DirectMusic was a component included with earlier versions of the DirectX collection of APIs and tools for multimedia content on the Microsoft Windows operating system. It was built on top of DirectSound, composed of a high-level set of objects. It is now deprecated. It allowed music and sound files to be created and played with flexible interactive control over the processes. Nowadays, it can only be accessed with 32-bit operating systems (it was introduced with Windows 98 Second Edition) because it is incompatible with the newer 64-bit applications.
Other DirectX related glossary:
DirectX Media Objects