yes the diagnostics for DID state the alters can ......not...... be because of imaginary (my location also uses the terms fantasy, made up, playing pretend for this) friends or fantasy play. even if the alters have their own personality\way of being, if they are created due to fantasy\imagination DID diagnosis is ruled out.

DID type alters are not imagined into being, and what they can and cant do is not imagined into being, nor can they or what they do be imagined out of being.

maybe looking at your post will help to clarify what I posted......your post states

I heard music in my imagination as a child, but I could never stabilize my attention on it long enough to write it down. Then later I lost the music in my imagination. I can't hear music any more in my imagination, not even just remembering music I've heard before. I have actually done a lot of study of music now and I can compose with the help of a piano or computer (to help me hear the sound) but it's not very fun compared to using my imagination (and not very good either). Every once in a while I get a little hint of music, or dream that I'm hearing music.

and your post also states....
What I wonder is whether the function of imagining sound split off into a sub-part.

do you see the parts of your post where it says the words ...imagination, and imagining.....

well...if going according to the DSM 5 and my location what you posted would ....not ....be dissociative or DID type problem and would disqualify the diagnosis of DID because you associate these split of parts and the sound you heard and want back as imagination, imaginary.

if I had this same problem my treatment providers would call this split off part and the sound I imagined to be an auditory hallucination, not a dissociative type alter.

to find out what this is with in you, you will need to contact your (or a) treatment provider in your off computer location