At this point, one might wonder if a musical note is nothing but a sine wave with a fixed frequency, then why does the standard A from an oboe sound differently from the same note coming out of a flute? To answer this question, we need to look more closely at the wave forms generated by the instruments in reality. The waveforms below are generated from three different instruments playing the same note. Click on the waveforms to hear the sound samples.
Fig. 5 (Hollis, 2014) indicates that although the three waveforms share the same frequency, their shapes differ drastically from each other. And it is this difference of shapes, which is also called timbre, the “color of tones”, that separates a violin from a piano, as well as someone’s voice from that of any other human being on the earth.
If we dig a little deeper, we might ask what causes timbre to take place? The answer is harmonics or overtones. Now let us study them more closely. Before we start to analyze harmonics, we need to introduce an important theorem in math, called Fourier’s theorem. Fourier’s theorem states that, “Any periodic oscillation curve, with frequency f, can be broken up, or analyzed, into a set of simple sine curves of frequencies f, 2f, 3f, . . . Each with its own amplitude” (Parker, 2009, p. 65). Fourier theory tells us that any periodic wave form, no matter how “strange” it might look, as long as it is periodic with a fixed frequency f, can be broken down to multiple simple sine waves. Below is an example of a “complicated” waveform broken down into simple sine waves (IMS PTY Ltd., 2004).
If we dig a little deeper, we might ask what causes timbre to take place? The answer is harmonics or overtones. Now let us study them more closely. Before we start to analyze harmonics, we need to introduce an important theorem in math, called Fourier’s theorem. Fourier’s theorem states that, “Any periodic oscillation curve, with frequency f, can be broken up, or analyzed, into a set of simple sine curves of frequencies f, 2f, 3f, . . . Each with its own amplitude” (Parker, 2009, p. 65). Fourier theory tells us that any periodic wave form, no matter how “strange” it might look, as long as it is periodic with a fixed frequency f, can be broken down to multiple simple sine waves. Below is an example of a “complicated” waveform broken down into simple sine waves (IMS PTY Ltd., 2004).
Now it is clear that the composite waveform in Fig 6. is the addition or superposition of all the composing harmonics. The first harmonic with frequency f is also called the fundamental harmonic, which often (though not always) determines the frequency of the composite waveform. The second, third, forth, ... and nth harmonics have a frequency of 2f, 3f, 4f, ...nf. If two tones are played on two different instruments, and they share the same fundamental frequency f, we say these two tones have the same pitch, even though the human perception of the these two tones are quite far apart, due to the timbre or various combination of harmonics that play in the role (Giordano, 2010).
Theoretically, if we select a fundamental frequency and then mix it with all the other harmonics, we are adding timber, the tone color to it and making it sound like any instrument. This is exactly how a synthesizer works (Parker, 2009).
Theoretically, if we select a fundamental frequency and then mix it with all the other harmonics, we are adding timber, the tone color to it and making it sound like any instrument. This is exactly how a synthesizer works (Parker, 2009).