I want to transfer my music to my ipad

Setting aside the iCloud options, an item has to be in your library in order to sync. You can have items on an external drive in a library and remain on the external. The annoying thing will be unless you keep the external turned on and attached they will appear in your library as broken links. If you can live with that (there is not real harm) then fine. There are also more refined answers depending upon your exact habits in syncing. You could, for example, put a copy of the library on the external that you only use for syncing and another on the internal.

iTunes is great at ignoring aliases and symbolic links, particularly to other drives.

Copy your entire iTunes folder to the external drive. Hold down the option/alt key and start iTunes. When prompted to select a library select the iTunes Library.itl file in the moved folder (you can rename the folder but not the file). You are now using what will for a very short time be an identical library to your first. Your device will sync to this library

Okay, hold everything. Are you signed up for iTunes Match or Apple Music? All this iCloud stuff introduces new complications and I am not sure how it handles users who have multiple iTunes libraries. I have 4 libraries but I don't even have an iTunes Store account so I blithely do as I wish with them.

I don't have Match so I am just doing research here. The way I see to do it is to first back up everything. Then temporarily add all your music to your library, but do so with a method to leave the added media files on the external drive. Next send it all up to iCloud using Match followed by deleting the ones you really don't want on your computer but not deleting them from iCloud. The ones on the external drive we can delete the iTunes entries but not the actual files.

This second part is partly outlined in:

http://www.eprcreations.com/can-i-delete-my-music-library-after-using-itunes-mat ch/

http://www.imore.com/how-i-saved-140-gb-hard-disk-space-using-itunes-match