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;
}