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About this paper
X. Hernandez, Luis Nasser, Pablo Garcia-Valenzuela
An interdisciplinary team from UNAM, Loyola University Chicago, and SAE Institute Mexico developed an "Elastic Overtone" 12-tone equal temperament system that redefines the octave and harmonic series to achieve
Key insights
- The physical constraints of traditional 1D vibrating instruments (2:1 octave, integer harmonics) are not fundamental to musical perception and can be altered in digital sound environments.
- A slightly non-2:1 octave ratio (specifically x = 1.9725786270914...) allows for 'perfect' harmonic alignment of key intervals like the fifth within an equal temperament framework.
- By designing a custom, 'elastic' overtone series, it is possible to achieve the desired harmonic coincidences that contribute to consonance while maintaining the structural benefits of 12-TET.
Summary by alphaXiv.
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