Tag: 12-tone


  • Music and Mathematics: Tonnetz, Tuning, and 12-Tone

    Music and Mathematics: Tonnetz, Tuning, and 12-Tone

    Harmony as a Mathematical Map Music and mathematics share a long, intertwined history. A striking illustration of their bond is the Tonnetz, a geometric diagram that encodes the harmonic relationships among the notes of the musical scale. First glimpsed in Euler’s Tentamen Novae Theoriae Musicae (1739), the Tonnetz organizes closely related tones into visual clusters.…