understanding the history. In the 70's, vinyl got to be very expensive with the oil shortage. Manuafacturer's tried everything they could think of to cut costs, including making the vinyl thinner, using re-cycled vinyl, using fillers and additives. Records became so thin, they just "wilted" when you held them in the middle - like Dali's clock paintings. But the biggest culprits were re-cycled vinyl and the various fillers and additives. The formulation of the vinyl can make a big difference in getting good sound. Different formulations DO sound different. Thus, in the early 80's one started seeing in the marketing materials references to "virgin vinyl."
But there truly is a downside to thin vinyl that is TOO thin.
Stereo discs are cut with both a lateral motion and a vertical motion. Really thin vinyl limits how deeply the grooves can be cut, and this in turn compresses the information that can be encoded in the grooves. Also, I've read that you can get interference from the reverse side of the disc. (This was part of the rational for Classic Records and Speakers Corner to cut their 45 rpm recordings on one-side discs; the other part of the rational was to improve contact with the turntable platter on the underside. Only those manufacturers can address how much practical difference they heard when they tested this, if they ever did. Acoustech/Analogue Productions are pressing their 45 rpm reissues on two sides with marvelous results.) The industry standardized on 120 gram vinyl as the point at which this problem was largely resolved.
Also, vinyl resonates just like anything else. Here a bit more mass helps damp the resonance created by the stylus in the groove.
Still, with good quality virgin vinyl and reasonable record thickness (e.g., 120 grams), standard 120 gram records can sound very very good, and like another person commented, some of the best sounding records in my collection are 120 gram records. Might those records sound better if pressed on heavier vinyl? Probably, all things being equal. But all things are never equal for us as end users/listeners. There are too many variables for most of us to be able to do a listening tests where the variable are controlled.
My subjective experience over the years leads me to the conclusion that it is not all a marketing gimmic, at least not between 120 and 180. However, I think the differences in made by changing the weight can be swamped by difference created by changing the vinyl formulation or using re-cycled versus virgin vinyl. Is there a difference between 180 gram and 200 gram? I don't think so; I think that is marketing gimmick. But, the only 200 gram vinyl out there is a different vinyl formulation, so there are two variables at play. My guess, and its only a guess, is that the bigger difference heard (and I do hear it) is the result of a difference in the formulation of the vinyl, not the weight.
All theory aside, the results are what matter. I, too, have heard heavy-weight vinyl that sounds terrible and light weight vinyl that sounds marvelous. But, I think the mastering experts, like Stan Ricker and Steve Hoffman, would tell us that they prefer to have their work pressed on heavier vinyl given a choice.
And, to Newbee's point, the difference in thickness does mean that we have to adjust our VTA settings when switching between 120 and 180 gram vinyl. If one is not doing that, the sound of one or the other is going to be way off from what it can be.
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