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Basic Audio Wave Shapes

01/24/2006:  The most important characteristic of sounds that have a definite pitch is that they have a repeating waveform.  With audio oscillators we can generate what are considered to be the 4 most basic waveforms, the sine, triangle, square, and sawtooth (or "ramp") waves.  These waveforms, in that order, represent a steadily increasing complexity of shape and of timbre as the number and strength of the harmonics for each wave form increases.  (Some folks consider the 'pulse' wave to be among the basics but I consider it a more complex cousin of the square wave so I haven't included it here.)

For each of the following waveforms, I have provided a 10-second audio sample of the wave played at a frequency of 110-Hz and a level of -18dBFS

1:  Sine Wave - sounds like the lowest of the samples because it is only playing the fundamental frequency or "pure tone" of 110-Hz.

 

2:  Triangle Wave - sounds somewhat higher, richer, and a bit louder because the fundamental frequency is joined by the odd harmonics which are those frequencies 3x, 5x, 7x, etc. above the fundamental, in this case 330-Hz, 550-Hz, 770-Hz, etc.

 

3:  Square Wave - sounds higher, richer, and a bit louder still.  It is similar to the triangle wave in that only odd harmonics are present, however the harmonics are louder relative to the fundamental frequency and so have a greater impact on the timbre of the wave.

 

4:  Sawtooth Wave - also called a "ramp" wave for obvious reasons is the most complex of the basic wave shapes.  You can view it as the 'front end' of a triangle wave and the 'back end' of a square wave.  The more complicated shape generates more overtones, in this case every harmonic is present at gradually decreasing levels.

 

Although we've not yet discussed these in class, I would also like to place two additional sound samples here on the page for future use.  These are samples of "random" noise, which naturally enough for us is not really so random as it seems.

The first sample is White Noise which can be described as including all frequencies at equal levels.  Imagine 20Hz, 21Hz, 22, 23...210, 211, 212...2100, 2101, 2102, etc. all the way up the spectrum at equal volume.  You'll notice it sounds somewhat thin and 'bright' because of all those high harmonics present.  This sample was recorded at a reference level of -18dBFS.

 

By comparison, this next sample is Pink Noise which can be described as including all frequencies but at steadily decreasing levels.  The rate of decrease is generally set at -3dB per octave, with the idea being that since there are twice as many individual frequencies present as we move up the spectrum (think 1,000 steps between 1kHz & 2kHz, but 2,000 steps between 2kHz & 4kHz, etc.) that we then need to decrease the volume of each successive frequency.  Of course, a difference of only -3dB is dividing the overall signal strength by 1.4 as opposed to a decrease of -6dB which would divide the signal strength by 2.  This is probably why this sample sounds louder that the white noise even though the sample was also recorded at a reference level of -18dBFS.  It also sounds 'darker' because the higher frequencies are not overpowering the lower ones.  Pink Noise is used to test and balance live sound systems.

And if that's not enough for you, click here to listen to the Harmonic Series.