I have an Epiphone Les Paul Standard PlusTop Pro I purchased in 2016. I think it has a glued in neck as opposed to a bolt-on but is not a guitar made from a single piece of wood.
Whenever I'm tuning the guitar and put pressure on the neck the tuning changes with it.
If I push the guitar neck towards me and pluck a string, the tuning meter will tell me the note is sharper proportional to the amount of pressure I put. If I pull the guitar neck and pluck a string, the tuning meter will turn proportionately flatter. The change in pitch is more than a few cents. I'm guessing the pitch also changes when I hold down frets.
Ideally, the pitch should stay the same even if there is pressure applied to the neck. When looking for a new guitar, are there factors which predict the guitars that are less likely to do this? I guess one tell-tale sign would be whether the guitar is made from a single piece of wood. Are there any others, let alone going in to the store and trying it out? May be the kind of wood use for the body?
For my guitar I did put in a lighter set of strings so the truss rod may need to be adjusted.
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