Not listening to music while I learn, for me, it's the same as walking the street without shoes or going without an umbrella below the pouring rain.
It's a huge no-no, now that I've been regularly listening to music as I learn, that I see such a huge difference.
I haven't read any research on the matter but I can confidently say that not only my memory seems greatly improved by listening to music but my mood while learning also gets a boost. I have a set of albums for each of the different topics I learn, they are almost exclusively soundtracks of popular movies. For example when studying Physics I usually listen to The Theory of Everything soundtrack on Youtube.
I cannot pinpoint exactly what's happening under the hood but I can say, in my case, that the music needs to be instrumental and not be so "loud" or with huge changes in harmony. Further, I've found that some music does not work for certain topics.
On this comment I talk about a little bit about relation of sleep and learning via a interview of a sleep researcher (DR. Matthew Walker) who also talks in that interview about the relation of music while learning and specially listening back that music while sleeping as to repeat patterns and solidify long-term memory. I have not pursued this particular experiment but as far as listening to music for me has been a great improvement.
I often find that I am able to appreciate the beauty of a subject more while listening to music (especially instrumental music). Hearing the notes while I think about the topic helps creates a lot of subconscious connections with the material, solidifying what I am learning as a distinct set of memories. In general I think that associations with powerful sensory experience is just a good way to remember things and learn.
However, I have also heard that listening to music can distract you when you are trying to do deep work. Apparently, there is some research on this, but I have barely scratched the surface of the literature, and I wouldn't know where to start.
Is there an optimal way to use music to learn? Should I employ certain strategies, like putting on the music only after I've read something, so that I can think about what I just read while music floats through my consciousness?