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How / Can you definitively and accurately test an instruments mouthpiece (brass) and scientifically quantify and express that data beyond just a simple "On a scale of 1-5 how would you..." style survey? Are there machines or instruments used by corporations to do this?

I need to be able to quantify and express how well some homemade mouthpieces work on a scientific level for the Colorado State Science Fair.

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You can't. Apart from anything else, this presupposes that there is an ideal mouthpiece for each instrument. When you come around to doing subjective tests (unless you discard the whole project in avour of something more workable) I suggest you ask players to choose the worst mouthpiece from a batch, not the best. I suspect this will produce slightly more useful data.

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