论文标题
音乐的分形维度：旋律轮廓和音高的时间序列
The fractal dimension of music: Melodic contours and time series of pitch
论文作者
论文摘要
我们分析了古典音乐和民间音乐音乐的旋律轮廓和音调时间系列的分形维度。从盒子计数和下降波动分析获得的分形维度显示出显着差异。它们归因于接近两个的尺寸的盒子计数的低精度以及可能的偏差，因为时间序列中的音高通过线路连接以获得盒子计数分析中使用的旋律轮廓。我们观察到一种趋势，即民间音乐表现出比古典音乐较低的分形维度，但是需要进一步的研究才能评估相对较短的民间音乐音乐中的截止效果。我们得出的结论是，降解的波动分析是对音乐分形分析的优选方法，这验证了先前对短时间分析的研究。
We analyze the fractal dimension of melodic contours and pitch time series of classical music and folk music tunes. The fractal dimensions obtained from box counting and detrended fluctuation analysis show significant differences. They are ascribed to the low accuracy of box counting for dimensions close to two as well as to a possible bias because the pitches in the time series are connected by lines to obtain the melodic contour used in the box counting analysis. We observe a tendency that folk music exhibits lower fractal dimensions than classical music, but further studies are needed in order to assess cutoff effects in the comparatively short folk music tunes. We conclude that detrended fluctuation analysis is the preferable method for fractal analysis of music, and this verifies previous studies of analysis of short time series.
