jQuery Ajax POSTing array to ASP.NET MVC Controller

Just set the traditional parameter to true:

$.ajax({
    type: "POST",
    url: "/update-note-order",
    dataType: "json",
    traditional: true,
    data: {
        orderedIds: orderedIds,
        unixTimeMs: new Date().getTime()
    }
});

Since jquery 1.4 this parameter exists because the mechanism to serialize objects into query parameters has changed.