Background: Understanding the nature and extent of sensorimotor decline in ageing individuals and those with neurocognitive disorders NCD, such as Alzheimer's disease, is essential for designing effective music-based interventions. Objective: Our understanding of rhythmic functions remains incomplete, particularly in how ageing and NCD affect sensorimotor synchronisation and adaptation to tempo changes. This study aims to fill this knowledge gap. Methods: Patients from a memory clinic participated in a tapping task, synchronising with metronomic and musical sequences, some of which contained sudden tempo changes. After exclusions, 51 patients were included in the final analysis. Results: Participants' mini-mental state examination scores were associated with tapping consistency. Additionally, age negatively influenced consistency when synchronising with a musical beat, whereas consistency remained stable across age when tapping with a metronome. Conclusions: The ability to extract a beat from a musical signal diminishes with age, whereas the capacity to maintain a beat remains relatively constant. However, both processes may decline at moderate or severe stages of NCD. Moreover, the results indicate that the initial decline of attention and working memory with age may impact perception and synchronisation to a musical beat, whereas progressive NCD-related cognitive decline results in more widespread sensorimotor decline, affecting tapping irrespective of audio type. These findings underline the importance of customising rhythm-based interventions to the needs of older adults and individuals with NCD, taking into consideration their cognitive as well as their rhythmic aptitudes.