Designing a scale for an inharmonic instrument requires FFT analysis followed by computing dissonance curve minima

To find the natural scale for an inharmonic instrument: (1) record the instrument and apply FFT analysis (using windowing to reduce spectral leakage); (2) identify the most significant spectral peaks (simplify: keep only the peaks that survive across multiple recordings and analysis windows); (3) construct the simplified spectrum as a list of partial frequencies and amplitudes; (4) compute the dissonance curve by sweeping the interval ratio from 1:1 to 2:1 (or beyond), at each interval calculating the total sensory dissonance between all pairs of partials of the two sounds; (5) identify local minima — these are the consonant intervals; (6) the set of minima defines the related scale. Practical considerations: spurious peaks cause extra scale steps; missing peaks cause missing steps; analyzing multiple recordings improves reliability.

Examples

Tingshaw bell: FFT reveals peaks at 2368, 4784, 5553, 7921, 10103 Hz. Simplified spectrum with those five peaks. Compute dissonance curve → minima at specific ratios → these define a pentatonic-like scale for the tingshaw. Chaco rock: multiple FFT snapshots averaged to find consistent peaks before scale design.

Assessment

Describe step by step how you would determine what scale to use when composing for a set of metal mixing bowls. At which step is it most critical to simplify the spectrum, and what goes wrong if you include too many spectral peaks or too few?