Why is mentally reproducing music so hard to control? How can it be counteracted?

In practicing meditation, if you hear something(maybe music or voice), just note "hear, hear". No more thinking further. If all these cannot noted mindfully, surely will lead to other things one may think related or unrelated, actually all are really related, related to your past events not only this life. So the main aim of meditation is to get rid of all these clinging to the past and present action one have to do is note down very mindfully every phenomenon. But sitting meditation is easier to get rid of these thing, later in every posture, every situation you can get rid of it. Never try to control it. Just note "hear, hear", sometimes just "know it, know it" is enough so that no need to analyse whether hearing or thinking or knowing.

Yes I don't know if my answer is on-topic; maybe it helps you to recognize what music is.

Music is kind of designed to be memorable.

The music which you (and other people) remember is music which has proven itself to be memorable.

I read that The Beatles didn't know how to write music: and so their songs (especially their early songs), which they played, were only whichever songs they were able to remember the next day.

My grandfather had a similar technique, by the way, for writing children's stories: he would tell children a story, and then asked the children the next day to tell the story back to him -- whichever bits of the story the children were able to remember were the memorable bits, and popular with the children, and those were the bits of story which he wrote in the official/published version of the story.

Anyway, components of a music (e.g. a popular song) which help to make it memorable include:

• Words:
  • Familiar words (e.g. in a language you know)
  • A story (narrative) and/or characters (people), which are emotive (a love song, a sad song, a let's-get-to-work song)
  • Rhythm and rhyme (i.e. poetry)
  • A chorus (repeated words)
• Music:
  • Familiar scale (selection of notes)
  • Melody
  • Harmony
  • Rhythm
  • Repetition (not only is the chorus repeated, but also all the verses of a song usually have the same tune)

You also (in this age of recorded music) hear the music more than once.

Music is surprisingly memorable. A music radio station, which I used to hear, used to have a phone-in competition: they'd play a fragment (maybe half a second or two seconds) of a popular song, and ask the listeners to name the song.

The ability to recognize small bits of sense-input and associate it with the whole of a larger previous learned experience is more-or-less what brains do: e.g. hear a spoken word, recognize that as mother's voice, associate that with etc.

Another reason it's difficult to control is because you think that you can (and to some extent you train yourself to be able to) listen to music while you're doing something else.

When we sit, we pass through different phases of consciousness. At first our mind is active and discursive. It ruminates over all manner of things, rehearses events to come, and rehashes those that have past. As we move towards stillness - which can be done simply by sitting quietly in one place - our mind settles into a more passive state. Rather than taking an active role in the creation of our thoughts, our mind relaxes, revealing its deeper layers. At this point, things may begin to spring up unbidden. Sometimes we can experience memories from long ago, other times we may see fragments of pictures in our minds, and sometimes we may experience traces of emotion that have no obvious cause. If you spend any amount of time listening to music, recollection of song is also exceedingly common.

Don't worry about about the music. If you persist in your sitting, it will begin to fade. Song is just a different kind of thought. Treat it like you would any other - let it have its space, don't try to chase it down or drown it out, sit still, and do your best to maintain attention on your breath.