Major thirds in 12-tone Equal Temperament are 'off' by quite a lot. It's part of the price you pay for being able to play in all keys without rebuilding the instrument. If, like most of us, you grew up with 12-tone ET you don't tend to notice it. Until you do. Then the problems never go away. Sadly, it's mathematically impossible to construct a scale that has all of the fifths and octaves 'pure', so we're left with using some form of 'temperament'; applying a fudge factor that makes things at least tolerable.
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