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 );

#define WIN32_LEAN_AND_MEAN
#include < windows.h >
#include < stdlib.h >
#include < richedit.h >
#include < commctrl.h >

HWND _rich;
HMODULE _hRich;
char className[14];

LRESULT CALLBACK WndProc(HWND hWnd, UINT msg, WPARAM wParam, LPARAM lParam)
{
	switch(msg)
	{
	case WM_CREATE:
		_rich = CreateWindowEx(WS_EX_CLIENTEDGE,
							className,
							"Sample Text",
							WS_CHILD | WS_VISIBLE | ES_MULTILINE | WS_BORDER | WS_VSCROLL,
							10, 10,
							200, 200,
							hWnd,
							0,
							GetModuleHandle(0),
							0);
		
		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 );
		break;

	case WM_CLOSE:
		DestroyWindow(hWnd);
		break;

	case WM_DESTROY:
		PostQuitMessage(0);
		break;
	}

	return DefWindowProc(hWnd, msg, wParam, lParam);
}

int WINAPI WinMain(HINSTANCE hInstance, HINSTANCE hPrevInstance, LPSTR lpCmdLine, int nShowCmd)
{
	WNDCLASSEX wc;
	HWND _hWnd;

	ZeroMemory(className, 14);
	InitCommonControls();

	_hRich = LoadLibrary("RICHED20.DLL");
	if (!_hRich)
	{
		_hRich = LoadLibrary("RICHED32.DLL");
		if (!_hRich)
		{
			MessageBox(0, "Richedit control not loaded!", "Error", MB_ICONERROR);
			exit(0);
		}
		else
		{
			strcpy(className, "RichEdit");
		}
	}
	else
	{
		strcpy(className, "RICHEDIT_CLASS");
	}

	wc.cbClsExtra = 0;
	wc.cbSize = sizeof(WNDCLASSEX);
	wc.cbWndExtra = 0;
	wc.hbrBackground = (HBRUSH)(COLOR_WINDOW);
	wc.hCursor = 0;
	wc.hIcon = 0;
	wc.hIconSm = 0;
	wc.hInstance = hInstance;
	wc.lpfnWndProc = (WNDPROC)WndProc;
	wc.lpszClassName = "MainWindowClass";
	wc.lpszMenuName = 0;
	wc.style = 0;

	if (!RegisterClassEx(&wc))
	{
		MessageBox(0, "Error", "", MB_ICONERROR);
		exit(0);
	}

	_hWnd = CreateWindowEx(WS_EX_WINDOWEDGE,
					"MainWindowClass",
					"",
					WS_OVERLAPPEDWINDOW,
					0, 0,
					300, 300,
					0, 0,
					hInstance, 0);

	ShowWindow(_hWnd, SW_SHOW);
	UpdateWindow(_hWnd);

	MSG msg;

	while (GetMessage(&msg, 0, 0, 0) > 0)
	{
		TranslateMessage(&msg);
		DispatchMessage(&msg);
	}
	return msg.wParam;
}