Music Theory and Composition : Music Theory and Composition

Thursday, December 14th, 2017

Fast Fourier Transform – Acoustics of Music – Part 5


Main Article Photo - Scales

A Tonal System – Scales in Music

Acoustics of Music – Part 5

Fast Fourier Transform

Welcome to Part 5 of our series Acoustics of Music. This article will describe the Fast Fourier Transform tool or the FFT Meter which is part of the Steinberg computer program called Wavelab v6.0.

For those who wish to pursue college level lectures on the Fast Fourier Transform and it applications please see the references at the end of this article.

For others not so inclined, this paper will briefly and broadly discuss the FFT and some of the possibilities with regard to music and music production rather than the mathematics behind it.

Fast Fourier Transform – The wonders of technological improvements have made it possible to analyze more than one pitch at a time. A digital software program called Wavelab includes a frequency analyzer tool called a Fast Fourier Transform tool or FFT for analyzing a collection of frequencies of music which can be seen in the graphs produced when using this meter.

What I like about it is that it measures frequencies in real time so a person can not only hear a piece of music that has been performed and recorded, he or she can see it from the standpoint of the frequency range perspective as music is performed live.

The FFT meter makes it possible to look at and to perform an analysis of the various frequencies involved in a given piece of music rather than limiting the scope to only one frequency or fundamental tone at a time or relying on wave files as the only means to master your music or audio files. The Fast Fourier Transform Tool is highly useful as a feedback mechanism when editing and when utilizing sound frequencies for finalizing an audio mix. It is only one possible tool that a sound engineer may use when “tweaking” the music that you have created.

The screen shot below shows a still photo, when using the FFT meter, to graphically display a series of frequencies as taken from a small part of a single musical recording. In our example below, the snapshot is taken of a stereo recording so both channels are represented in the photo. Also, take note that clearly more than one frequency is shown in the graph.

FFT - Multiple=For reference – The y axis or the left side of the graph moving upwards is measured in decibels or loudness. The bottom or x axis running from left to right on the bottom of the photo measures the frequency, lowest to highest, left to right. A number of frequencies are shown representing the frequency values of various notes being played in the mp3 file used in this example.

The video below is a demonstration, in two parts woven together, of the Fast Fourier Transform principal from two different perspectives. First is with Professor P. J. Moriarty from the University of Nottingham describing the Fourier Principal with the guitar and the effects on the wave pattern when of using a wah-wah pedal altering the sound waves. The second presentation is another Professor using a rubber wire to demonstrate the harmonic divisions along a string as well as a brief comment on how the length affects the harmonic divisions. The video helps to further explain what is meant by a series of frequency waves. It further explains that sound is not static or still rather it is dynamic.

The video was taken from YouTube and it is being used under the embed license offered through them.

Working with the FFT Graph

OK, so what does all this mean and how is it useful? As you have probably guessed, looking at frequency graphs is quite different than working with wave files. Wave files tell you when a sound begins and ends, among other things, whereas frequency graphs helps you to understand the timbral or the unique characteristics of the contents of a given recording of sound or a series of sounds. It is not based upon time like the wave file it is based upon frequencies and this is where you can make important, specific and finely tuned adjustments when “tweaking” the recorded sound for a result more to your liking.

It becomes even more useful when you want to see how the frequency spectrum is represented in a recorded mix. Here you can make the necessary adjustments to remove or repair improper frequencies, for example. Further it allows you to visually know where to boost a portion of the sound or to lower another portion of the recorded sound when EQing your mix.

Another key benefit of using the FFT meter is where an unwanted background noise is present. It can be identified and removed if necessary by filtering out the noise and cleaning up the mix. All of these are part of the mastering process for recorded sound (and that includes music).

The Fast Fourier Transform is only one of the tools included in the Wavelab software as offered through Steinberg. If you are creating, editing, mixing or mastering music I highly recommend that you consider using this excellent product.  By using it you become exact just like a brain surgeon when finalizing and mastering your recorded music.

The next article in the Acoustics of Music series includes a review of amplitude or loudness in music. It is Part 6 of Scales in Music – a Tonal System article series.

Please continue to Part 6 of the Acoustics of Music. It is titled Acoustic Principals – Amplitude.

Mini Series Links

To return to the Music Theory – Level 1 directory for the article listings within the series, please proceed to Music Theory Section – Level 1 – Series Introduction – Part 10.

To continue onto Music Theory – Level 2 directory for the article listings within the series, please proceed to Music Theory Section – Level 2 – Series Introduction – Part 20

To proceed to Acoustics of Music directory for the listings within the mini-series, please proceed to Acoustics of Music – Part 1 – Series Introduction.

Valuable Resources

For those of you who wish a jolt of mathematical splendor please visit either of these two links. They will certainly enlighten you with a short series of articles about some of the physics, mathematical concepts and formulas behind the Fourier Transform and the Fast Fourier Transform which are detailed in these two articles.

Also, for those of you highly interested in a comprehensive look into the Fourier Transform and its various applications, Professor Brad G. Osgood from Stanford University offers a 30 part multimedia lecture series available at no charge courtesy of Academic Earth and Stanford University.

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