This plus the shape of the body ends up causing the drum to have harmonics at a fifth (ratio of three to two), a major seventh (a ratio of 15 to eight) and an octave (ratio of two to one) above th...This plus the shape of the body ends up causing the drum to have harmonics at a fifth (ratio of three to two), a major seventh (a ratio of 15 to eight) and an octave (ratio of two to one) above the fundamental. Without these tubes the sound from the top of the bar would be exactly out of phase with sound from the bottom and tend to cancel since the top and bottom move in the same direction when struck (as was the case for a drum head without a body, mentioned above).
