Fig. 7: Controlling modulation in music stimuli.
From: Rapid modulation in music supports attention in listeners with attentional difficulties

Modulation in sound can be summarized by the modulation spectrum: The vertical axis on these 2D plots depicts audio frequency (0–8 kHz). The horizontal axis shows the amplitude modulation spectrum (amplitude fluctuations from 0 to 100 Hz). a Applying modulation to music results in a modulation spectrum with a peak corresponding to the rate of the added modulation. Upper: The pressure wave is multiplied by a modulator (in this case 16 Hz) to produce a modulated signal. Lower: This pressure wave is bandpass filtered, and fluctuation rates in each channel are shown in the modulation spectrum. b Validation of stimulus manipulations used in Experiment 4. The stimulus space is illustrated by these panels, each of which shows the difference in modulation spectrum (normalized power) between an unmodulated track and the experimental conditions derived from this track. The rate of added modulation increases moving rightward, while depth increases moving upward. The absence of differences elsewhere on the modulation spectrum shows that the experimental conditions were altered in a controlled way, with modulation properties different from the original only as specified (stimulus validation).