Can you show us what you mean? I don’t know what Joseph and
Technicolor Dreamcoat are.

Welcome Rhonda.

Can we have an image, a link, or something to look at ?

Rhonda, in order for us to help it would be best if you showed us an image of the type you want us to identify. That musical has been out a long time and there have been several designs used for the lettering for the show. Which one do you want ID‘ed?

Sorry — I realized this a bit late and then couldn’t add an attachment when I edited my post.
Here it is…
Thanks again!

I think it’s pretty obviously hand-lettered — no two instances of the same letter (E, A, C and R, for example) are the same.

That said, the ’70s vibe and tiny serifs remind me of ITC Serif Gothic.
http://www.myfonts.com/fonts/linotype/itc-serif-gothic/