Harmonic-temporal model with multiple function for sound synthesis.
Toru Nakashika, Tetsuya Takiguchi, Yasuo Ariki · The Journal of the Acoustical Society of America · 2011
The most popular method for synthesizing musical timbre sound is additive synthesis, where the timbre sound is obtained by adding multiple harmonic partials with different time envelopes. Additive synthesis has many advantages such as high flexibility to control each partial individually and easy way to reconstruct musical tones from the spectrum. However, it is difficult to control the harmonic partials as a whole because time envelopes of each harmonic are independent of one another. Furthermore, the model has many parameters which are difficult to control. For example, many instruments require dozens of harmonics, where each envelope consists of about 1000 time points, and the parameters are hard to handle. In this paper, additive synthesis is extended to easily control a whole sound with only a few parameters. In this approach, all the time envelopes of each harmonic are parametrically modeled by a 2-D function, called multiple function. Two types of multiple functions are introduced with the update rules of their parameters based on an EM algorithm. The harmonic-temporal shape of an instrument sound can be directly controlled by changing the parameters of the proposed function slightly.