I have a huge collection of brass and have tried about everything. Brasso is all rub scrub rub. Lemon nd salt is a waste of time. But Twinkle (as in the silver and copper polishes) makes one for brass. It works great and doesn't have a solvent type of gaggy odor. The secret is to wet the surface with hot water, hotter the better. For something big like your hall tree you'll need to get it in the shower.
There is also a polishing cloth that works well, but I don't have one at the moment and don't remember the brand. It comes in a zip-lock bag appr. 5" X 9" and is yellow with a white polishing cloth included.
For detailed pieces or really bad tarnish (when it starts going greenish and pitting)I use a fine car buffing paste. This works great for pieces that are dulled from fine scratches. You can make brass mirror-like if you start with coarse enough to remove worst scratches and keep stepping down to finer ones. Just like sanding wood.