The intransitive (no object) verb 'melodize' might work for you:
1. intr. To make or play music....
["melodize, v.". OED Online. June 2016. Oxford University Press. http://www.oed.com/view/Entry/116225?rskey=bqbvyt&result=8&isAdvanced=true (accessed July 19, 2016).]
Caveat: Differing definitions in common dictionaries suggest the sense of "to make or play music" might not be widely understood without a defining context, so there's a danger of misinterpretation.
While Collins English Dictionary (British), for example, defines an intransitive 'melodize' as "to sing or play melodies", which may be close enough to the desired meaning, other dictionaries (for example, Random House and American Heritage) define intransitive use of 'melodize' in terms of composing melodies, without mentioning playing music.
The 'play music' intransitive sense of 'melodize' may be more common in British English than American. Oxford Dictionaries provides a definition that agrees with the OED Online definition shown above and resembles the Collins English Dictionary definition.
1 [no object] Play music
Oxford Dictionaries also provides examples of use:
The sound isn't the greatest but still at its best with weird chimes melodisiing every time you enter a town.
I'm really bad at it, but if I sing a straightforward tune my girlfriend melodises with it.
I spent two days in this small town, making yoga on the lawn and melodising with my clarinet in the mornings until it was time to go to lunch at the steward's house.
Note that all the examples use the British 'melodise' rather than the American 'melodize' spelling.