Abstract: An apparatus or apparatus system for vibration control, by harmonic optimization technology, of vibrations in the cantilever or barrel, portion of a device from which projectile is fired or launched along the centerline of the cantilever. More particularly this invention relates to rifles, where the rifle barrel is a cantilever portion, and methods and apparatus for increasing the accuracy of firing projectiles. The invention is principally directed to a method and apparatus including a mass device affixed to a flexible cylinder extension at the muzzle end, inertial mass devices, having combustion pressure reduction features, affixed intermediate the muzzle end and the cartridge chamber, and a spring suspension system between barrel and rifle stock affixed proximal to the cartridge chamber. This system decreases the angular dispersion of barrel vibrations at the muzzle resulting from the firing of projectiles through such barrels.