Eth is the character you’re thinking if, not thorn.
Eth has voice on and thorn voice off.
Eth has voice on and thorn voice off.
Ð/ð (eth) certainly is the voiced th in Old English and modern Icelandic. I’m not sure why thorn was being used for ‘the’.
It’s a very old reference and may not be online, but what my germanic linguistics professor used with us Germanic linguistics grad students. He was a world renowned expert on the various futhark versions.
Note modern English collapsed the distinction into simpler orthography, “th” for both eth and thorn, so simplicity in spelling certainly happens.