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The lack of fine structure information in conventional cochlear implant (CI) encoding strategies presumably contributes to the generally poor music perception with CIs. To improve CI users' music perception, a harmonic-single-sideband-encoder (HSSE) strategy was developed -, which explicitly tracks the harmonics of a single musical source and transforms them into modulators conveying both amplitude and temporal fine structure cues to electrodes. To investigate its effectiveness, vocoder simulations of HSSE and the conventional continuous-interleaved-sampling (CIS) strategy were implemented. Using these vocoders, live normal-hearing subjects' melody and timbre recognition performance were evaluated: a significant benefit of HSSE to both melody (p <; 0.002) and timbre (p <; 0.026) recognition was found. Additionally, HSSE was acutely tested in eight CI subjects. On timbre recognition, a significant advantage of HSSE over the subjects' clinical strategy was demonstrated: the largest improvement was 35% and the mean 17% (p <; 0.013). On melody recognition, two subjects showed 20% improvement with HSSE; however, the mean improvement of 7% across subjects was not significant (p > 0.090). To quantify the temporal cues delivered to the auditory nerve, the neural spike patterns evoked by HSSE and CIS for one melody stimulus were simulated using an auditory nerve model. Quantitative analysis demonstrated that HSSE can convey temporal pitch cues better than CIS. The results suggest that HSSE is a promising strategy to enhance music perception with CIs.