Tag: Bach
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An inner duty: 35 years to bring Bach’s lost organ works to light
Introduction: a long pursuit, a sudden breakthrough In the world of classical music scholarship, some discoveries arrive like a bolt from a clear sky, while others simmer for decades until the moment of revelation finally crystallizes. The recent unveiling of two previously unknown organ works attributed to Johann Sebastian Bach marks one of those rare…
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An inner duty: Unveiling Bach’s Lost Organ Works After 35 Years
Introduction: A quest that never truly ended When a musicologist names a discovery world sensational, listeners expect fireworks. Yet the newest revelation about Johann Sebastian Bach’s music—two previously unknown organ works—arrived not as a sudden eruption but as the culmination of a patient, lifelong pursuit. Peter Wollny, the scholar at the center of this breakthrough,…
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An inner duty: the 35-year quest to bring Bach’s lost organ works to light
Introduction: A patient hunt for Bach’s hidden organ works In a field where manuscripts can vanish as easily as they appear, a long, quiet pursuit finally yielded a remarkable discovery. The recent revelation of two previously unknown organ works by Johann Sebastian Bach has electrified classical music circles. The work belongs to a narrative of…
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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.…
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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…