there is no Download button next to the songs on Apple Music on my Mac.

chillypop Said:

"there is no Download button next to the songs on Apple Music on my Mac."

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Two Things:

1. New iCloud Session:

Sign out of iTunes and then sign back in. Do so in the Account menu of the TV app or the Music app.

then...

2. Re-Authorize the Computer:

Go Here: Authorize or Deauthorize your Computer for iTunes Store purchases - Apple Support. You'd Deauthorize it, then Authorize it, using the Account menu of the TV app or the Music app.

See Authorization vs. association - Apple Community. You're allowed up to five authorized computers and a mix of ten associated computers and devices, no more than five of which are computers. Perhaps there are some authorizations or associations that you no longer need.

tt2

Do you have a subscription to either Apple Music or iTunes Match?

Right-click and see if either Download or Remove download are options for you.

tt2