[xaMdaM]

Short of going to headphones, the only other "best bet" is to contact your landlord and let them know that while you feels your neighbor's complaints aren't entirely justified, you want to bring the situation to their attention.

In that if you are listening to music at reasonable residential levels, the building is not constructed so as to minimize this issue.

While well made, upper end apartments are well made to isolate the neighbors from each other, the construction of your apartment may be sub standard from a couple of standpoints... to wit;

If you can hear each others conversations
If you have excessive heating and cooling bills
If you cannot listen to music at nominal levels (sub 72db)

I would suspect that there is little to no insulation in the stud cavities, nor is there likely a firewall between the units.

The property manager should be made aware that this is something that they really should advise the property owner about. e.g. local ordinances regarding firewalls and insulation and that the property owner may not have received, yet paid for... (IF this is a newer structure.)

Most states here, have minimum noise isolation codes, to ensure at least a reasonable amount of individual privacy. If your building falls under these ordinances, the property owner should ensure that the structure complies with these codes.

If it's an older building.... Say, 15 years or older, there prolly ain't squat you can do except wear cans...... or move.