This study aimed to adapt a method used in sound quality measurements named CI-MUSHRA (the multiple stimuli with hidden reference and anchor for cochlear implant users) to the Turkish language. The effect of low-frequency information and non-native musical stimuli on sound quality perception was investigated. Subjects completed the Turkish version of the MUSHRA test, called TR-MUSHRA, and the original CI-MUSHRA test. Participants also completed the Turkish monosyllabic word recognition test and the spectral temporal modulated ripple test (SMRT). 19 cochlear implant (CI) users and 16 normal-hearing (NH) adults were included. CI users demonstrated a lack of ability to detect the sound quality differences between original stimuli and stimuli with omitted low-frequency information up to 600 Hz in both tests. There was no significant main effect of the test version on sound quality ratings for the two groups. No significant correlation was found between mean sound quality scores, SMRT, and speech recognition in quiet and noise conditions. Our study suggests that CI users perform poorly in discriminating high-pass filtered musical sounds regardless of the language of the musical stimuli. The TR-MUSHRA can be used as a reliable research tool to evaluate the perceived sound quality.