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The sine wave is the simplest form of periodic motion. A tuning fork creates a pure sine wave.
All other periodic waveforms are more complex. The original sine wave (fundamental frequency), is layered with other waves that are multiples of the original. These additional tones are considered to be overtones.
For example: a frequency fundamental of A-110 Hz , will have overtones of A-220, E-330 , A-440, 550 , E-660, etc.
Fast Fourier Transform (FFT) analysis determines the frequency spectrum of a sound. It breaks the sound down into individual sine waves that make up the sound and also show how the sine waves change over time. The result of FFT can often be shown on a 3-D (XYZ) graph with frequency, amplitude and time along the three axis. (See example of FFT analysis at the end of the chapter). Digidesign's Sound Designer II program offers FFT analysis.
FFT gives to us the ability to examine the frequency spectrum of sound which can help in sound design, EQ, and how the frequencies combine to create the sound.
square waves,
saw tooth waves ,
and even more complex waves. Lets take a look at the square wave.
To build a square wave, we add a number of sine waves together. Each new wave flattens the top of the original sine wave by pushing up valleys and pulling down peaks , causing steeper sides. The waves are exact multiples of the first. In other words, in a square wave, the first added wave fits two cycles in the original wave's cycle (2nd harmonic) , the next wave fits three cycles in the same period ( 3rd harmonic) , and so on.
The frequencies of any wave's harmonics are once again , exact multiples of the fundamental. A wave with 440 Hz has a second harmonic of 880 Hz, a third harmonic of 1320 Hz and so on.
There is no limit to the number of harmonics a wave can have. (Any frequency over 20 kHz can not be heard, but still may add characteristics to the sound in a sub-conscious manner).
If N = the fundamental amplitude , the 2nd harmonic's amplitude is N/2 , the third N/3 , etc.
For example: if N = 10 dB , the 2nd is 5 dB , the 3rd is 33.5 dB , etc.
As the amplitudes of the different harmonics evolve over time, the shape of the wave produced by adding them together also evolves.
Also, even numbered harmonics create a different complex sound than un-even harmonics.
Therefore, every complex waveform has a particular spectrum of which is defined by the harmonics which make it up.
** Illustrations are snapshots of a shareware program called Harmonics 1.1 by Marco Carra, Sound Designer II by Digidesign, and Alchemy by Passport.**
