Several points would make my dreamed headphones, divided on 2 main subjects: Sound quality and comfort/use
I - Sound quality (not particular order)
1- Great bass extention. Not boomy but with authority. Able to separate between bass drums and bass notes from keyboards, basses and other instruments
2- Clear mids with warm feel. No voices sibilances, no harshness. Great sense of air, space and integration. Great soundstage
3- clear highs WITHOUT being bright/shrill. This is one of the hard-to-find point on headphones
II - Comfort/use
1- Excellent comfort on ears and head to use them for long periods (over hours) without any problems
2- Good impedance and qualities to drive them WITHOUT an amp.
3- Good portability enough. Carrying bag must be included
4- Chord should have 2 lenghts: one for portable devices (something like 1,2 mts) and extention for hi fi devices (another 2- 2,5 mts). Cable should not come from both sides.
5- Isolation: if closed-back, good isolation not to hear what's happening around, yet keeping soundstage and musicality
6- Look: great design.
and many others
