How can I display a specific category on Front-Page

That’s easy, just add following code in your theme’s functions.php file:

function 348118_my_home_category( $query ) {
    if ( $query->is_home() && $query->is_main_query() ) {
        $query->set( 'cat', '1234' );
    }
}
add_action( 'pre_get_posts', '348118_my_home_category' );

In the above code change 1234 with the ID of your music category.