You don't need prefect pitch at all, as shown in the answers, just use the harmonics and listen to the overtones (term?) triggered by your current note. However, a professional tuner can create a certain timbre (warm, jazzy etc) for you by tuning just below or above the 400 cents. That said, trying it yourself is quite fun, albeit very time consuming)))

'Not close enough not to be noticeable' is an understatement. If played together, i.e. on a harp, where that's possible, they sound very bad to anyone's trained or untrained ears. It's an excellent example of how impossible equal temperament actually is.