Tikalon Blog by Dev Gualtieri

Music Analysis

August 13, 2014

In the dim past, our ancestors found that they could make sound by beating on hollow logs and shaking seeds in dried gourd shells. From that time until the late 19th century, we could only experience sound aurally. An additional means of sensing sound appeared in 1880, when Alexander Graham Bell, assisted by Charles Sumner Tainter, invented the photophone.[1]

Bell's photophone used a flexible mirror to convert sound waves into a modulated light beam. Acoustic vibrations would deform the mirror to focus and de-focus light, thereby changing the light intensity in response to the sound intensity. I wrote about the photophone in a previous article (Free-Space Optical Communications, August 18, 2011).

There was a receiver part of a photophone that converted the modulated light to an alternating current signal with a selenium photoresistive cell. The photophone transmitter, however, was a passive device that required no electricity to operate. As a consequence, the light modulation wasn't that strong.

With the advent of vacuum tube electronics, a different type of sound-to-light converter was invented by William Duddell (1872-1917). His electromagnetic oscillograph, as shown in the figure, used electromagnets to move a mirror to produce a bouncing light beam similar to what's displayed on the now familiar cathode ray oscilloscope. A description of a similar electromagnetic oscillograph is given in the references.[2]

A Duddell oscillograph.

This electromechanical instrument could respond to frequencies up to the kilohertz range. The primary elements were the electromagnet coils (C) and their cores (B).

(From vol. 6 of Hawkins Electrical Guide, Theo. Audel & Co., 1917, via Wikimedia Commons.)

The electromechanical oscillograph was superseded by the cathode ray oscilloscope, which responded to much higher frequencies. A popular science demonstration in my childhood was showing a person's voice on an oscilloscope. In that case, the oscilloscope functioned more like a light show than an analytical instrument.

The idea of a sound-driven light show was popularized as the "color organ" circuit (a.k.a., light organ) by which the intensity of sound in different audio frequency bands was displayed as multi-colored lights. In my undergraduate days, I designed and built a five channel color organ using Sallen-Key filters as the bandpass filters, and triacs to control the lights.

The advent of ubiquitous computing devices has led to many ways to visually display music. The simplest of these is the bargraph spectrum analyzer that shows the sound intensity in many small bandwidth slices across the audio band. You can see the operation of one of these in this YouTube video.

Of course, computers can do much more than just present the intensity distribution of the frequencies in an acoustic source. There's the capability for analysis. In an earlier article (Scoring the Hits, January 4, 2012), I summarized research into the computer analysis of music, both for selecting tunes similar to others, and for predicting the next best-selling songs.[3-5] Every record label wants a machine that would automatically sort the musical wheat from its chaff.

Although the particular orchestration and vocal artist are big factors in making a record a hit, let's just consider the melody. What does it take to distinguish one tune from another? As I estimated in a very old article (Name That Tune, June 24, 2008), each note in a melody, except for the first, could possibly have 1 of 48 different combinations of pitch (8) and duration (6). We're only considering popular music, so we're not going as far as needing twelve tones in our scale. There are also rogue notes, appropriately called accidentals, that inflate this number, but our calculation is a Fermi problem, so we'll ignore them.

For technical reasons, the pitch of the first note, which sets the tonic, is not important, only its duration, which would be about one in six different choices. To honor the recent passing of James Garner, I'll use Mike Post's opening theme to The Rockford Files as an example. The initial musical phrase, which instantly identifies this melody, has ten notes. This is just one melody of 6 x (48)⁹ = 8,115,632,763,568,128 possible ten note melodies.

Just as in English, where "u" will follow "q" with nearly a hundred percent certainty, there's a greater probability that some note will follow others in a melody. This reduces the number of "musical" melodies considerably, so that there are actually more like 10¹² "musical" melodies. This is a large number, but much smaller than 10¹⁶. It still appears that an adequate analysis might need a supercomputer.

This estimate shows that there are still many more songs forthcoming from "Tin Pan Alley," which has apparently emigrated to Sweden, as the composition credits of Max Martin demonstrate. Instead of tackling the problem of deciding which new melodies will be hits, two computer scientists at Lawrence Technological University (Southfield, Michigan) have developed an artificial intelligence algorithm for analysis and comparison of musical styles. Interestingly, they use audio analysis tools they had developed for analysis of whale song.[6-7]

Plaque marking Tin Pan Alley, New York City

A plaque marking the area of Tin Pan Alley in New York City.

London, England, has its own Tin Pan Alley at Denmark Street.

(Photograph by Ben Sutherland, via Wikimedia Commons.)

Their analysis program takes as an input the audio recording, itself.[6-7] This is converted into a series of spectrograms, and they use image analysis techniques to convert these into a set of 2883 numbers that allow comparison with other pieces of music.[6-7] The comparison between songs is done using the common weighted K-nearest neighbor scheme by which it was possible to automatically arrange the thirteen Beatles studio albums in their chronological order.[6-7] The algorithm correctly placed "Let It Be," the last released album, before "Abbey Road," a fact consistent with their recording chronology.[7] Similar results were obtained for other musical groups.

The algorithm attempts to derive a representation of a recording's "DNA." The utility of this type of analysis is highlighted by the recently announced acquisition of Booklamp by Apple. Booklamp worked on what it called its Book Genome Project that analyzed book qualities like action, viewpoint and dialog to derive a book's "DNA."[8]

Music Analysis

References: