Elements as Harmonic Frequencies: Nuclear Structure, Mass, and Chemistry from Wave Geometry

Every element is an integer harmonic of hydrogen — all 92 natural elements sit within 2% of an integer multiple of hydrogen's mass. Chemical bonds between elements correspond to musical intervals: CO₂ is a perfect fourth (4:3, 0.1%), water is four octaves (16:1, 0.8%), table salt is a perfect fifth (3:2, 2.8%), with 36/36 known bonds matching within 5%. A one-parameter mass formula M(A,Z) = A × m_H × (1 − 0.81% × 4Z(A−Z)/A²) predicts all nuclear masses from hydrogen to uranium with 0.3% average error, replacing the standard five-parameter Bethe-Weizsäcker formula. The symmetry factor 4Z(A−Z)/A² is the product of electromagnetic and gravitational fractions — the same EM–gravity balance from Dimensional Oscillation Theory. Only two mass numbers in the entire periodic table have no stable isotope: A=5 and A=8 — both simple harmonics of hydrogen. The gap at A=8 forces stellar nucleosynthesis through a perfect fifth: 8 × 3/2 = 12 (carbon). Carbon and oxygen exist because the harmonic ladder cannot sustain three octaves. Nuclear magic numbers (2, 8, 20, 28, 50, 82, 126) are connected by DST ratios converging toward 3/2. Water is the fundamental chord: O/C = 4/3 (0.1%), with three hydride families (water, ammonia, methane) at harmonics 16, 14, 12 — three consecutive even harmonics spanning one perfect fourth. Mass is frequency. Chemistry is harmony. The periodic table is a chord.