(I'm a novice myself, so do not swallow my words.)<br />Smyth explains that accute is a "rising" tone (greek is said to have tones, rather than stresses as Latin does), grave "falling", and circumflex "rising and then followed by falling" tones.<br />(Chinese pronunciation signs have similar accent system.)<br />You can find some samples here:<br />
http://www.oeaw.ac.at/kal/agp/<br />By "wierd half-circle thing", if you don't mean it "circumflex" I have no idea what you mean. (A circumflex over the breathing sign???)