Half right. What I mean is... all the information carried on a full wave is within a 1/4 wave. A half wave is a duplication of a 1/4 wave, as it is a reciprocal wave, just different because of time, and on a horizontal path. A half wave is the same as a full wave, just turned upside down. So... (and now my head is starting to hurt...) a 1/4 wave propagation will accurately reproduce sound to the human ear, which is a complicated enough machine to resolve the missing tones.