how to backup not purchased music to icloud

Music, whether purchased or synchronised from your PC/Mac iTunes Music Library, is not backed-up to iCloud. Instead, should Music need to be restored to your iOS/iPadOS devices, you simply re-synchronise your iDevice with your PC/Mac.

Music cannot be natively transferred back from an iOS/iPadOS device to your PC/Mac Music Library. If you have an existing Music Library on PC/Mac, the Library itself must be transferred from old to new computer.

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how do I transfer my purchased music from Iphone7 to my new iMac

Purchased music can be downloaded from the Music app on your Mac by going to the purchased section in the iTunes Store. If you want new purchases on both devices turn on automatic downloads.