For the curious, the spectral formula of a waveform gives a simple relationship between the partial number and its amplitude (remember, we know its frequency from the Fourier theorem).

For example, the formula for a square wave is:

an amplitude of:

1/n, where n is odd

0, when n is even

Using the formula, we can compute the following partial strengths for a square wave:

1st partial = 1/1

2nd partial = 0

3rd partial = 1/3

and so on.

There are some other simple waveforms whose formulae are well known:

Sawtooth wave: 1/n when n is even or odd.

Triangle wave: 1/n² when n is odd, O where n is even.

Note how "fast " the amplitudes of a triangle wave drop off—it's said to be a "not very bright" timbre. Surprisingly, as we mentioned in an earlier section, symmetrical waveforms (like the square and triangle) have no even partials.