Do chromosomes change with time?
Short Answer: Probably, at least a little, much research still needs to be done.  For a great paper on this see here.

Your question can be answered in two parts:


Can Epigenetics be inherited - The answer to the simple question in your title, do chromosomes change with time, is yes.  There are copying errors, and carcinogenic mutations that can permanently change cells' genomes.  Less permanent is epigenetics, which are temporary chemical modifications to the DNA which changes how it is expressed. The epigenetics of the cell may change for various reasons from the cell undergoing mitosis to a wildly changing diet.  However, when sperm and egg cells are formed these epigentic modifications are typically wiped from the genome in order to remove any possible damaging marks.  However, there is a growing body of literature which states that some marks escape the purge and change the characteristics of the progeny.  Studies include scare-treating mice, 1836 famine, fatty rats, human psychological changes.  While the exact genes causing the change is unknown, there is clearly a strong correlation
Can Music Skill be Captured in Epigenetics - Music skill is to difficult to measure biologically, but likely has some links in speech skills, which would be captured in the brain, and muscle skills.  While there is some evidence for there being an muscle epi-memory, brain epigenetic inheritance is more tenuous (although see this exciting paper on RNA causing memory changes through epigenetics).  I would say the general scientific consensus is that there is some relation between epigentics, and memory, and music skill - there is a great deal of work still to be done.