Chemists! Homemakers! How would you clean/untarnish aluminum?

I am a big fan of PBS nerd Haley who has helpful Haley's hints such as using vacuum cleaners and garbage bags as a DIY clothes compactor
and vinegar for cleaning just about everything.
But I'm afraid the acid in the vinegar might react weirdly with aluminum. Sounds like a job for science!

light acid is fine, vinegar etc.

Vinegar, or make a paste with cream of tartar (tartaric acid) and rub that on to clean and polish. You can also dilute the vinegar. The white oxidation you get on aluminum is a reaction with caustics - a major reason not to put aluminum in the dishwasher (detergent is very very caustic).

Much thanks!

alternately, you could lick it