Cut a lemon, peel it, take a chunk of peel and sprinkle salt on the inside of it. Rub the brass with it. When it's clean enough, turn it over and rub the exterior of the peel on the brass, the oil protects it.
If the brass is really grubby, leave a bit of the pulp in the peel, if it's not, you probably don't need it. Too much acid eats the details on your brass down if you do it too often.
Combine the juice of half a lemon with a teaspoon of baking soda and stir until it becomes a paste. Apply the paste with a soft cloth. If the tarnish is heavy, let the piece sit with the paste on it for 30 minutes. Rinse with warm water and dry.
I'm going to agree with Thomas on the ketchup. A customer restoring an old Harley asked me what to use to clean a brass carburetor. I suggested the lemon and salt and mentioned the ketchup. He opted for the ketchup and the carburetors came out beautifully.
Our inability to change everything should not stop us from changing what we can.
Sounds like you're wanting something acidic (citric acid, lemon, ketchup) and salt.
This makes sense to me, because what you're doing is removing the patina by eroding it with acid and salt. I've recently been learning about mordants and metal-based wood stains the common recipe is salt and vinegar.
Nicole is right. To get the grime off you need to use an acid to remove the patina.
Just how dirty is your brass?
I bought a beat up old house years ago. It had a 2 foot piece of brass railing in a bathroom. It was used as a handicap bar to get into the tub. Probably installed 50 years ago before there were handicapped items. It looked like it had NEVER been cleaned. It was black! Seriously black! Tried a dozen products, scrubbed it till my knuckles bled. Nothing worked.
Until I found 'Barkeepers Friend Cleanser'. Made a paste with water. Wiped it on. 15 minutes later scrubbed it off. And the brass was beautiful! With no patina left it is the color of solid gold! The natural patina comes back after a few months.
It has an abrasive agent but the main ingredient is oxalic acid which is also in spinach, brassicas and rhubarb. It's a lot stronger then lemon juice. I use it most of the time now. Works great on stainless steel, the stove and lots of other things. And I too use ketchup on copper.
Get's the job done so I spend lots more time in my garden.
Check your pockets for water buffalo. You might need to use this tiny ad until you locate a water buffalo: