Most Western music is based on a twelve-tone octave with the smallest interval being a half step (or half tone, or "semitone") up or down. Microtonal music contains intervals smaller than a semitone. (Imagine playing notes between the keys on a traditional piano.) You can hear microtonal music compositions in the work of modernist and experimental composers, from Charles Ives and Claude Debussy to Wendy Carlos and Aphex Twin.
Tolgahan Coğulu is a Turkish musician known for designing an adjustable microtonal guitar and performing unique arrangements of Anatolian folk music and Ottoman maqam music. Most recently though, he took a cue from his young son and built a fantastic microtonal guitar from LEGO!