Modeling Perceptual Loudness of Piano Tone: Theory and Applications

The relationship between perceptual loudness and physical attributes of sound is an important subject in both computer music and psychoacoustics. Early studies of "equal-loudness contour" can trace back to the 1920s and the measured loudness with respect to intensity and frequency has been revised many times since then. However, most studies merely focus on synthesized sound, and the induced theories on natural tones with complex timbre have rarely been justified. To this end, we investigate both theory and applications of natural-tone loudness perception in this paper via modeling piano tone. The theory part contains: 1) an accurate measurement of piano-tone equal-loudness contour of pitches, and 2) a machine-learning model capable of inferring loudness purely based on spectral features trained on human subject measurements. As for the application, we apply our theory to piano control transfer, in which we adjust the MIDI velocities on two different player pianos (in different acoustic environments) to achieve the same perceptual effect. Experiments show that both our theoretical loudness modeling and the corresponding performance control transfer algorithm significantly outperform their baselines.