Abstract:
Mathematics and music have always been very closely related to each other. Here, we are going to discuss some of the mathematical and statistical characteristics of music using techniques from time series analysis. First, we will see how music can be transcribed by applying time series analysis to it – we will look at and discuss the time series and autocorrelation plots of different songs. Then, we will observe how we can use the analysis in order to obtain the musical score from an audio recording. Here, we will work on note identification through a Fourier series representation of the wave function of the melody. For this purpose we will use the statistical program R, and its add-on musical package tuneR.

Table of contents:
Abstract……………………………………………………………………………… ….i
Introduction…………….……………………………………………………………..…...1
Section I: Analyzing music from the musical score
A. Encoding and displaying music..………………………………………………… ……2
B. The statistical package R………………………………………………………… ….4
C. Time series and Autocorrelation plots…………………………………………………6
Section II: Analyzing music from a vocal recording
A. Wave-files and tuneR……………………………………………………………… 12
B. Wave plot…………………………………………………………………………..12
C. The Fourier Function and Frequencies...………………………………………… ..14
D. The periodogram………………………………………………………………… .16
E. Obtaining the frequencies of notes………………………………………………… 18
F. Obtaining the musical score from a recording…………………………………….. .19
G. The Melody plot……………………………………………………………… …20
Conclusion……………...……………………………………………………… …..24

 

 

 

created: August 30, 2005