同時発音の相関を考慮した確率モデルによる音楽の和声推定

摘要

近年，楽曲検索・推薦技術を目的とした音楽的特徴を考慮した音の生成モデルが提案されている．音楽的特徴の中でも和声は重要な要素のひとつであり，音の組み合わせパターンと，前後の和声との関係から決定される要素である．しかし，従来しばしば用いられるマルコフモデルは同じ和声が継続するときの継続長や同時に鳴る音の相関を適切に表現することができず，和声推定の精度が不十分である原因と考えられる．そこで本研究では，和声の状態遷移確率にセミマルコフモデルを導入し，音の観測確率に音の同時発音の相関を表現できるボルツマンマシンを用いた手法を提案する．この提案モデルを実装し，実験を行った結果，従来手法に比べ高い推定精度を持ち，より正確に和声の遷移を表現できることが示された．%Recent research in music retrieval and recommendation requires a rich musical feature set in order to analyze the contents more deeply. One of the most important musical features is chord. Chord is determined by the pattern of the simultaneous tones, but is also dependent on the previous and the following notes. Raphael, et al., (2003) proposed to use a hidden Markov model to represent the temporal correlation. However, their model could not represent the real state duration well, that is, the same chord tends to continue and frequently transits to the other chord synchronizing with the rhythm. Moreover, the model ignores the correlation of simultaneous tones, and assumes that the chord probability is determined independently of the presence of other notes. In this study, we propose a new chord estimation model, in our model, the transition probability is represented by a semi-Markov model, which can consider the periodicity of the rhythm, and the observation probability is represented by a Boltzmann machine, which can represent the correlation of simultaneous tones. The experimental results show that our model yields the higher estimation accuracy of the chord than the existing study.