Changing attachment urls?

How can I change the format of attachment page urls from /[post-url]/[attachment-name]/ to /media/[attachment-name]/? I understand that I can override the output of get_attachment_link via the attachment_link filter, but I guess I need to change the redirect structure so WordPress knows how to handle these urls?

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You can do the following:

/* add new rewrite rule */
function attachment_rewrite( $wp_rewrite ) {
    $rule = array(
        'media/(.+)' => 'index.php?attachment=' . $wp_rewrite->preg_index(1)
    );

    $wp_rewrite->rules = $rule + $wp_rewrite->rules;
}
add_filter( 'generate_rewrite_rules', 'attachment_rewrite' );

/* redirect standard wordpress attachments urls to new format */
function redirect_old_attachment() {
    global $wp;

    if( !preg_match( '/^media\/(.*)/', $wp->request ) && isset( $wp->query_vars['attachment'] ) ) {
        wp_redirect( site_url( '/media/' . $wp->query_vars['attachment'] ) , 301 );
    }
}
add_filter( 'template_redirect', 'redirect_old_attachment' );