While Chilean-American singer-songwriter Francisca Valenzuela doesn’t possess Fiona Apple’s antipathy, an artist she is often compared to, she does have equal command of the piano. So Tuesday night, playing solo in the Penthouse of the Cooper Square Hotel, surrounded by the New York City skyline, she pounded out a honky-tonk riff. Leading off with “Quiero Verte Más”, in her peach skirt and Ramona Quimby legs, she was peppy and playful. Her strong vocals became poignant (and English) when she covered Nine Inch Nails’ “Hurt”, but then quickly reverted back. She closed with one number on guitar, “Muerdate La Lengua”, before lingering with fans under the exquisite views.