Scientists found out as the brain ages the ability to store memories declines leading to decline in cognitive processes such as short-term memory.  Neuroscientists discovered that memory development involves many parts of the human brain. To memorize music people need to use auditory, visual, and motor memory. People use visual memory while looking at the piece of music sheet. This is similar to memorizing words. Auditory memory is a memory memorizing the piece sound. Trained musicians show stronger brain activation in auditory tasks. Motor memory is connected to the movements of the body such as moving fingers. This enhances the ability of memorization. 

Image source https://images.app.goo.gl/beTiDtttkJWm4JJh8

This study shows the relationship between age and the ability to memorize music. Scientists used Quasi-experimental study design. Scientists tested participants from 23 years old to 66 years old and high school students from 14 to 18 years old. All the participants learned music and played the instruments for at least one year. Tasks for the participants were to identify the errors in a short music to test auditory memory. To test visual memory, participants memorized and played difficult music based on their memory. 

Three types of memory were discovered; speed of memory, auditory. Data showed how age affects the speed of memory. The adult age group was faster than younger age groups.There was no significant difference in visual memory accuracy between two different age groups. However, the adult age group had a slightly higher average score. In the Auditory Memory test, the adult group also had a higher score in accuracy than the younger age group.

Source

View of the neuroscience between musical stimulation and enhancing short term memory with age. (n.d.). https://www.jsr.org/hs/index.php/path/article/view/497/210