Harmonic Series

01/24/2006:  The following audio samples are 10-second long Sine Waves which, if I set them up right, should loop until you hit the Pause button.  They have all been recorded at a reference level of -18dBFS.  I setup the page so you can play any or all of the clips at the same time to 'build' a more complicated wave by stacking harmonics.

For the sake of having a frame of reference, I've chosen to use three octaves worth of harmonics built up from A=110 Hz which includes, of course, the international reference tuning pitch of A=440.  I chose this because the math is easy, these are "real" notes that are easy to locate on a musical instrument or in musical notation, and because the pitches are low enough that they don't seem 'piercing' when we climb up several octaves.

1:  110 Hz Sine Wave:  "A"

2:  220 Hz Sine Wave:  "A"

3:  330 Hz Sine Wave:  "E"

4:  440 Hz Sine Wave:  "A"

5:  550 Hz Sine Wave:  "C#"

6:  660 Hz Sine Wave:  "E"

7:  770 Hz Sine Wave:  "G"

8:  880 Hz Sine Wave:  "A"

OK, so hopefully someone out there decided to try and recreate a Triangle Wave by switching on only the odd harmonics, 1, 3, 5,& 7.  Come on... anyone?  Well, if you do, you'll notice they don't sound quite as 'rich' or 'bright' as the samples from the Waveforms page and that's for a pretty good reason... there aren't enough harmonics here.  I've covered a span of 3 full octaves and provided clips of the first 8 harmonics, but as nature has a tendency to do, these things just keep going and going.  So if we were to add the 9th harmonic at 990 Hz, the 11th at 1210 Hz, the 13th at 1430 Hz, and so on, then yes we could get a sound closer to the Triangle or Square waves.  For now, even when we switch on all eight harmonics we get a really nice "Dominant 7th" chord instead of a Sawtooth wave sound.  But it's a start.