How to get max of sound quality for music listening? Yo,
I like to listen to music through headphones, so I'd like to tweak the sound parameters on my phone and tablet to my taste.

What can be done in this direction? My devices are not rooted.
Sound purely depends on phone make and model and the headsets too. Most of the phones support 5-band custom Equalizer (you can tweak them just like that) and some phones only support the given presets like Bass, Flat, Treble , 5.1 Channel etc. Sony phones have their own technology like xLoud and ClearBass. So it depends on various things. Also you can download music players from Play Store if the stock music player doesn't support all these options.
Try all of these and pick the best as you've not mentioned your phone and tablet model and are not rooted.