If you played with the synthesizer simulation you probably started to realize that adding different frequencies to the fundamental changes the quality or timbre of the sound you hear. If you did the mini lab you should have detected a different Fourier spectrum for instruments or voices that were different, even when they were playing the same note. According to Fourier, complex waveforms can be constructed from combinations of sine waves. It is these additional frequencies that are the main property that give a musical tone its timbre. As shown in the graphs below, we can tell a trumpet from a trombone, even when they play the same note because there are different frequencies present. These variations in frequency change the waveform (top two graphs which can be seen with an oscilloscope) and the Fourier spectrum (lower two graphs which can be determined from a Fourier analysis).

Below the Fourier analysis of each of the above waveforms using the program Audacity. Notice that the fundamental frequency (the lowest frequency) is the same for both instruments (around 230 Hz) so they are playing the same note, even though they will sound different.

Most notes produced by musical instruments have higher frequencies that are multiples of the fundamental, or lowest frequency. When the higher frequencies are multiples of the fundamental they are called harmonics. The more generic term for frequencies produced by an instrument or voice that are higher than the fundamental (whether multiples or not) is overtone. We will discuss this in more detail in Chapter 11 on strings and stringed instruments.

**Video/audio examples:**

**Fourier spectrum of a piano, trumpet, white and pink noise, sine, square, triangle, sawtooth.**

**A review of a few major points.**