DDX7

Frequency Modulation (FM) synthesis generates complex timbres by modulating the frequency of a carrier oscillator using another modulator oscillator.

A signal $x[n]$ is expressed as:

$ x[n] = A_c \sin\left(2\pi f_c n T + I \sin\left(2\pi f_m n T\right)\right) $

where $A_c$ and $f_c$ are respectively the amplitude and frequency of the carrier, while $f_m$ is the modulator frequency, and $I$ is the modulation index that determines the spectral complexity. FM synthesis gained prominence in the 1980s with Yamaha’s DX7 synthesizer. It became a standard for generating bright, dynamic timbres in electric piano, bass, brass, and bell sounds.

DDSP Implementation

The DDX7 architecture employs a TCN decoder conditioned on a sequence of pitch and loudness frames to drive the envelopes of a few-oscillator differentiable FM synthesizer that features a fixed FM configuration with fixed frequency ratios, effectively mapping continuous controls of pitched musical instruments to a well-known synthesis architecture.

Audio Examples

	Reference	Anchor (LPC)
🪈 Flute
🎺 Trumpet
🎻 Violin
🎹 Piano

DDX7

	Full	Reduced	Reduced+AD	Reduced+CD
🪈 Flute
🎺 Trumpet
🎻 Violin
🎹 Piano