Tag: equal temperament
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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…
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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.…