The two probabilistic models of rhythm vector and rhythm pattern can be combined in the HMM framework as shown in Table 1 and Fig. 2. This HMM gives the probability , where is the probabilistic model of rhythm score and is that of rhythm vectors and tempo fluctuation.
Rhythm estimation is to find the time sequence of states in the state
transition network, , that gives the maximum a posteriori
probability, , given a sequence of observed note lengths series,
. Maximizing is equivalent to maximizing
according to Bayes theorem. The optimal sequence of states in HMMs is
efficiently found through the well-known Viterbi algorithm. The sequence
of intended notes is estimated in the maximum likelihood sense.