Buddhism can sometimes appear as am austere tradition. Indeed, in the earliest known monastic rules monks & nuns are forbidden to listen to listen to music as it might distract them from their mindfulness practices. These rules are still found in the monks' rules in Thailand, along with a few other countries, but monks do often appear to enjoy music in the land of smiles, as observed by this author. There are some monastics that do not indulges in music, but music is played in public a lot in Thailand, even in festivals and other activities within Buddhist temples, so it's difficult for many monks to avoid, really.
In other Buddhist traditions, as found in Tibet and China, for example, music is not only listened to by monastics, but actually performed by them, especially during Buddhist services. Chinese Buddhist chanting is often accompanied by music, and is itself most melodious, and the image of Tibetan monks blowing on long horns and clanging cymbals is an enduring image. Thai Buddhist chanting, on the other hand, is normally performed a cappella, and is pretty monotone in style. It is done this way to avoid any indulging in music or melody, thereby avoiding getting caught up in the beauty of music. (Many Buddhists will tell you, however, that it is possible to get entranced by the hypnotic qualities of such plain chant - this author included!)
Buddhist laity, whatever the tradition, are not proscribed from listening to - and enjoying - music. Only when staying in certain meditation temples are they discouraged from listening to or performing music. This author knows from personal experience that music can have all kinds of effects on the mind, sometimes calming, other times agitating. As these words are being written, Beethoven's Violin Concerto in D major is emerging from the same computer that these words are being typed into. Such music can complement mindfulness practice if attenuated to correctly - and it can help to avoid the boredom that so often drives us away from being heedful of this present moment.
Listening to music can be a mindfulness practice in itself. Like mantra recitation, or shamanic drumming, it can be used to keep the mind in this current moment. This assists in cultivating present-moment awareness so important in Buddhist practice. Something I've enjoyed since a teenager is listening to music on headphones or earphones, giving the impression that music is coming from within rather than without. This enables one to focus even more clearly on the music, being able to follow a particular instrument through a song from beginning to end. Attaching attention to Paul McCarney's often very creative bass lines in those great old Beatles' records is an enjoyable example of this. Just listen to his bass guitar work on Lucy in the Sky with Diamonds and you'll see what I mean.
When listening to music attentively, something wonderful can happen; awareness moves from the sound of the music to the sound of the silence in which it arises. This silence is amazing in that it is capacity not only for Beethoven, the Beatles and other great composers' music, but for any sounds that occur. It doesn't judge them or discriminate between them, bit rather gives them all the space they need to exist. Moreover, this silence isn't something separate from the listener, but is in fact his or her core nature. Sounds (along with all other phenomena, both mental as well as physical) arise, exist and end in this silent awareness. Both in meditation and in general mindful living, this spaciousness is the impartial host to all that is. To awaken to it is to begin the real Buddhist journey towards realization of the Buddha within; this 'Buddha Space.'
Making our everyday life our Buddhist practice is a crucial aspect of walking the Buddhist path. Monastics do this by adapting their environment so that many ordinary occurrences simply do not arise for them, enabling them to focus their attention more easily on their subject of awareness, whether it be their mind or body. We laypeople can do the same to some extent, but then as most of us do not live in a monastery or a cave, we can't cut out all of the distractions and pleases that monastics can. But what we can do is to adapt what we do experience to fit into a meditative regime. Beethoven and the Beatles can be used this way - as can most, if not all, music - moreover, our enjoyment of their music can help us to stick to the mindful path, not slipping off so often into the dream worlds of past and future. So, if you enjoy music, whether making it or listening to it, why not use as a focus for mindfulness practice - and you can hear your way to enlightenment!