An improved mallet for percussive musical instruments comprises, in one embodiment, a shaft (1100, 1200, etc.), an adapter or inner core (300, 1400), an elastomeric surrounding core (400), and an elastomeric core overlay (1200). Optionally a cover (1300), or optionally two simultaneously-wound layers of yarn or other wrapping material (1705, 1710) are attached over the assembly. The adapter or inner core and the elastomeric surrounding core are formed together in molds (700, 900). Yarns are wrapped either by hand or with the use of a wrapping machine comprising a rotary motive source, a chuck (1810), and wrapping arms (1825, 1830) for interweaving the layers of yarn. In an alternative embodiment the adapter has a through-hole to permit extension of the shaft through the adapter to near the top of the mallet head. Numerous percussive sound effects are achieved by selection of the properties of the adapter or inner core, surrounding core, overlay, and yarn layers.