In a large number of electronic devices, users interact with the system by navigating through various menus. Auditory menus can complement or even replace visual menus, so research on auditory menus has recently increased with mobile devices as well as desktop computers. Despite the potential importance of auditory displays on touch screen devices, little research has been attempted to enhance the effectiveness of auditory menus for those devices. In the present study, I investigated how advanced auditory cues enhance auditory menu navigation on a touch screen smartphone, especially for new input gestures such as tapping, wheeling, and flicking methods for navigating a one-dimensional menu. Moreover, I examined if advanced auditory cues improve user experience, not only for visuals-off situations, but also for visuals-on contexts. To this end, I used a novel auditory menu enhancement called a "spindex" (i.e., speech index), in which brief audio cues inform the users of where they are in a long menu. In this study, each item in a menu was preceded by a sound based on the item's initial letter. One hundred and twenty two undergraduates navigated through an alphabetized list of 150 song titles. The study was a split-plot design with manipulated auditory cue type (text-to-speech (TTS) alone vs. TTS plus spindex), visual mode (on vs. off), and input gesture style (tapping, wheeling, and flicking). Target search time and subjective workload for the TTS + spindex were lower than those of the TTS alone in all input gesture types regardless of visual type. Also, on subjective ratings scales, participants rated the TTS + spindex condition higher than the plain TTS on being 'effective' and 'functionally helpful'. The interaction between input methods and output modes (i.e., auditory cue types) and its effects on navigation behaviors was also analyzed based on the two-stage navigation strategy model used in auditory menus. Results were discussed in analogy with visual search theory and in terms of practical applications of spindex cues.