Minimax Viterbi Algorithm for HMM-Based Guitar Fingering Decision

Previous works on automatic fingering decision for string instruments have been mainly based on path optimization by minimizing the difficulty of a whole phrase that is typically defined as the sum of the difficulties of moves required for playing the phrase. However, from a practical viewpoint of beginner players, it is more important to minimize the maximum difficulty of a move required for playing the phrase, that is, to make the most difficult move easier. To this end, we introduce a variant of the Viterbi algorithm (termed the “minimax Viterbi algorithm”) that finds the path of the hidden states that maximizes the minimum transition probability (not the product of the transition probabilities) and apply it to HMM-based guitar fingering decision. We compare the resulting fingerings by the conventional Viterbi algorithm and our proposed minimax Viterbi algorithm to show the appropriateness of our new method.