Make the Play/Pause/etc controls available from all tabs
The controls at the bottom of the main tab could be visible in all of the tabs, to allow us to control the currently playing music without having to return to the main tab.
Jim Kelly commented
Sounds essential, including a long-press "Mute" to use when the phone rings!
And maybe a quick-press gives a "Half-mute" to use if the music just needs to be quieter for a few moments (rather than off)? I'd imagine that some punters would want that quick action to cycle through half-down > mute > half-louder > back to original volume.