A beam that resembles a Bessel beam on two scales is generated using a tunable acoustic gradient index of refraction (TAG) lens. The minor scale of the TAG-generated Bessel beam is nondiffracting and self-healing. The major scale of the beam diffracts while still forming a Bessel pattern due to the specific geometry of the TAG lens. The acoustic and optical theory behind the TAG lens is outlined, and the experimental beam itself is presented. The major and minor rings are explained, and the TAG beam is compared with both axicon-generated and conventionally focused Gaussian beams.