Formulation of a Cubic Difference Tone Spectra framework

Determine whether a coherent Cubic Difference Tone Spectra (CDTS) framework can be formulated for synthesizing cubic difference tones, particularly the lower cubic difference tone at 2f₁ − f₂, while accounting for cubic nonlinearity, frequency-ratio-dependent perceptual gain, and sensitivity to stimulus and listener conditions.

Background

The paper identifies Cubic Difference Tones (CDTs), especially the lower CDT at 2f₁ − f₂, as a demanding direction for future research. Unlike the quadratic case, the cubic distortion function would be homogeneous of degree three and would generate a system with greater multiplicity of local inverses. More fundamentally, the perceptual amplitude of the lower CDT depends strongly and non-monotonically on the primary-frequency ratio, so the approximately interval-invariant assumptions underlying Quadratic Difference Tone Spectra do not transfer directly.

A viable CDTS framework would therefore need a distortion function incorporating a frequency-ratio-dependent gain whose form is not yet well established. It would also need to address the lower CDT’s greater sensitivity to absolute level, primary-level imbalance, and individual cochlear variability, all of which complicate the definition of a generally valid synthesis target.