Phonetics Phriday: Fundamental Frequency, Harmonics, and Formant Frequencies

One of the most common questions teachers receive in introductory acoustic phonetics is, “What’s the difference between f0, harmonics, and formant frequency?” The best way to explain these concepts is by beginning with the Source-Filter Model.

The Source-Filter Model

The Source:

Forget about the filter for a moment. We’re going to start with the Source, which is where the sound comes from; more specifically, the vocal fold vibration.

• f0 – Also known as the fundamental frequency,  f0 is a property of the source and is perceived by the ear as pitch. The f0 of the adult human voice ranges from 100-300 Hz.

To Find the f0 in Praat:

There are several ways to find the fundamental frequency:

1. Highlight the vowel. Then go to the Spectrum menu up top and select “view spectral slice.”  In the spectrum window, you’ll see several peaks. Click on the top of the first peak. The value of the first peak in Hz is the fundamental frequency.
2. You can also find the fundamental frequency by counting and highlighting ten full periods of the vowel. Apply the 10 periods and their duration to the following formula: number of periods/ total duration. So if 10 periods of a vowel last .089 seconds, then your formula is 10/.089, which results in a fundamental frequency of 112.36 Hz.
3. Another way to find the fundamental frequency is to go to the “Pitch” menu above and select “Show Pitch.” A blue line will appear on your spectrogram. Click on one of the blue dots located near the midpoint of your vowel. The fundamental frequency will be displayed in Hertz on the right side of the spectrogram. You can also get a mean pitch of the entire vowel by selecting the vowel, going to the “Pitch” menu above, and selecting “Get  Pitch.”

• Harmonics- The vocal signal is a complex periodic wave made up of several simple periodic waves. Each of the simple waves is called a harmonic. The fundamental frequency, or f0, is the first harmonic, or H1. There is a harmonic at each interval of the f0 up to infinity. Vocal fold vibration produces many harmonics above f0, all the way up to 5000Hz in the adult human vocal tract. These harmonics decrease in amplitude as the frequency increases.

To Find Harmonics

Begin with the fundamental frequency. The formula for finding the different harmonics is:

H(k)=k * f0

Where k is the harmonic you’re trying to find and f0 is your fundamental  frequency. So, if you’re trying to find the second harmonic, and your fundamental frequency is 112 Hz, H2= 2 * 112, or 224 Hz.

The Filter:

You can now forget about the Source, as we are now going to talk about the Filter. The only thing you need to remember about the source in relation to the filter is that the vocal fold vibration sets the vocal tract vibrating as well. The vocal tract above the larynx is constantly changing shape as we speak, which in turn changes the quality of the vowel. While acting as a filter, the vocal tract attenuates some frequencies and accentuates others. How does the vocal tract decide which frequencies to accentuate? The size and shape of the resonator (your vocal tract) is set into forced vibration by another vibration (the source, your vocal folds) to determine its natural frequencies. This forced vibration is called resonance. The resonant frequency is the preferred frequency at which an object oscillates when set to vibration. Keep in mind that this has nothing to do with fundamental frequency.

• Formant Frequency- Resonances of the vocal tract are called formants. By changing the shape of the vocal tract, you also change the frequency of the formant. These formants can be seen as dark bands in the spectrogram. Each vowel has its own characteristic filter functions. High vowels have a low F1, while low vowels have a high F1. Front vowels have a high F2, while back vowels have a low F2.

How to Find Formant Frequencies in Praat:

Select the mid-point of the vowel and go to the “Formant” menu above. Select “Formant Listing.” The first number will be the time in the recording you’ve selected. The second number will be the F1 value, which roughly corresponds to the height of the vowel. The third number will be the F2 value, which roughly corresponds to the frontness/ backness of the vowel.

I hope this has helped to explain the differences between fundamental frequency, harmonics, and formant frequencies. Feel free to e-mail me at Ashley.94@osu.edu if you have any further questions.

Nichole Ashley

UnderLings President

The Ohio State University