Music "sync" without using Apple Music subscription or losing current music
I have a new iMac. I have an iPhone X. I have music on my phone that is from an old computer I no longer have. I have recently purchased some songs (not from iTunes) and gotten them into the music app on my new computer. How can I get these songs from my computer onto my phone without deleting all my songs? When I go to "sync" it says it will erase all the songs from my previous computer because I cannot sync to two computers at one time. "Sync" implies the two devices will be synchronized. Having the computer with 8 songs override my phone with 100s is asynchronous. It should make them match; adding music from both devices until they mirror each other. How can I make this happen?