The nodes corresponded to the composers, and the connections among the nodes are established according to the difference between the exponents of any two composers over all of their movements. When the difference is not significant (P>0.05) in t test, a line linking the two composers is assumed. The composers in the network were put into two groups (red and blue) according to the network modularity. The size of the circle indicates the degree (the number of lines).
Abstract: Harmony is a fundamental attribute of music. Close connections exist between music and mathematics since both pursue harmony and unity. In music, the consonance of notes played simultaneously partly determines our perception of harmony; associates with aesthetic responses; and influences the emotion expression. The consonance could be considered as a window to understand and analyze harmony. Here for the first time we used a 1/f fluctuation analysis to investigate whether the consonance fluctuation structure in music with a wide range of composers and genres followed the scale free pattern that has been found for pitch, melody, rhythm, human body movements, brain activity, natural images and geographical features. We then used a network graph approach to investigate which composers were the most influential both within and across genres. Our results showed that patterns of consonance in music did follow scale-free characteristics, suggesting that this feature is a universally evolved one in both music and the living world. Furthermore, our network analysis revealed that Bach’s harmony patterns were having the most influence on those used by other composers, followed closely by Mozart.
Citation: (2015) Bach Is the Father of Harmony: Revealed by a 1/f Fluctuation Analysis across Musical Genres. PLoS ONE 10(11): e0142431. doi: 10.1371/journal.pone.0142431