what's the difference between harmonics and formants?
Harmonics come from vibrations of the vocal folds
Formants come from vibrations of air inside the vocal tract
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Simple answer:
Harmonics are wiggles in the air that occur in response to a periodic sound. We call that sound source the fundamental frequency. Harmonics are always directly, mathematically related to the fundamental frequency. Harmonics come from the vocal folds in the human voice. You can't change which harmonics are possible without changing the fundamental frequency. All harmonics flow mathematically from the fundamental frequency. You can change the harmonics present in a given sound by changing the shape of the vocal folds and therefore changing the fundamental frequency being created. More closure in the vocal folds will create stronger, higher harmonics by increasing energy in all harmonics, but doesn't change which harmonics are present. Harmonics are considered part of the source of the sound. Formants acoustically amplify or dampen harmonics that are created by the vocal folds. Formants come from the vocal tract. The air inside the vocal tract vibrates at different frequencies depending on its size and the shape of opening. We call these frequencies formants. You can change the formants in the sound by changing the size and shape of the vocal tract. Formants filter the original sound source from the vocal folds. After harmonics go through the vocal tract some become louder and some become softer. |
harmonics
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During an exhale, air comes up from the lungs and passes through the larynx. If the vocal folds are closed inside the larynx during the exhale, they will begin to vibrate. As the vocal folds vibrate, they create a periodic frequency vibration that in turn creates a harmonic series.
The strongest and slowest vibration in the series is the fundamental frequency . The faster vibrations that occur simultaneously are called overtones or harmonics. For most purposes, the terms overtones and harmonics are interchangeable. The difference is one of accounting. Harmonics are all partials of the fundamental including the fundamental. Overtones are all partials of the fundamental starting at the second harmonic. They are, by definition, "over" the fundamental. In the below example where the fundamental is 100Hz, you would call the 200Hz wiggle the second harmonic, but the first overtone. |
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Harmonic Series
For the Harmonic Series to occur the original vocal fold vibration must be periodic. This means the vocal fold vibration must repeat it self in a pattern (e.g. 100 times per second=100Hz). However many air molecules the vibration pushes apart must be the same amount of air molecules that come back together. If the original vibration (or the fundamental frequency) is periodic, then the higher vibrations will be at predictable frequencies. The 2nd harmonic will always vibrate twice as fast as the fundamental. The 3rd harmonic will always vibrate three times as fast as the fundamental, etc. The harmonics will always be an integer multiple of the fundamental. |
An example of the harmonics created from the vocal folds if the fundamental pitch was 100 Hz.
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Here is how the harmonic series looks written out on the staff.
1 - The fundamental frequency is C2 which vibrates 65 times per second (written as 65 Hz).
2 - The second harmonic is an octave above the fundamental. It vibrates twice as fast as the fundamental at 130 Hz.
3- The third harmonic is an octave and a fifth above the fundamental. It vibrates three times as fast as the fundamental at 195 Hz.
4 -The fourth harmonic is two octaves above the fundamental. It vibrates four times as fast as the fundamental at 260 Hz.
And so on.
When a person sings a C2, the fundamental frequency on this staff, all of these different sounds are inherent within the C2. They are created in response to the C2 vibration. This phenomenon occurs often in nature. One vibration creates other measurable vibrations inspired by the original vibration.
1 - The fundamental frequency is C2 which vibrates 65 times per second (written as 65 Hz).
2 - The second harmonic is an octave above the fundamental. It vibrates twice as fast as the fundamental at 130 Hz.
3- The third harmonic is an octave and a fifth above the fundamental. It vibrates three times as fast as the fundamental at 195 Hz.
4 -The fourth harmonic is two octaves above the fundamental. It vibrates four times as fast as the fundamental at 260 Hz.
And so on.
When a person sings a C2, the fundamental frequency on this staff, all of these different sounds are inherent within the C2. They are created in response to the C2 vibration. This phenomenon occurs often in nature. One vibration creates other measurable vibrations inspired by the original vibration.
