Wu Dan, Kendrick Keith M, Levitin Daniel J, Li Chaoyi, Yao Dezhong
Department of Biomedical Engineering, School of Computer and Information Technology, Beijing Jiaotong University, Beijing, China.
Key Laboratory for NeuroInformation of Ministry of Education, School of Life Science and Technology, University of Electronic Science and Technology of China, Chengdu, China.
PLoS One. 2015 Nov 6;10(11):e0142431. doi: 10.1371/journal.pone.0142431. eCollection 2015.
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.
和谐是音乐的基本属性。音乐与数学之间存在着紧密的联系，因为二者都追求和谐与统一。在音乐中，同时奏响的音符的协和性在一定程度上决定了我们对和谐的感知；与审美反应相关联；并影响情感表达。协和性可被视为理解和分析和谐的一扇窗口。在此，我们首次运用1/f涨落分析来探究，在广泛的作曲家和音乐流派的音乐中，协和性波动结构是否遵循已在音高、旋律、节奏、人体运动、大脑活动、自然图像和地理特征中发现的无标度模式。然后，我们使用网络图方法来研究哪些作曲家在流派内部和跨流派方面最具影响力。我们的结果表明，音乐中的协和性模式确实遵循无标度特征，这表明该特征是音乐和生物界中普遍进化而来的。此外，我们的网络分析表明，巴赫的和声模式对其他作曲家使用的模式影响最大，莫扎特紧随其后。
