the fourier analysis

Joseph Fourier (1768 – 1830), along with many other mathematicians in the 17th and 18th century focused on simple problem: “How could a string vibrate with a number of different frequencies simultaneously?”  Needless to say they were specialists in harmonic analysis.   I highly recommend Dave Benson’s writings:  “Music: A Mathematical Offering” for a study on the mathematical theories and concepts.

In music and audio, the Fourier Transform “is the operation that decomposes a signal into its constituent frequencies.”  This means you can deconstruct a chord into its individual frequencies, isolating the monophonic material from the polyphonic material.  Spectral audio plugins often have a setting labeled “FFT” which stands for Fast Fourier Transform.  Other pitch-adjusting software such as Melodyne employs derivatives of such formulas, giving you the ability to edit the pitches embedded within a polyphonic sound.

The free software SPEAR also gives the composer a hands-on experience for analyzing and processing audio in the “frequency domain”.  Applications like SPEAR are very much part of a new branch in digital audio technology, a territory fertile for further development.  Conceptually speaking, whatever can be analyzed can be processed; and, whatever can be processed can be created anew.  In this case, formulas derived from the 17th century are being utilized in today’s cutting-edge audio processes!  It’s somewhat unfortunate that most users don’t necessarily realize where all these breakthroughs come from, not to mention what thought processes were employed to allow for the discovery of these possibilities in the first place.  I raise my glass to the spectral mystic.