A band of high-frequency modes in the range 50-150 kHz with intermediate toroidal mode numbers 4<n<10 are commonly observed in the core of supershot plasmas on TFTR [R. Hawryluk, Plasma Phys. Controlled Fusion 33, 1509 (1991)]. Two distinct varieties of magnetohydrodynamic (MHD) modes are identified, corresponding to a flute-like mode predominantly appearing around the q=1 surface and an outward ballooning mode for q>1. The flute-like modes have nearly equal amplitude on the high-field and low-field side of the magnetic axis, and are mostly observed in moderate performance supershot plasmas with tau(E)<2 tau(L), while the ballooning-like modes have enhanced amplitude on the low-field side of the magnetic axis and tend to appear in higher performance supershot plasmas with tau(E)>2 tau(L), where tau(L) is the equivalent L-mode confinement time. Both modes appear to propagate in the ion diamagnetic drift direction and are highly localized with radial widths Delta r similar to 5-10 cm, fluctuation levels (n) over tilde/n, (T) over tilde(e)/T-e<0.01, and radial displacements xi(r) similar to 0.1 cm. Unlike the toroidally localized high-n activity observed just prior to major and minor disruptions on TFTR [E. D. Fredrickson et al., Proceedings of the 15th International Conference on Plasma Physics and Controlled Nuclear Fusion Research, Seville, Spain (International Atomic Energy Agency, Vienna, 1995), No. IAEA-CN-60/A-2-II-5], these modes are typically more benign and may be indicative of MHD activity excited by resonant circulating beam ions. (C) 1996 American Institute of Physics.