The following snippet
    [DllImport("winmm.dll", EntryPoint = "timeBeginPeriod")]
    public static extern uint TimeBeginPeriod(uint uMilliseconds);
    static void Main(string[] args)
    {
        if (TimeBeginPeriod(1) != 0)
            Console.WriteLine("TimeBeginPeriod failed!");
        Console.WriteLine("Sleep");
        Stopwatch sw = Stopwatch.StartNew();
        for (int i = 0; i < 10; i++)
        {
            Thread.Sleep(1);
            Console.WriteLine(sw.ElapsedTicks * 1000d / Stopwatch.Frequency);
            sw.Restart();
        }
        Console.WriteLine("Threading.Timer");
        sw = null;
        System.Threading.Timer t = null;
        int n = 0;
        t = new Timer(state =>
        {
            if (sw == null)
                sw = Stopwatch.StartNew();
            else
            {
                Console.WriteLine(sw.ElapsedTicks * 1000d / Stopwatch.Frequency);
                n++;
                sw.Restart();
            }
            if (n == 10)
                t.Change(Timeout.Infinite, Timeout.Infinite);
        }, null, TimeSpan.FromMilliseconds(1), TimeSpan.FromMilliseconds(1));
        Console.ReadKey();
    }
will produce e.g. this output:
Sleep
0.151834939915548
0.757358826331279
0.786901687225611
0.712520725399457
0.715593741662697
0.798704863327602
0.5724889615859
0.648825479215934
0.436927039609783
0.517873081634677
Threading.Timer
15.5841035662354
14.8620145856526
15.1098812837944
14.4202684978119
15.3883384620112
14.7210748852159
15.307462261265
15.7125416777831
14.5991320125882
15.6035194417168
According to the net, e.g. a comment by Hans Passant, timeBeginPeriod affects the regular (.net) timers. So why does my timer still have this coarse granularity? Thread.Sleep seems to do just fine.
Maybe relevant: This runs on Windows 7, 64bit, .net 4, inside VMWare.