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• The sample rate;
• The actual frequency being played;
• The DFT size (number of samples);
• The amount of audio being analyzed (the length of the recording);
• The choice of "window function" (this item has a particularly outsize effect. Audacity has several to choose from), and:
• The fact that the OP is trying to represent a DFT with over 16,000 data points on an image which is only 1300 pixels wide. Some points are being omitted.

• The sample rate;
• The actual frequency being played;
• The DFT size (number of samples);
• The amount of audio being analyzed (the length of the recording);
• The choice of "window function" (this item has a particularly outsize effect. Audacity has several to choose from), and:
• The fact that the OP is trying to represent a DFT with over 8,000 data points on an image which is only 1300 pixels wide. Some points are being omitted.

Before drawing conclusions from a spectrogram of this type, it's important to understand the limitations of the algorithm being used -- in particular, the errors that are present the DFT.

Notice how wide the spectrum is. We can be sure that this is not due to dispersive effects, because we know beforehand that the wave is perfect (neglecting quantization error and so forth); it was generated by a computer.

• The sample rate
• The actual frequency being played
• The DFT size (number of samples)
• The amount of audio being analyzed (the length of the recording)
• The choice of "window function" (this item has a particularly outsize effect. Audacity has several to choose from)
• The fact that the OP is trying to represent a DFT with over 16,000 data points on an image which is only 1300 pixels wide. Some points are being omitted.

2. The location and manner in which the string is plucked. As mentioned by @fraxinus and others, this will emphasize certain harmonics. For an electric guitar, pickup location will also play a role.

3. The fact that the fundamental simply does not have to be the most powerful tone. Even though the fundamental is likely to be the most powerful, all things being equal, there is nothing that says it has to be, and your ear tends to perceive the tone favorably even if the fundamental is highly attenuated.

Before drawing conclusions from a spectrogram of this type, it's important to understand the limitations of the algorithm being used -- in particular, the errors that are present in the DFT.

Notice how wide the peak is. We can be sure that this is not due to dispersive effects, because we know beforehand that the wave is perfect (neglecting quantization error and so forth); it was generated by a computer.

• The sample rate;
• The actual frequency being played;
• The DFT size (number of samples);
• The amount of audio being analyzed (the length of the recording);
• The choice of "window function" (this item has a particularly outsize effect. Audacity has several to choose from), and:
• The fact that the OP is trying to represent a DFT with over 16,000 data points on an image which is only 1300 pixels wide. Some points are being omitted.

2. The location and manner in which the string is plucked. As mentioned by @fraxinus and others, this will emphasize certain harmonics. For an electric guitar, pickup location will also play a role.

3. The fact that the fundamental simply does not have to be the most powerful tone. Even though the fundamental is likely to be the most powerful (all things being equal), there is nothing that says it has to be, and your ear tends to perceive the tone favorably even if the fundamental is highly attenuated.

Before drawing conclusions from a spectrogram of this type, it's important to understand the limitations of the algorithm being used -- in particular, the errors that are present in a DFT of this type.

The actual reason for the louder 3rd overtone is likely a combination of several factors already mentioned in other answers.

Before drawing conclusions from a spectrogram of this type, it's important to understand the limitations of the algorithm being used -- in particular, the errors that are present the DFT.

The actual reason for the louder 2nd overtone is likely a combination of several factors already mentioned in other answers.