What is the musical term for someone who has natural talent in hearing?

Far as Playing without sheet music or formal training It is play by ear ,

but far as talent Perhaps, musically inclined might be the wording your looking for?

Or there's Absolute pitch , or perfect pitch, is the ability to name or reproduce a tone without reference to an external standard.

The naming/labeling of notes need not be verbal. AP can also be demonstrated by other codes such as auditory imagery or sensorimotor responses, for example, reproducing a tone on an instrument. Therefore a musician from an aural tradition, with no musical notation, can still exhibit AP when asked to reproduce a sounded note.

Possessors of absolute pitch exhibit the ability in varying degrees. Generally, absolute pitch implies some or all of the following abilities when done without reference to an external standard:

* Identify by name individual pitches (e.g. A, B, C♯) played on various instruments

* Name the key of a given piece of tonal music just by listening (without reference to an external tone)

* Identify and name all the tones of a given chord or other tonal mass

* Accurately sing a given pitch without an external reference

* Name the pitches of common everyday noises such as car horns

* Identify the numerical value in hertz of a given note.

Individuals may possess both absolute pitch and relative pitch ability in varying degrees. Both relative and absolute pitch work together in actual musical listening and practice, although individuals exhibit preferred strategies in using each skill.

Are these the type of skill's you are referring to, or something else?

I'm sorry I don't have answer, but I had the same question!! Not to brag, but I'm "musically inclined". :)) I can hear a song, and noodle around on the piano Or guitar and figure out the entire song...I've done that with the phantom of the opera and Mamma MIA! Soundtrack. :)) great question. :))

Can she identify notes without needing reference? That would be perfect pitch!!! Which sounds pretty impressive!