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 /spl mu//sub A/(y/sub n/) and "conformability between tonality and relative keys" as the degree of fitness /spl mu//sub T/(y/sub n/). The degree of fitness /spl mu//sub C/(y/sub n/) for each tonality is obtained from /spl mu//sub A/(y/sub n/) and /spl mu//sub T/(y/sub n/). The system has two fuzzy sets of "conformability between melody and chord" as the degree of fitness /spl mu//sub Mi/(x/sub m/) and "validity of chord progression" as the degree of fitness /spl mu//sub Pi/(x/sub m/,x/sub i-l/). The degree of fitness /spl mu//sub Qi/(x/sub m/) for chord in melody i section is obtained from M/sub Mi/(x/sub m/) and /spl mu//sub Pi/(x/sub m/, x/sub i-l/). /spl mu//sub Mi/(x/sub m/) is obtained from three membership functions of /spl mu//sub chord-A/(note), /spl mu//sub chord-B/(note) and /spl mu//sub chord-C/(note) which show an importance to each chord in each note, and /spl mu//sub Length/(note) which is a relative importance about an existence time of each note, and M/sub MS/(note) which shows a relative importance. /spl mu//sub Pi/(x/sub m/,x/sub i-l/) is obtained from three membership functions of /spl mu//sub FC/(c/sub m/) which shows an importance of each function chord, and /spl mu//sub FP/(x/sub m/) which shows a strength of the dominant motion of the function chord, and /spl mu//sub S/(x/sub m/,x/sub 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.