cpt-rewrites.php

<?php
add_action( 'init', 'rewrites' );
add_filter( 'post_type_link', 'filter_post_link', 1, 2 );

function rewrites() {
	add_rewrite_tag( '%artist%', '([^/]+)' );
	add_rewrite_rule(
		'songs/([^/]+)/([^/]+)?$',
		'index.php?artist=$matches[1]&songs=$matches[2]',
		'top'
	);
	add_rewrite_rule(
		'albums/([^/]+)/([^/]+)?$',
		'index.php?artist=$matches[1]&albums=$matches[2]',
		'top'
	);
}

function filter_post_link( $permalink, $post ) {
	// Check if the %artist% tag is present in the url:
	if ( false === strpos( $permalink, '%artist%' ) ) {
		return $permalink;
	}
	$permalink = replace_artist_rewrite_tag( $permalink, $post );

	return $permalink;
}

function rewrite_preview_url( $permalink, $post ) {
	if ( in_array( get_post_type( $post->ID ), array( 'albums', 'songs' ) ) ) {
		$permalink = add_query_arg( 'artist', '%artist%', $permalink );
		$permalink = replace_artist_rewrite_tag( $permalink, $post );
	}
	return $permalink;
}

function replace_artist_rewrite_tag( $permalink, $post ) {
	if ( 'albums' === $post->post_type && get_post_meta( $post->ID, 'compilation', true ) ) {
		$artist = 'compilations';
	} else {
		if( 'songs' === $post->post_type ) {
			$artist_id = get_post_meta( $post->ID, 'primary_artist', true );
		} else if( 'albums' === $post->post_type ) {
			$artist_id = get_post_meta( $post->ID, 'artist', true );
		}

		$artist_query = new WP_Query( array(
			'post_type' => 'artists',
			'p' => absint( $artist_id ),
		) );

		$artist = $artist_query->have_posts() ? $artist_query->posts[0]->post_name : 'unknown-artist';

	}

	$artist = urlencode( $artist );

	// Replace '%artist%'
	$permalink = str_replace( '%artist%', $artist , $permalink );
	return $permalink;
}