(Basically what was in my comment, but hopefully a bit clearer here.)
The only command that I can find which is defined in both tengwarscript and musixtex is \Tten. In tengwarscript it is defined with \newcommand which checks to see if it has already been defined (and throws an error if so). In \musixtex it is defined via a \let (which doesn't check), specifically \let\Tten=\ttie. Moreover, there is no other explicit use of \Tten in musixtex. So I would keep the tengwarscript definition of \Tten. For the musixtex version, you can use \ttie itself, or define another command to be equivalent to it, say \mTten. As tengwarscript explicitly checks to see if \Tten has been defined already but musixtex doesn't, the correct order to load them in is tengwarscript first and musixtex second. The following is a way to do this:
\documentclass{article}
\usepackage{tengwarscript}
\let\tengwarTten=\Tten
\usepackage{musixtex}
\let\mTten=\Tten
\let\Tten=\tengwarTten
\begin{document}
\end{document}
(Oh, and I'd like to see the final document ...)
\Tten.tengwarscriptlooks pretty good at namespacing all its internal macros (withteng@). Musixtex doesn't use that for anything specific other than to define it, so I would loadmusixtexfirst, thentengwarscriptand use\ttiefor themusixtexversion of\Tten(since\Ttenis just\letto\ttie). Of course, I may be missing something else that conflicts ... – Andrew Stacey May 18 '11 at 20:59tengwarscriptfirst, save the definition of\Tten, and then restore it after loading\musixtex:\usepackage{tengwarscript}\let\origTten=\Tten\usepackage{musixtex}\let\Tten=\origTten). – Andrew Stacey May 18 '11 at 21:02