Piano virtuoso Chucho Valdes is a welcome visitor whenever good fortune brings him to this country. The winner of Grammy Awards, Latin Grammy Awards, multiple doctorates and enough honors to fill this page leads his band, the Afro-Cuban Messengers, on a cross-country tour, arriving at George Mason University’s Center for the Arts on Friday. His mission is to perform the remarkable music from his latest recording, “Chucho’s Steps,” in every major American city. Along the way, he will make his first appearance on the Carnegie Hall main stage since 1978. The inspiration for “Chucho’s Steps” was the mathematical scheme developed by John Coltrane for his recording of “Giant Steps,” a system too complicated for most musicians to emulate. Predictably, Chucho triumphed over it, composing his own parallel improvisations and variations. The album is a collection of eight numbers incorporating jazz, bop, swing, world fusion and Afro-Cuban ritual music. Since beginning the project eight years ago and recording the album in 2009, he has continually revised every number.

Speaking from Spain through an interpreter, Valdes explained, “I modified the Afro-Cuban rhythm beat of 6/8 by changing it to 11/8 and 13/8. I mixed it with rhythmic changes from the drums and percussion to give a freshness.”