単旋律におけるギター運指の最適化

抄録

This paper presents an optimization method for guitar fingering. The fingering is to determine a unique combination of string, fret and finger corresponding to the note. The method aims to generate the best fingering pattern for guitar robots rather than beginners. Furthermore, it can be applied to any musical score on single notes. A fingering action can be decomposed into three motions, that is, a motion of press string, release string and move fretting hand. The cost for moving the hand is estimated on the basis of Manhattan distance which is the sum of distances along fret and string directions. The objective is to minimize the total fingering costs, subject to fret, string and finger constraints. As a sequence of notes on the score forms a line on time series, the optimization for guitar fingering can be resolved into a multistage decision problem. Dynamic programming is exceedingly effective to solve such a problem. A level concept is introduced into rendering states so as to make multiple DP solutions lead a unique one among the DP backward processes. For example, if two fingerings have the same value of cost at different states on a stage, then the low position would be taken precedence over the high position, and the index finger would be over the middle finger.