Sound theory: Waveforms

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1.8.1. Pure sinusoid

Pure sinusoids have been fully described in the previous paragraphs [Properties of sound ] . It is perceived as a frequency tone equal to the sinusoid's frequency. It is easily generated electronically and is often used as a testing instrument.



1.8.2. Square wave

This waveform's rate and harmonic content are described in the following figure:

Sound theory - Square wave

Square wave

As we can see the harmonic content of a square wave is composed purely by odd harmonics. The amplitude decreases at a rate of 1/f. Empirically speaking, this means that the third harmonic (the one that has triple the frequency of the fundamental, since the one that has double the frequency is not present) has an amplitude of 1/3 of the fundamental, the fifth harmonic has 1/5 and so on.

The following are the sounds of a square wave, one having a frequency of 440 Hz (the equivalent of an A note) and one having a 1 KHz frequency:

Square wave (f=440 Hz)  [Track 4]

Sound theory - Square wave (f=440 Hz) [Track 4]

Square wave (f=1 KHz)  [Track 5]

Sound theory - Square wave (f=1 KHz) [Track 5]


1.8.3. Sawtooth wave

Sound theory - Sawtooth wave

Sawtooth wave

Sawtooth waves contain all the harmonics with the amplitude decreasing at a rate of 1/f.

The following are the sounds of a sawtooth harmonic: one has a frequency of 440 Hz (the equivalent of an A note) and one having a 1 KHz frequency:

Sawtooth wave (f=440 Hz)  [Track 6]

Sound theory - Sawtooth wave (f=440 Hz) [Track 6]

Sawtooth wave (f=1 KHz)  [Track 7]

Sound theory - Sawtooth wave (f=1 KHz) [Track 7]


1.8.4. Triangular wave

Sound theory - Triangular wave

Triangular wave

A triangular wave's harmonic content is very similar to that of a square wave. The only difference is that its amplitude decreases with at a rate of 1/f2.

The following are the sounds of a triangular wave, one has a frequency of 440 Hz (the equivalent of an A note) and one having a 1 KHz frequency:

Triangular wave (f=440 Hz)  [Track 8]

Sound theory - Triangular wave (f=440 Hz) [Track 8]

Triangular wave (f=1 KHz)  [Track 9]

Sound theory - Triangular wave (f=1 KHz) [Track 9]









  • posted on 27-03-2011 20:23
    Thank you Angelo for your suggestion! What I meant was something different, but still I can't find a proper name for it. For the time being I removed the wrong text about hypertones.
  • posted on 16-03-2011 21:58
    Hello, sorry to correct you, but hypertones have nothing to do with sound. Hypertonia is an overgrowth of muscle tissues. Probably you meant to write overtones. And yes, they're harmonically related to the fundamental frequency: overtones and undertones are just harmonics that are higher and lower than the fund. Instead, some partials (all these are partials) are not related harmonically to the fundamental. ATB