Harlem trap king Asap Ferg is riding high on the success of his most recent album, “Always Strive and Prosper,” which entered at No. 2 on the Billboard R&B, hip-hop and rap charts, garnering strong reviews in The New York Times and Rolling Stone. And the stormy rapper’s recent single, “New Level,” featuring Future, was certified gold. He’ll be cranking it up on his North American Turnt and Burnt tour, which also features rising San Diego rapper Rob Stone. He recently had a breakthrough single with “Chill Bill,” which has been streamed more than 82 million times on Spotify and continues to move on the Billboard Hot 100 — it already has a remix version featuring D.R.A.M., Denzel Curry and Cousin Stizz. Also on the bill is Atlanta native Playboi Carti, a young artist whose music routinely gets described as “banging” and “turnt” by the hip-hop media promotion machine. The show is Tuesday, Nov. 22, at the National. Show starts at 8 p.m. and tickets cost from $25.50 to $30.50. thenationalva.com.