论文标题
音乐的几何形状
Geometry of Music Perception
论文作者
论文摘要
普遍的神经科学理论与来自各种研究的声学观察结合在一起，以创建音乐感知的一致几何模型，以合理化，解释和预测心理声学现象。所有和弦的空间都显示为惠特尼分层的空间。每个层是一种riemannian歧管，自然会在整个地层中产生大地距离。由此产生的度量与满足三角形不平等的语音领先兼容。几何模型允许对精神量化量（例如粗糙度和谐波）作为身高功能进行严格研究。为了展示如何在心理声学研究中使用几何框架，引入和分析了和弦决议的感知概念。
Prevalent neuroscientific theories are combined with acoustic observations from various studies to create a consistent geometric model for music perception in order to rationalize, explain and predict psycho-acoustic phenomena. The space of all chords is shown to be a Whitney stratified space. Each stratum is a Riemannian manifold which naturally yields a geodesic distance across strata. The resulting metric is compatible with voice-leading satisfying the triangle inequality. The geometric model allows for rigorous studies of psychoacoustic quantities like roughness and harmonicity as height functions. In order to show how to use the geometric framework in psychoacoustic studies, concepts for the perception of chord resolutions are introduced and analyzed.
