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:
DirectDraw
Direct2D
Direct3D
DXGI
DirectInput
DirectPlay
DirectPlay Voice
DirectSound
DirectSound3D
DirectMusic
DirectX Audio
DirectX Media
DxDiag
DirectX Media Objects
DirectSetup
XAudio2