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Recurrence relationships for the lcm(C) in terms of the gcd’s of the powerset of C, and for the gcd(C) in terms of the lcm’s, are derived to unveil how the harmonic quotient lcm(C)/gcd(C) depends on the common undertones and overtones.

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This page is a summary of: The Tonal Graph of a Musical Chord: Arithmetic Relationships Describing Harmonicity and Harmonic Symmetry, Axioms, April 2026, MDPI AG,
DOI: 10.3390/axioms15050323.
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