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Go to one of your woodwind-playing colleagues and ask to borrow their "cork grease." That's the stuff they apply to their cork-lined joints between sections of their instrument. Apply a little to your mute corks. My guess is that one treatment should last forever.

Sorry, I can't help with how a muted tuba sounds.

Cheers,
Allen

I spray the inside of my (lacquered) bell with lemon Pledge before gigs that require a mute. It works for me, and makes the horn pretty (and smells pretty good, too).