Membership functions in automatic harmonization system

We propose fuzzy reasoning to put harmony to melody in automatic harmonization system. We have been considering the following fuzzy sets and membership functions in the system. The system has two fuzzy sets of “conformability between melody and tonality” as the degree of fitness μ_A(y_n) and “conformability between tonality and relative keys” as the degree of fitness μ _T(y_n). The degree of fitness μ_C(y _n) for each tonality is obtained from μ_A(y_n) and μ_T(y_n). The system has two fuzzy sets of “conformability between melody and chord” as the degree of fitness μ_Mi(x_m) and “validity of chord progression” as the degree of fitness μ_Pi(x_m,x_i-l). The degree of fitness μ_Qi(x_m) for chord in melody i section is obtained from M_Mi(x_m) and μ_Pi(x_m, x_i-l). μ_Mi(x _m) is obtained from three membership functions of μ_chord-A(note), μ_chord-B(note) and μ_chord-C(note) which show an importance to each chord in each note, and μ_Length(note) which is a relative importance about an existence time of each note, and M_MS(note) which shows a relative importance. μ_Pi(x_m,x_i-l) is obtained from three membership functions of μ_FC(c_m) which shows an importance of each function chord, and μ_FP(x_m) which shows a strength of the dominant motion of the function chord, and μ_S(x_m,x_i-l) which shows a progression sense between two neighbor chords. It is shown in the good results that the natural chords, which don´t break the tonality of the music, are achieved