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Higher harmonics in the series are softer in amplitude (volume). Each higher harmonic is quieter by the same percentage as the one before it.
If the vocal folds were on their own without a vocal tract, the fundamental would be the strongest vibration and the higher harmonics would be much more quiet. This is because of another mathematical phenomenon called the spectral slope. It says that each harmonic will diminish in volume by an equal amount. If the second harmonic is 6% softer than the first, the third will be 6% softer than the second and so on. But the vocal folds are not on their own, and higher harmonics in the vocal signature can be louder than the fundamental. This is where the resonator comes in . |
An example of spectral slope.
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formants
If you blew across the top of these bottles, you would hear a pitch.
Why?
The air inside the bottle would vibrate and create a sound wave.
The air inside these containers wants to vibrate at a certain pitch based on the
size
shape
density of walls
and size of opening
of the container it's in.
Why?
The air inside the bottle would vibrate and create a sound wave.
The air inside these containers wants to vibrate at a certain pitch based on the
size
shape
density of walls
and size of opening
of the container it's in.
resonators |
This is the basic concept of resonators.
Resonators are containers of air. Resonators do not start the sound. They cannot initiate the first vibration. However if they come in contact with a sound wave that is similar to the one they want to vibrate at, they join in with that vibration. |
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Almost all instruments have containers of air that act as resonators.
The containers of air vibrate at different frequencies based on the size, shape, density of walls and size of opening of the container. |
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Simply put, smaller containers of air vibrate at higher pitches.
Larger containers of air vibrate at lower pitches.
You can remember this because small things in nature tend to make higher sounds and large things tend to make lower sounds.
Larger containers of air vibrate at lower pitches.
You can remember this because small things in nature tend to make higher sounds and large things tend to make lower sounds.
what is the resonator for voice?
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The resonator for the voice is called the vocal tract. It goes from the top of the larynx to the tip of the lips. See our page on the Vocal Tract for more information.
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Just like the bottles example, the vocal tract is a container of air. Yet, because the vocal tract can change shape in radical and rapid ways, it can be thought of as multiple containers of air that vibrate at different, specific, mobile frequencies.
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To make it simple start by thinking about two containers of air.
Container 1 - the air behind the tongue. From the top of the larynx to the hump of the tongue. Container 2 - the air above and in front of the tongue. From the hump of the tongue to the tip of the lips. Formant 1 - the pitch of the air that vibrates in container 1. Formant 2 - the pitch of the air that vibrates in container 2. note: This is a gross oversimplification because formants are actually quite complex. In reality, all of the vocal tract influences each formant, and nearly an infinite number can exist in our vocal tracts. However, only the largest/lowest pitched formants have measurable impact on vocal timbre. Further, formants can be defined in many ways: by their location, by frequency, by potential energy, and by kinetic energy, to start. As you begin your exploration, focus on the two lowest formants until you settle on the difference between formants and hamonics, and how they interact. Once you do, you will realize why you can let the bottle of air metaphor go and begin to ask new questions, but stick with it to start. |
how do you change the size and pitch of the resonator?
The voice is a very unique instrument because the resonator, the vocal tract, can change shapes and sizes and frequencies. This is very different than a guitar or piano, which once the wood is carved, the resonator cannot change size or pitch.
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The containers of air inside the vocal tract change shape and size when the muscles of the
tongue
neck
jaw
soft palate
lips
and pharynx engage.
tongue
neck
jaw
soft palate
lips
and pharynx engage.
Puzzle out with us some of the vocal tract shape changes that are most visible, and how they impact the first two formants (containers of air). It's interesting to note that the IPA system is built on these variables.
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If the jaw drops , Container 1 (behind the tongue) gets smaller and Container 2 (in front of the tongue) gets larger.
