Perhaps it should be emphasized here that for good piano synthesis, multiple filtered delay loops should be employed for each note rather than the single-loop case shown here, as discussed in §4.11. The multiple delay loops may correspond to multiple strings hit by the same hammer, both polarization planes on a single string, and/or longitudinal waves. Thus, in a piano synthesizer, there should be at least two filtered delay loops, slightly detuned (different loop delays), both excited by in some manner6.4 (e.g., they can each receive an identical copy), and the delay loop outputs should be summed or else realistically coupled as described in §G.11 [416]. A digital waveguide piano synthesis implementation including both transverse and longitudinal waves is described in [27].