Tag: tuning systems
-
Music and Mathematics: The Tonnetz and the Harmonious Link
Introduction: The intimate bond between math and music Music and mathematics are often described as two sides of the same coin. The Tonnetz, a geometric diagram that maps the harmonic relationships between notes, provides a vivid illustration of this bond. Originating in the 18th century and popularized by Euler, the Tonnetz reveals how closely intertwined…
-
Music and Mathematics: How Tonnetz, Tuning, and Tonal Systems Reveal a Harmonic Universe
Introduction: When Numbers Meet Notes Music and mathematics share a rich, long-standing dialogue. The Tonnetz, a geometric diagram that maps harmonic relationships between notes, offers a vivid illustration of how numbers and ratios shape the sounds we hear. From Euler’s early iterations in 1739 to modern interpretations, this diagram helps illuminate why certain chords feel…