Music can be about physics and math as well as art. This year’s Grammy Award for Best Historical Album went to a team that included University of New Hampshire mathematician Kevin M. Short and sound engineer Jamie R. Howarth for restoring a fragile, live 1949 wire recording of legendary folksinger Woody Guthrie. The technique developed for the restoration cleverly exploits background noise present in a recording.
The story began with two rolls of steel wire—a bootleg recording sent to the Woody Guthrie Archives in 2001. Like tape, steel wire can be run through a magnetic recorder to capture electrical signals transmitted by a microphone. Such recordings are especially susceptible to mechanical degradation. The wire (or tape) stretches, slips, breaks and kinks; rollers and bearings get worn spots; and motors develop subtle imperfections. The result is timing variations that cause artifacts known as wow and flutter.
The Guthrie recording was a particularly damaged example. “One section was so bad when I first heard it,” Short says, “that it sounded like Charlie Brown’s teacher.” Yet now that same audio is intelligible and of listenable quality.
Aside from the custom-built, converted tape machine needed to play the Guthrie recording, the secret to its restoration lay in a key insight of Howarth’s. Alongside the music being recorded, analog tape recorders lay down a “bias signal,” a pure tone at 40 kilohertz or above (well outside the range of human hearing). Such a bias signal makes a tape more effective at capturing audio. Howarth’s idea: if properly extracted, the bias signal could serve as a reference to identify and correct those timing variations and restore the audio to its original quality. In 2003 he took this idea to Patrick J. Wolfe, an electrical engineer at Harvard University, and asked him if he thought it would work. “It struck me as a nice idea,” recalls Wolfe, who shares the resulting patent with Howarth.
But poring over the Guthrie recording, Howarth found no bias signal—wire recorders may not have used them. What he did find was a faint but usable hum at 60 hertz, a cross-feed from an electrical power line. Any steady tone, Howarth realized, could be used as a reference.
Howarth had other details to smooth out, such as the best way to digitize the analog signals. The process involves sampling audio signals tens of thousands of times per second (for CD-quality sound), but it also introduces additional timing variations. Howarth then turned to Wolfe, who “came up with a rather interesting approach using irregularly spaced sampling theory,” Howarth says—a contrast to the standard method of sampling at regular intervals. Specifically, Wolfe identified ideal points at which the damaged analog signal should be sampled, and these points turned out to be irregularly spaced over time. For the Guthrie project, Short used his expertise in music compression and chaos theory to adapt Wolfe’s code and to fix the time orientation. Chaos theory, Short says, enabled the team to see structures in what appeared to be random signal variations, thus allowing them to reconstruct the actual music.
Most of Howarth’s work through his company, Plangent Processes in Nantucket, Mass., is on far less damaged audio—chiefly commercial film and audio from the analog era. The restoration of the Guthrie recording has, Short remarks, inspired many new ideas for approaches that may prove promising in the future. For now, it has given folk music fans a chance to hear a great American legend like never before.