Hi Tweagle,
It sounds like you're hearing a short sound between music tracks. We're glad you've joined us in Apple Support Communities. Let's see if this helps.
If you haven't already, let's restart your Mac and see if the issue remains. Here's a quick guide: Log out, sleep, wake, restart, or shut down your Mac. A restart is a great step when experiencing unexpected behavior.
If the issue remains after following those steps, let us know if this happens with the same album or multiple tracks. If it's only one album please let us know which album. Additionally, are you an Apple Music subscriber, or are these tracks ones that were imported differently. Lastly, if you turn on Notifications in Apple Music > Preferences > General > and check When Song Changes, can you attempt to see if there's a name of a track that appears as a notification when this happens? This will defintively rule out the possibility of this being a short audio track causing the issue.
We hope that helps with your question and take care!