Spectral mapping transforms the partials of one sound to a target spectrum while preserving the overall tonal character

A spectral mapping is a frequency transformation applied to the partials of a source sound: each partial at frequency fᵢ is moved to a new frequency dᵢ according to a mapping function f→d. This is applied in the frequency domain (FFT), then reconstructed via inverse FFT. The goal is to create sounds with a desired spectrum (e.g., matched to a non-12-tet scale) while preserving the richness and character of an existing instrument. For example, to create a ‘flute-like’ sound for 11-tet music: take a real flute recording, extract its spectral envelope, apply a mapping that relocates partials to the 11-tet-related spectrum, and reconstruct. The mapped sound has the tonal quality of a flute but will be consonant in 11-tet. Amplitude and phase information from the source are grafted onto the destination partial structure.

Examples

Chapter 13: transforming a harmonic guitar sound into one compatible with an 11-tet tuning by mapping harmonic partials to the 11-tet-related spectrum positions. The result sounds guitar-like but is built for 11-tet. Spectral mapping for 7-tet Thai music: transform various timbres to have bar-like spectra while retaining their original sound character.

Assessment

Describe the block diagram of a spectral mapping system. What are the source spectrum and destination spectrum? Why must the number of partials in source and destination match in the simplest version? What goes wrong if the destination spectrum is much sparser than the source?