Common and distinct quantitative characteristics of Chinese and Western music in terms of modes, scales, degrees and melody variations

Music is in general mutually understood among different cultures worldwide but can sometimes vary by different styles. The Western music system (heptatonic system) and the Chinese music system (pentatonic system) have common and different characteristics in terms of modes, scales, degrees, and melody variations. In this paper, we show these characteristics through quantitative analysis and comparison and have identified two common characteristics of Chinese pentatonic and Western heptatonic music with respect to modes, scales, and degrees. Although the structures and profiles of the modes, scales, and degrees of both kinds of music are different, they both show a preference to bright modes and scales, and their preference to tonal centres and degrees are consistent with the generating orders via their primal tuning temperaments. Based on the structural characteristics of the musical scales of Chinese pentatonic and Western heptatonic music, we present three interval-dividing metrics to examine the melody variations quantitatively. We find that the melody variations of Chinese pentatonic and Western heptatonic music measured by the interval-dividing metrics both follow the power law, a physical-mathematical law existing in many natural and engineering systems. This study fills the gap in the quantitative analysis of Chinese pentatonic music and provides an approach to studying the common characteristics of different types of music.