Hi WDR1701,
To redownload purchased music to your computer, you will need to authorize it with your Apple ID you used to purchase the music and follow the steps in Redownload music deepening on the type of computer you have:
"Redownload music in iTunes on your PC
Before you can redownload music that you purchased from the iTunes Store, you need to authorize your PC using your Apple ID.
- Open iTunes.
- From the menu bar at the top of the iTunes window, choose Account > Purchased. If you use Family Sharing, you'll see Family Purchases instead of Purchased.
- Choose Music from the menu in the upper-left corner of the iTunes window.
- Find the music that you want to redownload. If you use Family Sharing, choose a family member next to Purchased to see their purchases.
- Click the download button next to a song or album.
Don't see the music that you purchased?"
"Redownload music from the iTunes Store in the Apple Music app on your Mac
Before you can redownload music that you purchased from the iTunes Store, you need to authorize your Mac using your Apple ID.
- Open the Apple Music app.
- From the menu bar at the top of your screen, choose Account > Purchased. If you use Family Sharing, you'll see Family Purchases instead of Purchased.
- Find the music that you want to redownload. If you use Family Sharing, choose a family member next to Purchased to see their purchases.
- Click the download button next to a song or album.
Don't see the music that you purchased?"
Take care.