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Contemporary cochlear implants (CIs) use cathodic-leading symmetric biphasic (C-BP) pulses for electrical stimulation. It remains unclear whether asymmetric pulses emphasizing the anodic or cathodic phase may improve spectral and temporal coding with CIs. This study tested place- and temporal-pitch sensitivity with C-BP, anodic-centered triphasic (A-TP), and cathodic-centered triphasic (C-TP) pulse trains on apical, middle, and basal electrodes in 10 implanted ears. Virtual channel ranking (VCR) thresholds (for place-pitch sensitivity) were measured at both a low and a high pulse rate of 99 (Experiment 1) and 1000 (Experiment 2) pulses per second (pps), and amplitude modulation frequency ranking (AMFR) thresholds (for temporal-pitch sensitivity) were measured at a 1000-pps pulse rate in Experiment 3. All stimuli were presented in monopolar mode. Results of all experiments showed that detection thresholds, most comfortable levels (MCLs), VCR thresholds, and AMFR thresholds were higher on more basal electrodes. C-BP pulses had longer active phase duration and thus lower detection thresholds and MCLs than A-TP and C-TP pulses. Compared to C-TP pulses, A-TP pulses had lower detection thresholds at the 99-pps but not the 1000-pps pulse rate, and had lower MCLs at both pulse rates. A-TP pulses led to lower VCR thresholds than C-BP pulses, and in turn than C-TP pulses, at the 1000-pps pulse rate. However, pulse shape did not affect VCR thresholds at the 99-pps pulse rate (possibly due to the fixed temporal pitch) or AMFR thresholds at the 1000-pps pulse rate (the overall high performance may have reduced the changes with different pulse shapes). Notably, stronger polarity effect on VCR thresholds (or more improvement in VCR with A-TP than with C-TP pulses) at the 1000-pps pulse rate was associated with stronger polarity effect on detection thresholds at the 99-pps pulse rate (consistent with more degeneration of auditory nerve peripheral processes). The results suggest that A-TP pulses may improve place-pitch sensitivity or spectral coding for CI users, especially in situations with peripheral process degeneration.