Formant

What Are Formants in Linguistics?

Formants are the bread and butter of vowel analysis in linguistics.

You can see formants by looking at a spectrogram. Vowel formants show up as dark horizontal bands along the spectrogram of a speech sample. The higher the horizontal band on the spectrogram, the higher the frequency of the formant. When viewing a spectrogram, you should be able to see three or four formants.

Fig. 1 - The dark horizontal bands represent formants. There are four visible formants on this spectrogram.

The darkness of each formant band represents amplitude or how loud the formant is.

Three formants in particular help distinguish vowels from one another. These are the first, second, and third formants, also known as F1, F2, and F3. These formants signal a vowel's relative height and backness.

Harmonics vs. Formants

Formants are closely related to another series of frequencies: harmonics.

When you produce a vowel, you push air from your lungs through your glottis, causing your vocal folds to vibrate. The vibration produces a pressure wave; this wave is the sound of your voice.

The glottal source wave is a large wave made up of several smaller (higher-frequency) waves. Each of these higher-frequency waves is a harmonic of the glottal source wave.

Harmonics are visualized on a vowel's spectrum. The spectrum displays frequency on the x-axis and amplitude on the y-axis. It looks like a spiky row of frequencies that gradually decrease in amplitude. Each "spike" on the spectrum is a harmonic.

The formants, on the other hand, are the loudest groups of harmonics. If you look at the spectrum of a vowel, you'll see that the tops of the harmonic "spikes" form a wavy shape. The peak of each "wave" is a formant. In Fig. 2, you can see four distinct wave shapes. These are the same formants visible in Fig. 1.

Fig. 2 - Each "spike" on the spectrum represents a harmonic, and each "wave" represents a formant.

To summarize simply, harmonics are elements of the glottal source wave, and formants are elements of the vowel shape.

Formant Structure

The position of your mouth when you produce a vowel determines the structure of the vowel's formant frequencies. Here's a basic overview of how this works:

• F1 tells you how high the tongue is situated in the mouth.
• Higher vowels (like [i] and [u]) have a lower F1 than lower vowels (like [a] and [ɑ]).
• F2 tells you how far back the tongue is situated in the mouth.
• Back vowels (like [u] and [ɑ]) have a lower F2 than front vowels (like [i] and [æ]).
• F3 is not as informative as F1 and F2, but it helps to signal r-colored vowels.
• R-colored vowels have a lower F3 than other vowels.

First Formant (F1)

F1 is the lowest formant frequency in a vowel. It corresponds to vowel height.

High vowels are produced with a high tongue position. If you say the words Peter and potter to yourself, you'll notice that you place your tongue higher in your mouth for the [i] in Peter than for the [a] in potter.

F1 correlates inversely with height. The higher the vowel, the lower the F1 value. Because it involves a higher tongue position, the [i] in Peter has a lower F1 value than the [a] in potter.

Second Formant (F2)

The next formant is F2, which corresponds to vowel backness.

When you produce back vowels, you push your tongue further back into your mouth. Say the words bead and booed to yourself. You'll notice that your tongue shifts back and forth in your mouth as you alternate between the front [i] and the back [u].

F2 correlates inversely with backness. The further back the vowel, the lower the F2 value. Because it requires the tongue to be further back in the mouth, the [u] in booed has a lower F2 value than the [i] in bead.

Third Formant (F3)

F3 doesn't change based on height and backness as drastically as F1 and F2, but it does change in response to r-colored vowels.

R-colored vowels are produced with the bunched-up tongue characteristic of the American r sound. For example, the vowel in a general American English pronunciation of bird is an r-colored vowel. R-colored vowels have a very low F3 value compared to other vowels.

Formant Examples

Now for some examples of relative formant values. The vowel chart of the International Phonetic Alphabet (IPA) plots the different vowel categories by their F1 and F2 values. It shows F1 on the y-axis in inverse order: the vowels with the lowest F1 are closest to the top of the vowel chart. The chart shows F2 on the x-axis, also in inverse order. The vowels with the highest F2 are closest to the left of the chart.

Fig. 3 - The IPA vowel chart shows F2 (high to low) on the x-axis and F1 (high to low) on the y-axis.

By looking at the chart, you can identify a vowel's F1 and F2 values relative to the other vowels. For example:

• The high front vowel [i] at the top left corner has one of the lowest F1 values and the highest F2 value of all the vowels on the chart.
• The upper-mid front vowel [e] is lower and slightly to the right of [i], so you would expect it to have a higher F1 value and a slightly lower F2 value.
• The low central vowel [a] is at the bottom of the chart and thus has one of the highest F1 values. Since it's in the middle of the x-axis, it probably has a central F2 value.
• The upper-mid back vowel [o] is above [a] but below [u] on the chart, so it probably has a central F1 value. It lines up with [u] on the x-axis, so you would expect it to have a similar F2 value to [u].
• Because it's at the same height and further to the right on the chart, you would expect the high back vowel [u] to have a similar F1 value and a lower F2 value compared to [i].

Formants in Speech

Looking at the chart allowed for some predictions about the formant values of different vowels in natural speech. So, how accurate were those predictions?

Fig. 4 - You can see on this spectrogram how F1 and F2 change with each vowel.

In Fig. 4, you can see the spectrogram for a sequence of synthesized vowels [i, e, a, o, u]. The formants are marked with red dots.

The lowest band is F1. You can see that the vowels that are highest on the chart, [i] and [u], have the lowest F1 band. The lowest vowel, [a], has the highest F1 value, and the mid vowels have F1 frequencies between those of the high and low vowels.

The next band after F1 is F2. The vowels in Fig. 4 are shown in order from the left to the right side of the vowel chart or from the front to the back tongue position. You can see that F2 is highest for [i] and gradually steps down as the vowels move further back.

Since none of these vowels are r-colored, F3 stays fairly constant on the spectrogram.

There you have it! Vowel height and backness are reliable predictors of F1 and F2 frequencies. Likewise, F1 and F2 frequencies reliably signal vowel positions.