“Transposing Time” Fourier Transforms for Music Analysis

by Shankar Singh

Submitted : Spring 2018

 The objective of the project was to determine whether or not the Fourier Transform was a viable method to transcribe music given an electronic sample; whether or not there is a method to transcribe music for someone who knows little about music theory. A fourier series is based on the idea that any real wave is composed of an infinite amount of smaller waves that can be added together to produce the original wave, and that the intensity of these waves can be measured for any given frequency. The testing method was to record a chord and a series of notes, then view the return of the fourier transform to see whether or not the dominant note was the most prevalent frequency in the output range. Using an audio program which calculated the fast fourier transform, the frequencies of individual notes came resulted almost as expected, though when combined to form a whole chord a unintuitive result was given. The graphs showed that the frequency intensity across a C chord was even amongst the 5 that composed it. The data proves that a fourier transform is able to transcribe music to a down to a note, although an understanding of music theory would still be required to make the correct assumption about the octave level of a certain note, as the fourier transform gave intensity results that did were not concise to the note played. Some data was shifted up an octave.

Overall this method is surprisingly accurate and offers a great service to the music community with a method that is easy to execute with some basic computer skills.

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