I totally understand.
A couple of questions... I haven't had time to read the entire thread so sorry if you've already answered this...
Do you have the same landlord that they do? Or do you both own your places or have different landlords.
It helps when they are NOT able to call someone who has power over you such as a landlord to complain.
And getting into some pi#$@ing match with them is not recommended.
I recently had a neighbor who was renting in the same building as myself. They lived right above me. They were rude, nasty, unfriendly from day one. The wife, come to find out was mentally ill and her paranoid nature made it impossible for her to accept sharing a space with anyone. My place is a flat. There is just two units in the building. Come to find out they had run off the three previous tenants. Which in itself is insane. Nice rental space is hard to find in LA. And so of course once a place comes available it's filled the next week with someone new.
From day one they'd stomp on their floors (my ceiling) and she'd pace back and forth, one end of the place to the other, sometimes until 3am. Then she'd take a 45 minute long shower. The husband would park his truck and block the driveway where my wife would have trouble getting out of our garage. Crap like that.
I never once called the landlord, who happens to be a guitarist friend of mine and we've been friends for years.
I practice through my computer, GuitarRig4 and headphones. Always have. I have an Ampeg SVT-450 and matching 4x8 cabs.
My neighbors it would seem, were calling the landlord every other day about us. That our cat was meowing too loud, that we were running the water in our sink and wasting water... and we're on separate meters at that, that I'd leave my porch light on overnight. Silly, goofy stuff.
The landlord finally had enough and decided not to renew their lease. He gave them 30 days notice that they had to get out. And he gave me a courtesy call, inviting me to "practice all I wanted" out loud.
And I had FUN. My wife is a former FBI agent. We know ALL of the police in our area. They made the mistake of calling the police ONCE. I was smart enough to only practice 5 minutes or so full strenght, then I went back to my near silent comuter/headphones routine.
Their bedroom was above my garage. So at 2 or 3am I'd open and close the automatic garage door. I kept the remote next to my bed.
They moved out. I moved upstairs. New, really nice people moved into my old apartment. I wnt back to practicing through my headphones or down really low. Life is now good.
I say do what you do and let them complain. Some people are entitled and jerks and they don't see anything wrong with what they are doing, even as they point out the same thing as a fault in someone else.
I LOVE the dog whistle idea. I'd definately do that.
And if they do ever call the police, stay calm, rational, and agreeable with the police. The decible meter is a great idea. If you can show the officer that your playing is within whatever the city ordinances are... you're golden.
Ignore the neighbors. Do your thing. And let it go.