At the end of the nineteenth and beginning of the twentieth century a powerful musical phenomenon which would become known as "Jazz" began to take shape. New Orleans had had a strong culture of African American folk music and ragtime, and when the Creole musicians were kicked out of the orchestras on the basis of their "race," they were forced to take their classical instruments and professional chops to the streets. The subsequent merging of styles and instrumentations was an organic process from which many new types of music emerged ("Jazz" is often used as an umbrella term used).
The piece above is by Jelly Roll Morton, self-proclaimed inventor of Jazz. Listen as the left hand holds the bass in a single key while the right journeys wherever it wishes. You could call it a rag. Interestingly much of the classical, European piano music from the same era not only uses similar harmonies, but the same type of arrangement.
Listen again and hear how there are strategically placed "wrong" notes. They're not actually wrong (obviously) but they break out of the expected harmonic patterns and make you ear dance a little to catch up. "The Crave" has some examples of 'blue' thirds: when the major and minor third are played almost simultaneously to give an emotive quality seldom heard outside of Jazz. Interestingly, classical musicians of the same era were also fond of this sonority in different contexts. Below is a jazzy improvisation by Gabriela Montero on Rachmaninoff's third piano concerto: