By default, the Genesis header-right widget area uses an <aside> element. While this is fine most of the time, if you're using the header-right section for your primary navigation it is probably less than ideal for it to be wrapped in an <aside>. This will change the <aside> to a standard <div> element.

genesis-header-right-div.php

<?php

add_filter( 'genesis_markup_header-widget-area_output', 'prefix_opening_header_div', 10, 2 );
/**
 * Replace the opening header-right <aside> tag with a <div> tag to allow the
 * primary nav to be used in the header without being wrapped in an aside tag.
 *
 * @param   $tag   string  The current tag for the .header-right widget area.
 * @param   $args  array   The current args for genesis_attr()
 * @return  $tag   string  The modified tag for the .header-right widget area.
 */
function prefix_opening_header_div( $tag, $args ) {
	$tag = '<div ' . genesis_attr( $args['context'] ) . '>';
	return $tag;
}

add_filter( 'genesis_markup_', 'prefix_header_closing_div', 10, 2 );
/**
 * Replace the closing header-right </aside> tag with a </div> tag to allow the
 * primary nav to be used in the header without being wrapped in an aside tag.
 *
 * @param   $tag   string  The current tag for the .header-right widget area.
 * @param   $args  array   The current args for genesis_attr()
 * @return  $tag   string  The modified tag for the .header-right widget area.
 */
function prefix_header_closing_div( $tag, $args ) {
	if ( did_action( 'genesis_header' ) && ! did_action( 'genesis_after_header' ) ) {
		$tag = str_replace( '</aside>', '</div>', $args['html5'] );
	}
	if ( $args['echo'] ) {
		echo $tag;
	}
	return $tag;
}

Great snippet. This is probably the only example on the entire web of how / when to use the genesis_markup filter. I've been wondering how to use that.

I think for the example with the header right area you could also do this since it's a widget area (correct me if I'm wrong):

function wordpress_widgets_booststrapped_widget_params( $params ) { 
if ( ! is_admin() ) {
    if(isset($params[0]['id']) && $params[0]['id'] == 'header-right'){
      $params[0]['before_widget'] = '';
            $params[0]['after_widget'] = '';      }
        return $params;
  }
}
add_filter( 'dynamic_sidebar_params', 'wordpress_widgets_booststrapped_widget_params', 99 );