基于时间序列的音乐作品改编  

Adaptation of Music Works Based on Time Series

作　　者：刘思圻 李窈 赵慧 金萱 兰爽 李若慧 周国健 白晓东 

机构地区：[1]大连民族大学理学院,辽宁 大连

出　　处：《应用数学进展》2022年第11期8329-8339,共11页Advances in Applied Mathematics

摘　　要：首先,在了解基础乐理,选定了《约定之初》钢琴曲作为研究对象后,进行了乐谱结构化。由于原始数据为非平稳数据,需要进行差分运算,随后又对序列进行了LB检验以及单位根检验,结果表明该序列是平稳的非白噪声序列,可以继续进行建模。制作出差分后序列的ACF图和PACF图,根据所得图示选定用AR(2)模型建模。对模型的残差进行LB检验,结果显示没有证据表明残差是非白噪声序列,故接受该模型。然后,对序列进行预测,从而生成新的旋律。其次,由于原序列具有明显的周期性特征,本文还使用了Holt-Winters三参数指数平滑模型进行模型估计与预测,生成的新乐曲与AR(2)模型的结果一致,侧面印证了AR(2)模型预测的准确性。最后,将预测结果数据还原成五线谱模式,便可以听到基于时间序列模型上改编的新乐曲了。Understand the basic music theory, select the piano music of “The Beginning of the Appointment”as the research object, and then structure the music score. Because the original data is non-statio- nary data, difference operation is needed, and then LB test and unit root test are carried out on the sequence. The results show that the sequence is a stationary non-white noise sequence, and the modeling can be continued. Make ACF diagram and PACF diagram of differential sequence, and se-lect AR(2) model to model according to the obtained diagram. LB test of the residual error of the model shows that there is no evidence that the residual error is a non-white noise sequence, so the model is accepted. Predict the sequence and generate a new melody. Because the original sequence has obvious periodic characteristics, this paper also uses Holt-Winters three-parameter exponential smoothing model to estimate and predict the model. The generated new music is consistent with the results of AR(2) model, which confirms the accuracy of AR(2) model prediction. Finally, the pre-dicted data is restored to the staff mode, and then the new music based on the time series model can be heard.

关 键 词：乐谱结构化 时间序列建模与预测 ARMA模型 AR模型 Holt-Winters指数平滑方法 

分 类 号：J60[艺术—音乐]