The number of dimensions determines the possible types of instruments and the ways to produce sound.
In 2D wind instruments and string instruments would be possible. Wind instruments would be similar to 3D in principle, but their acoustic colour might be a bit different as there is one lateral direction missing. String instruments are nothing that may be plucked in 2D, those intruments are beaten like a dulcimer or a paino via keys. Complex string instruments might be difficult to implement.
In 3D suddenly there is the possibility of a brane. In contrast to a string, a vibrating brane gives less consonant sounds because the standing waves are confined in 2D instead of 1D resulting in more eigenfrequencies. There are two ways to produce sound with those instruments: Drums and cymbals may be beat, cymbals may be played using a bow, resulting in a continuous, sharp sound. Also there are two other possibilities to play string instruments: Plucking and bowing. New sound colours and softer sounds are produced and it's possible to change the length of the strings with one's hand.
In 4D branes with 3 dimensions become possible, resulting in even more dissonant sounds than 3D percussion gives. The more complex geometry allows for a broader range of timbre. Both 2D and 3D branes could be used as percussion or be bowed. 2D cymbals and even drumheads could be plucked like a quitar. Modifiying the pitch with one's hands would be difficult though, as you would need ridiculously long fingers to do so. Still pressing against those strings would have an effect by damping the sound while increasing the frequency (as in 3D). The additional dimension would allow for more 1D strings on one instrument if the fingers of the player have the same length. Similary keys of pianos could be packed more tightly making it easier to play demanding music. Bowed instruments with 1D strings would have to be played using a 2D bow in order to stay on top of the strings. 2D strings could be either played with 1D or 2D bows. In the second case the vibrations moving along the lateral direction the bow is extented into might be damped more strongly, so if the string is not totally symmetrical the player could modify the sound depending on the orientation of the bow.
(Now comes the idea of using cross- or net-shaped strings for instruments in 3D - two coupled waves. I wonder what that would sound like...)