Date of Last Revision
Bachelor of Science
Date of Expected Graduation
In an increasingly digital world, the analog tends to be neglected in exchange for the convenience and precision of digital devices. However, many analog systems exhibit physical phenomena that can be difficult to reproduce digitally. The purpose of this project is to explore the piano and parts of its sonic character that are not currently accounted for in digital systems. Specifically, when multiple notes are being propagated on a soundboard, they affect each other’s tone because each one changes the state of the soundboard. The effect is evident in the partials of each note: the partials (not quite harmonics but peaks in the power spectrum) will have the same frequencies but different power values. This changes the perception of the notes, the timbre. In digital devices, separately recorded notes are being summed as opposed to being played simultaneously on a piano, thereby losing this subtle change in timbre.
This work explores these two scenarios through computer simulations of a piano model. The model describes the soundboard, the strings, and the interaction between hammer and string. Using a finite difference method, we simulate the sound propagation of two notes being played separately and simultaneously. To investigate the effect of notes being played together, we determine power spectra for select locations on the soundboard and vibration patterns. To make the results relevant for real pianos within reasonable computational effort, we employ realistic parameters for materials and explore non-linear effects while maintaining a simplified soundboard geometry. Our results show measurable differences between the power spectra of two notes combined in the two scenarios (simultaneous and post-summed) and small non-linear effects.
Robert R. Mallik
Ben Yu-Kuang Hu
Thomas, Samuel, "Two Notes on a Piano" (2018). Williams Honors College, Honors Research Projects. 645.