2-6 Complex Tones
Listen to the following recording of a didgeridoo: Didgeridoo
Listen to the following recording of a violin: Violin Double Stops
Are the sounds produced by a single instruments always as simple as the wave forms we have studied thus far?
No, musical instruments produce complex tones.
What are complex tones?
Simply put, complex tones consist of the collision of many frequencies with different amplitudes.
Despite the complexity of having multiple frequencies there is still order in the collision of the waves. The wave forms of musical sound are repetitive with definite periods and frequencies.
What characterizes a complex tone?
The frequencies, amplitudes, and phases of the component tone affect the complex tone that is produced.
Harmonics and Overtones
Think again of a slinky being vibrated like a snake. This can also be seen here: Waves In A Slinky
As the waves travel down the slinky we can see them reflect off the end and interfere with the new waves being introduced at the start. The resultant wave produced is a standing wave.
However, it is important to know that this is not the only frequency that will produce a standing wave on the slinky. Various frequencies can be used to produce a variety of standing wave patterns. The various frequencies which will produce standing waves are known as the harmonics.
The relationship between frequencies and harmonics is shown here: Standing Waves on a Violin
Overtones are essentially the same thing under a different naming system. Overtones are one component off from harmonics so that the first overtone will be the second harmonic, the second overtone will be the third harmonic, etc.
This relationship is shown in the table below:
| f1 | 1st Component | "Fundamental Sound"/ 1st Harmonic | |
| f2 | 2nd Component | 2nd Harmonic | 1st Overtone |
| f3 | 3rd Component | 3rd Harmonic | 2nd Overtone |
| f4 | 4th Component | 4th Harmonic | 3rd Overtone |
- This pattern will continue for all the frequencies which produce standing waves for that tone.
Continue: #REDIRECT 2-7 Assessment
Home: #REDIRECT The Physics of Music