Click here to purchase the entire book in PDF format. Higher orders Ambisonics is a systems that works on ``orders'' - the higher the order of the system, the more accurate the reproduction of the sound field. If we just use the W-channel (the omnidirectional component) then we just get the pressure information and we consider it to be a 0th- (zeroth) order system. This gives us the change in pressure over time and nothing else. If we add the X-, Y- and Z-channels, we get the velocity information as well. As a result we can tell not only the change in pressure of the sound source, but also its direction relative to the microphone array. This gives us a 1st-order system. A 2nd-order Ambisonics system adds information about the curvature of the sound wave. This information is captured by a microphone that doesn't exist yet. It has a strange four-leaved clover shaped pattern with four lobes. Second-order periphonic $$U = P_{\Psi} \cos 2 \Psi$$ (11.39) $$V = P_{\Psi} \sin 2 \Psi$$ (11.40) $$W = P_{\Psi}$$ (11.41) $$X = P_{\Psi} \cos \Psi$$ (11.42) $$Y = P_{\Psi} \sin \Psi$$ (11.43) $$P_{n} = \frac{2 U \cos 2 \varphi_{n} + 2 V \sin 2 \varphi_{n} + W + 2 X \cos \varphi_{n} + 2 Y \sin \varphi_{n} }{N}$$ (11.44)