C / C++ / MFC

1. Displaying the animation -- This is probably the simplest part. You can either use DirectDraw (the DirectDraw interface is part of the DirectX 7 interfaces, available for C, C++, VB, and C# in the DirectX 9 SDK), GDI, SDL, Direct3D, or OpenGL. GDI or SDL are probably the easiest way to go here (imho).
2. Monitoring music being played -- Maybe try checking out the IDirectSoundCapture8 interface to get started.
3. Analyzing the BPM of the music -- Here you'll need to analyze the waveform and derive a beat. I haven't done signal analysis at all, so maybe somebody else can shed some enlightenment.

<br />
const void CCalFrameWnd::CCalendar::Note_EditChange()<br />
// Called from parent to signal that user are editing a note.<br />
{<br />
	TRACE(_T("Note_EditChange()\n"));<br />
	// Ensure usage of one charformat only.<br />
	long lChar_Start = 0, <br />
		 lChar_End = 0;<br />
	CHARFORMAT cf_def;<br />
	cf_def.cbSize = sizeof(CHARFORMAT);<br />
	m_pEdit_Note->GetDefaultCharFormat(cf_def);<br />
	m_pEdit_Note->GetSel(lChar_Start, lChar_End);<br />
	m_pEdit_Note->HideSelection(TRUE, FALSE);<br />
	m_pEdit_Note->SetSel(0, -1);<br />
	m_pEdit_Note->SetSelectionCharFormat(cf_def);<br />
	m_pEdit_Note->SetSel(lChar_End, lChar_End);<br />
	m_pEdit_Note->HideSelection(FALSE, FALSE);<br />
}<br />

    LPVOID lpMsgBuf;
FormatMessage(
    FORMAT_MESSAGE_ALLOCATE_BUFFER |
    FORMAT_MESSAGE_FROM_SYSTEM |
    FORMAT_MESSAGE_IGNORE_INSERTS,
    NULL,
    GetLastError(),
    MAKELANGID(LANG_NEUTRAL, SUBLANG_DEFAULT), // Default language
    (LPTSTR) &lpMsgBuf,
    0,
    NULL );
MessageBox( NULL, (LPCTSTR)lpMsgBuf, "Error", MB_OK | MB_ICONINFORMATION );
LocalFree( lpMsgBuf );