Carnatic classical music from south India uses a collection of rhythmic structures called tālas. Each tāla is cyclic and organizes time in a particular way, including the number of beats per cycle. In this video, the performer’s hand gestures indicate the tāla. These same gestures could accompany any piece using this tāla. Compare also the hand gestures used in the American tradition of shape-note singing and this over-the-top classical conductor.
James Brown, “The Godfather of Soul,” discusses grooves in his music in this 2005 interview with Terry Gross of NPR (starting around 3:00). He compares two versions of the “I Got You” groove. He also describes how his groove shifted with his 1965 song “Papa’s Got A Brand New Bag.”
Philip Glass wrote Knee Play 1 for his 1976 opera “Einstein on the Beach.” Glass has said that numbers were sung to help the chorus learn the difficult rhythm patterns. He intended to eventually replace them with other lyrics, but changed his mind.