Programming, Statistics

Music and Math

Many people claim there is a strong correlation between music and math.
Below, I demonstrate that the patterns in music are NOT well predicted by typical statistical approaches.

I have taken a MIDI file of Beethoven’s 5th, and analyzed the track using non-parametric estimation techniques. These techniques included panel data techniques, ARMA, and extensive non-parametric estimation techniques (polynomial and Fourier series to capture cyclical components). I then use the song’s notes and my estimation technique to create a forecast of following notes. I then play the “forecasted song”.  (I note that there has been a lot of recent development in this area and other techniques have been developed and popularized since I wrote this post.)

After listening, the “forecasted song” does does not well match the original. As a consequence, I can state that the mathematical techniques common to forecasting do not well predict a song.  Below are several attempts which I have highlighted:

The R-squared for these estimations are in fact VERY high, in the high 90’s. (Only few of the coefficients are significant, the data is clearly overfitted in some regressions.) This song in fact falls into the so-called uncanny valley, and is only slightly deviant from the actual Beethoven’s 5th. However, the ear is strongly cultured to perfection in the subject of music, and the errors are devastating to us.

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