If you are on an iOS device, you don't need the "Music" app to buy songs; there is a dedicated storefront. Open the app (the purple icon with a star). Search for the song or album you want.
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Tap the next to the item to purchase it using your Apple ID. If you are on an iOS device, you
You can browse and purchase music directly through a browser on any device. Navigate to the Apple Music Web Player. Sign in with your Apple ID. buy itunes music without itunes
The music will then appear in your library across your devices.