As the title says . Must have: Hardshell case or fold option Netural sound but with present bass  Closed back

I currently have the AKG K845BT and i think they are amazing in sound(from wire use not the BT option) and build quality , my only problem with them is that they are not really portable . i am looking to upgrade from the AKG K845BT or to get something similar to them just more of a portable...

I have been music fan my whole life and i come from very musical family but i never had headphones for over like 20$ maybe not even 5$ for music and i need your help to choose one . 1)I will be mainly using it in public (walks,travels and school) so only closed headphones or open back...