alphabetize the taxonomy term page without views
The taxonomy module uses the taxonomy_term_page function to build the page that list the nodes attached to a term. But the function that really do the query is the taxonomy_select_nodes that is called by this previous function.

Remember: Never hack core

So you can implement a custom module and use the hook_menu_alter to rewrite the page callback for the taxonomy/term/%taxonomy_term path using a new function based on the taxonomy_term_page to call your custom taxonomy_select_nodes function that perform the changes you need to order the nodes that way.

You'll need to do something like this:

function mymodule_menu_alter(&amp;$items) {
  // Rewrite the taxonmy term page callback
  $items['taxonomy/term/%taxonomy_term']['page callback'] = 'mymodule_taxonomy_term_page';
}


After that you'll have to implement the mymodule_taxonomy_term_page function in order to be able to make the changes you need on the taxonomy_select_nodes() call:

function mymodule_taxonomy_term_page($term) {
  # code...

  if ($nids = mymodule_taxonomy_select_nodes($term-&gt;tid)) {
    # code...
  }
  # code...
}


Finally:

function mymodule_taxonomy_select_nodes() {
  # code...
}


You'll must JOIN the node table to build the query in the mymodule_taxonomy_select_nodes function because the taxonomy_index table doesn't have the node title. 

Notice that will change the behavior of all taxonomy term pages.

For more info about how to create a custom module see http://drupal.org/node/361112.