Analysis and modeling of entrainment in chorus singing

The dynamics of the contour of the fundamental frequency (F₀) of singing voices in a chorus is analyzed from the view point of `entrainment´ in singing behavior. The One-Mass-Two-Spring (OMTS) coupled system is used as the mathematical model of the contour of the F₀ of singing voices that are concurrently singing the same melody. Using this model, the characteristics of the F₀ dynamics of a voice singing in a chorus are parameterized by the mass, the coefficients of friction, and the spring factors of an OMTS system. It is experimentally confirmed that a steepest decent method can estimate the four model parameters, so that the model can generate the F₀ contour of a voice singing in a chorus with a less than 44.4 cents of RMS error. Preliminary experiments also show that experienced and novice singers can be correctly identified using the parameters of our model, because their entrainment behaviors are significantly different.