Common quantitative characteristics of music melodies — pursuing the constrained entropy maximization casually in composition

Music with a beautiful melody has been appreciated by hu-mankind for thousands of years.Almost all music is gen-erally tonal,e.g.,Western music originated from ancient Greece and developed for more than 300 years from Baroque to classical,romantic,and modern music.Tonal music has a tonal center with a melody named tonic,and it is based on a specific pitch series called mode scale and harmonic progressions.On the contrary,atonal music experimented from around the 1900s,e.g.,the twelve-tone system advo-cated by Schoenberg[1],does not have a tonal center and a melody accordingly.A melody of tonal music consists of the permutation and combination of pitches in series,where the pitch marks the acoustic frequency of the note and the rhythm marks the duration of the note[2].It is desirable to know if there are some common characteristics,objective and quantitative,embedded in a melody.