Is there a template file to list all terms of a given custom taxonomy?

You can include the same file in template-composers-terms.php and template-interprets-terms.php like that :

<?php
/* Template Name: List of composers */

$tax = "composer";
require "include/file_which_does_all_the_work.php";

and if the page slug is the same that the taxonomy slug, you can save the line $tax = ... with that in the included file :

$tax = $GLOBALS["wp_query"]->query["pagename"];