Stochastic Modeling of Expressiveness: Representing the Temporal Evolution of the Descriptors Using HMM

Abstract

Different interpreters do not play identically during a music performance, introducing their own expressive features. Although these features are perceptually recurrent for each musician, the deterministic modeling is a difficult task, making it more interesting to model by a stochastic patterns approach. This paper aims to model the temporal evolu- tion of the acoustic features using HMM (Hidden Markov Model) note-by note, intrinsically related to the expressive intent of the artist performing the musical fragments. Descriptors related to changes in dynamics, tempo, attack and release have been implemented and tested. Dynamics was described by the RMS (Root Mean Square) energy changes for each note in comparison with the previous. Tempo was described by the IOI (Inter Onset Interval) deviation nor- malized by the note duration according to the score. Finally, the attack and release were described by the logarithm of their duration time. The methodology is divided into two parts: first the optimal number of states for each HMM is determined by taking the maximum of the curve between number of states and recognition rate. In the second, the recognition achieved by optimal number of hidden states is analyzed together with the structure of the probabilities of transitions between the states matrix. The training and testing data used in recognition tests were executions of the same fragment for clarinet of the fourth movement of Mozart's Quintet. Five musicians performing six times each were recorded. The results indicated better recognition rates using tempo, dynamics and attack time descriptors, reaching 60 hitting percent, with two, six and five hidden states respectively.