In this paper, we study Turkish makam music, a system of varied melodies and chords, computationally. Our main goal is to classify the makams using their notes. For this reason, we utilize the topology of complex networks. We first represent songs with weighted networks where vertices and edges correspond to musical notes and their co-occurrences respectively. We then define the diffusion Fréchet function over the weighted networks to encode the network topology and finally reach our goal by combining the function values with machine-learning algorithms. Our experiments show that such network representation with the diffusion Fréchet function is promising in classifying makam music and more effective than the n-gram technique, which is the most-used automated makam classification method. We believe that our method can be extended to any music, not only makam music.

在本文中，我们将通过计算研究土耳其makam音乐，这是一个由多种旋律和和弦组成的系统。我们的主要目标是分类makams使用他们的笔记。因此，我们利用了复杂网络的拓扑。我们首先用加权网络表示歌曲，其中顶点和边缘分别对应于音符和它们的共现。然后，我们在加权网络上定义扩散Fréchet函数以对网络拓扑进行编码，并最终通过将函数值与机器学习算法相结合来达到我们的目标。我们的实验表明，这种具有扩散Fréchet函数的网络表示法在对makam音乐进行分类方面很有希望，并且比n-gram技术，这是最常用的自动makam分类方法。我们相信，我们的方法可以扩展到任何音乐，而不仅仅是makam音乐。