Anonymous ajax GET always returns HTML or 404. Browsers work as expected.

I just set up a fresh Drupal 7 site and created 50 articles with the Devel module.
Everything seems to work fine when using a browser, but I can't get the site to return json when using jQuery's ajax function.
I have all necessary permissions granted.

Browser (Chrome, Firefox), also cURL from command line:
http://mysite.local/node.json works fine
http://mysite.local/node/1.json works fine

jQuery (see code below):
http://mysite.local/node.json returns "404 file not found"
http://mysite.local/node/1.json returns the full html page, as if I requested http://mysite.local/node/1

jQuery ajax:

$.ajax({
  url: "http://mysite.local/node.json", // I have tried many, many things here. none return json.
  type: "GET",
  contentType: "application/json",
  type: "json",
  success: function(result) {
    console.log(result);
  }
});