Hierarchical Custom Taxonomy Permalinks

I recently started playing around with the release candidate–which has been awesome so far–including trying to make some custom post types and taxonomies. Everything seems to be working really well except one small organizational issue in my taxonomy archive’s permalinks.

For this project, I’ve created a custom taxonomy called “type” for my custom post type “discography;” my register_taxonomy() function looks like this:

register_taxonomy('discotype',array('discography'), array(
    'hierarchical' => true,
    'labels' => $labels,
    'show_ui' => true,
    'query_var' => true,
    'rewrite' => array( 'slug' => 'discography/type' ),
  ));

The problem I’m having is that I’d like the urls of my individual taxonomy term archives to reflect the hierarchical relationships between terms. Right now, all term archives appear like this:

https://domain.com/discography/type/term
https://domain.com/discography/type/child-term

I’d like them to look like this:

https://domain.com/discography/type/term
https://domain.com/discography/type/term/child-term

Is there something I need to add to my register_taxonomy() function or .htaccess in order to get the links to look the way I want them to?

I feel like this is one of those problems with an obvious solution that I’m just missing and/or not googling the correct terms. Any direction would be greatly appreciated!