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3.2.5
The Overtone Series (or Harmonic Series)

If you have the right equipment, you can identify and measure all the overtones present when you pluck a single guitar string and produce Middle C. The frequencies of all the dozens of overtones turn out to be simple whole-number multiples of the fundamental.

Taken together, the fundamental and all the overtones are called the harmonic series or the overtone series (these two terms mean the same thing).

Table 4 below shows the frequencies of the first 15 overtones of Middle C. It’s important that you sit down right now and memorize every single number in the “Frequency” column.

(No, wait! It’s not important.)

TABLE 4 Fundamental and First 15 Overtones of the “Middle C” Overtone Series

Tone / Overtone Multiple of Fundamental Frequency (Hz)
  • Fundamental
  • 1st Overtone
  • 2nd Overtone
  • 3rd Overtone
  • 4th Overtone
  • 5th Overtone
  • 6th Overtone
  • 7th Overtone
  • 8th Overtone
  • 9th Overtone
  • 10th Overtone
  • 11th Overtone
  • 12th Overtone
  • 13th Overtone
  • 14th Overtone
  • 15th Overtone
  • 1 (f)
  • f x 2
  • f x 3
  • f x 4
  • f x 5
  • f x 6
  • f x 7
  • f x 8
  • f x 9
  • f x 10
  • f x 11
  • f x 12
  • f x 13
  • f x 14
  • f x 15
  • f x 16
  • 261.6
  • 523.2
  • 784.8
  • 1,046.5
  • 1,308.0
  • 1,569.6
  • 1,831.2
  • 2,093.0
  • 2,354.4
  • 2,616.0
  • 2,877.6
  • 3,139.2
  • 3,400.8
  • 3,662.4
  • 3,924.0
  • 4,186.0

These are just the first 15 overtones—they continue on and on, ever higher in pitch, ever softer. The next overtone in the series above would be the 16th overtone, with a frequency 17 times that of the fundamental, or 4,447.2 Hz.

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