Music I purchased on CD

Hi, I have read some previous posts and would like to clarify something.

I have a lot of music that i purchased on CD's many years ago. I have loaded them onto my Mac computer via iTunes, yet I cannot seem to access them on my iPad or other devices. Have I read it correctly that I must purchase and Apple Music account in order to have access to my already purchased music? That I have to pay a monthly subscription to Apple music just so I can hear music that I have already purchased? If I decide to do this ridiculous thing that once I cancel the subscription I will also lose the ability to listen to the music I had purchased? Is this correct?