This paper studies the best achievable reference tracking performance of MIMO linear time-invariant (LTI) feedback systems with partial reference information. The reference signal to be tracked is a multi-tone sinusoidal signal. It is assumed that, other than the instantaneous values of the reference signal, only the frequencies of the sinusoidal components are known. The tracking performance is measured by the energy of the tracking error. With this partial information of the reference signal, we consider an averaged performance measure and obtain an explicit expression of the best achievable performance. The expression shows how the harmonic frequencies and the zero directions may affect the performance, and further, how a performance degradation may result under the available partial information.