Is it considered against standard Buddhist doctrine to meditate with music?

The biggest issue with music is:

• you can get attached to it
• can created mental recitation of the lyrics which in turn creates verbal fabrications

Hence best is to resort to more conservative meditation pratice. Having said tha as an alternative meditation pratice Richard Shankman teachers mindfulness of sound. This is not necessarily all modern "music" but may be something like the sound of a Gong.

Alternative Meditation Practices

The breath is commonly taught as a universal meditation subject, suitable for everyone. But for some people the breath is not a good object to work with. I knew a man who had a choking incident as a child, and paying attention to his breathing brought up feelings of anxiety. Another person with asthma found that she became tense whenever she focused on the breath. If you are one for whom the breath does not work well, there is nothing wrong; this will not hinder your ability to meditate. It’s just a matter of finding the right practice in these early stages to substitute for breath meditation.

Here are some techniques you can try if you think mindfulness of breathing is not a good practice for you. These common alternatives are not the only methods that can substitute for mindful breathing, but the full range of possibilities is beyond our scope here.

Mindfulness of Sound

In the instructions for mindfulness of breathing we let all other experiences stay in the background of our awareness, not forcing or pushing them away but bringing a gentle sense of allowing them to be in the background while giving some preference or predominance to awareness of our breathing. In the same way, with this practice we allow other experiences to stay in the background and we give preference or predominance to the experience of sound. You may feel a natural draw or pull to awareness of hearing, and this practice can be very calming and settling. Those for whom mindfulness of sound works well commonly report it as an easily accessible and even compelling meditation object. You may be drawn to awareness of the sounds themselves or you may be more naturally aware of the act or the process of listening or hearing.

Mindfulness of sound entails working with either inner or outer sound. Even though it may be very quiet where you are meditating, you may feel drawn to rest your awareness in listening to however many or few sounds may be present at any time. Other people hear an inner sound, a clear perception of ringing or some other sound, experienced not through the ears but in the mind. You can see if you have such an experience and if you are drawn to rest in awareness of inner or outer sound.

If you are working with mental noting, you can mentally repeat hearing or sound if that helps keep you stay connected and centered with the auditory experience. If you practice mindfulness of sound, just substitute hearing every time I use the terms breath or breathing.

Source: Beginning Meditation Instructions: Excerpted from “The Art and Skill of Buddhist Meditation”.

Also see my related answer: What did the Buddha say about music?

Listening to music for entertainment and music in a meditation technique are two different things. Tibetan Buddhists use sounds of gongs a lot to facilitate disciples to enter deeper state. But it cannot be classified as music as it does not build up excitement. Modern music excites therefore it is incompatible with Buddha's path. But many other paths exist which rely on music and dance of certain kind (not modern music) to facilitate meditation. But if you are a disciple of Buddha you can check out through your experience if commonly available meditation music (like sound of gongs,nature etc) helps you or not. But eventually you will come to a point where all such things will become irrelevant. There will be a silence within which is not affected by anything outside.

I am aware of some studies that suggest that "noise" can be an aid to concentration - i.e. people who doodle at meetings tend to be more attentive, people who chew gum in class tend to remember more, and people who listen to classical music write more fluently. In preliminary stages of meditation, you might even find it easier to gather your mind when there is an outside stimulus. Guided mediation is just one example of this. That being said, all four of those activities refer to modes of thought that are distinctly different from what you are aiming at in deeper meditation. When sitting in a Buddhist sense (i.e. for jhana meditation, vipassana, koan practice, etc.), you need to work towards developing applied and sustained thought in a way that is as free from distraction as possible i.e. "Quite secluded from sense pleasures, secluded from unwholesome states of mind..." MN 4. This also infers that the influence of the five hinderances needs to be limited. It goes without saying that listening to music is fairly antithetical to that end.

Regarding your experience that you hear music more readily when sitting - that's a fairly common occurrence. You are just becoming aware of another level of your mind that was previously obscured by grosser thought (for what it's worth, I have the same experience when I'm backpacking or doing any other activity that isn't thought-intensive). You do need to get beyond that state, however. As you apply concentration, you will eventually push past that boundary and into deeper, more silent layers of the mind.

Based purely on my experience -- i.e. I don't know what any of the Buddhist literature says -- music is a two-edged sword.

On the one hand it doesn't at all help develop concentration or insight. It may feel like it is, but I think it is nothing but a feeling.

But on the other hand, it did serve to get me meditating at all. I found (still do) meditation to be difficult, and it wasn't something I enjoyed doing. Music made it a bit easier and got me on the cushion. However, once I'd built meditation into my routine, I stopped using music. So it served as "training wheels", and was best discarded as soon as possible.

Of those two effects, I think the first is the stronger. And with hindsight, perhaps a better approach for me would have been to join a local sangha, and used simple camaraderie to get me over the initial hump of starting to meditate. Then music wouldn't have been needed at all.