Harmonic Porch Swing

A regular porch swing or rocking chair is tuned to "ring" at a fundamental pitch, with a frequency of say one swing or rock per second, and is capable of, but not optimized for "ringing" at higher harmonics. I would like to have a porch swing or rocking chair that would ring at a number of different harmonics at once, so if you were swinging at one time per second you would also be waving back and forth at 2 time per second and bouncing up and down at 4 times per second and vibrating at 8 times per second, etc on up to the parts of the contraption being made to really ring with musical tones so that the overall experience would be wholistic -- rhythmic and chordal. This kind of a swing-rocker would of course have to be tunable. I suppose electronics could be added and feedback loops incorporated but better to work out the acoustic version first. Retire in style.