How to query for posts without a post_format

Question

You have to query post that has no post format attached:

$args = array(
  'post_type' => 'post',
  'tax_query' => array(
    array(
      'taxonomy' => 'post_format',
      'field' => 'slug',
      'operator' => 'NOT IN',
      'terms' => get_terms('post_format')
    )
  )
);

To improve performance you can hardcoding the post format instead of using get_terms to retrieve them:

$args = array(
  'post_type' => 'post',
  'tax_query' => array(
    array(
      'taxonomy' => 'post_format',
      'field' => 'slug',
      'operator' => 'NOT IN',
      'terms' => array('post_format-aside','post_format-chat','post_format-gallery','post_format-link','post_format-image','post_format-quote','post_format-status','post_format-video','post_format-audio')
    )
  )
);

Edit

Once you ask for it in comments, I’ll give you the raw SQL query that can perform same task. Please note that once post without post format are not stored anywhere (standard post format means no post format), to obtain what you want you need to nest 2 queries with the nested containing a join among 3 tables.
This is very far from what you can call a performant query. For this it’s a good idea cache the result in a transient:

function post_without_formats() {
    $cached = get_transient('post_without_formats');
    if ( $cached ) return $cached;
    global $wpdb;
    $post_without_format = $wpdb->get_results(
      "SELECT * FROM $wpdb->posts WHERE post_status="publish"
       AND post_type="post" AND ID NOT IN (
         SELECT p.ID FROM $wpdb->posts as p
         LEFT JOIN $wpdb->term_relationships as tr ON tr.object_id = p.ID
         LEFT JOIN $wpdb->term_taxonomy as tt ON tt.term_taxonomy_id = tr.term_taxonomy_id
         WHERE p.post_status="publish" AND p.post_type="post"
         AND tt.taxonomy = 'post_format'
         GROUP BY p.ID
       )"
    );
    set_transient('post_without_formats', $post_without_format);
    return $post_without_format;
}

function reset_post_without_formats($term, $taxonomy) {
  if ( $taxonomy == 'post_format' ) {
    delete_transient('post_without_formats');
    post_without_formats();
  }
}

add_action('edited_term_taxonomy', 'reset_post_without_formats', 99, 2);

As you can see I reset the transient everytime a post format is added or removed from a post. This will slow down a bit your backend but will increase the frontend speed.

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