Additive synthesis reconstructs sounds by summing sine wave partials; resynthesis verifies the accuracy of spectral analysis

Additive synthesis builds a complex sound as a weighted sum of sine waves: s(t) = Σ Aₙ · env_n(t) · sin(2π fₙ t + φₙ). Each partial has a frequency, amplitude, envelope shape, and phase. The synthesis is exact in principle — any waveform can be represented this way. In analysis/resynthesis, a real sound is analyzed (FFT or other method) to extract partial frequencies, amplitudes, and envelopes, and then reconstructed by additive synthesis. If the reconstruction sounds similar to the original, the analysis captured the perceptually important features. Differences between original and resynthesis reveal which partials matter. This technique is used to verify spectral analysis before computing dissonance curves: if important peaks were missed, the resynthesized sound will differ noticeably from the original.

Examples

Tingshaw bell analysis: 5 prominent peaks identified, resynthesized with those peaks. Original and resynthesis are perceptually similar, confirming that 5 peaks capture the essential character. Adding 3 smaller peaks to the resynthesis makes no perceptible difference — confirming those peaks can be ignored in dissonance curve calculations.

Assessment

You have analyzed an inharmonic instrument and identified 8 spectral peaks. Describe how you would use additive resynthesis to determine which of those 8 peaks are perceptually essential and which can be discarded in a simplified model for dissonance curve computation.