The pitch of formant 1 gets higher. The pitch of formant 2 gets lower. |
If the lips come forward both containers of air become larger. The pitches of both containers of air (Formant 1 and Formant 2) get lower.
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If the tongue goes forward, Container 1 (behind the tongue) gets larger and Container 2 (in front of the tongue) gets smaller.
The pitch of Formant 1 gets lower. The pitch of Formant 2 gets higher. If the tongue comes back, Container 1 (behind the tongue) gets smaller and Container 2 gets larger. The pitch of Formant 1 gets higher. The pitch of Formant 2 gets lower. |
If the pharynx narrows, Container 1 (behind the tongue) gets smaller.
The pitch of Formant 1 gets higher. If the pharynx stays neutral or "open", Container 1 (behind the tongue) remains large. The pitch of Formant 1 is lower. |
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If the larynx raises, both Containers 1 and 2 get smaller.
The pitch of Formant 1 and 2 gets higher. If the larynx lowers, both Containers 1 and 2 get larger. The pitch of Formant 1 and 2 gets lower. |
how vowels relate to resonator shapes
Examples:
The vowel for "heed", eeeee or [i]
Container 1 (behind the tongue) is large.
Container 2 (in front of the tongue) is small.
The pitch of the air in Container 1 (Formant 1) is low.
The pitch of the air in Container 2 (Formant 2) is high.
/i/ has a low F1 (@ 250 Hz) and a high F2 (@ 2000 Hz)
The vowel for "hod", aaahhhh or [a]
Container 1 (behind the tongue) is small.
Container 2 (in front of the tongue) is large.
The pitch of the air in Container 1 (Formant 1) is high.
The pitch of the air in Container 2 (Formant 2) is low.
/a/ has a high F1 (@ 750 Hz) and a close F2 (@ 1,000 Hz)
The vowel for "who'd", ooooooo or [u]
Container 1 (behind the tongue) is large.
Container 2 (in front of the tongue) is large.
The pitch of the air in Container 1 (Formant 1) is low.
The pitch of the air in Container 2 (Formant 2) is low.
/u/ has a low F1 (@ 250 Hz) and a low F2 (@ 800 Hz)
We use the @ symbol for formant frequencies for two reasons.
1) formants are mobile and move around, and are wider than a single frequency
2) the exact vowel color of all complex vowels (which is most vowels) is made up of a number of variables.
This means that any one formant can change its position a little and the complex vowel color will still be understood. An [u] can have a first formant of 250Hz or 400Hz and still be understood as [u]. In most cases, however, the center of the [u] first formant will be close to 250Hz.
Another variable to formants is that they can be wider and more diffuse (e.g. ranging from 250-350Hz with less power) or more narrow and concentrated (e.g. ranging from 250-275Hz with more power). This "Q factor" plays an important role in harmonic/formant interaction, but isn't discussed often. For most purposes, we can get enough out of realizing that formants are measured by a single frequency (e.g. 250Hz), but are actually wider than a single frequency. Harmonics have a fundamental that can be more or less a single frequency. The caveat to that point is that all voices waiver pitch a little, and intentional wavering in the form of vibrato can be quite wide, even up to dozens or hundreds of Hertz wide. We still say that the person is singing a single frequency.
The vowel for "heed", eeeee or [i]
Container 1 (behind the tongue) is large.
Container 2 (in front of the tongue) is small.
The pitch of the air in Container 1 (Formant 1) is low.
The pitch of the air in Container 2 (Formant 2) is high.
/i/ has a low F1 (@ 250 Hz) and a high F2 (@ 2000 Hz)
The vowel for "hod", aaahhhh or [a]
Container 1 (behind the tongue) is small.
Container 2 (in front of the tongue) is large.
The pitch of the air in Container 1 (Formant 1) is high.
The pitch of the air in Container 2 (Formant 2) is low.
/a/ has a high F1 (@ 750 Hz) and a close F2 (@ 1,000 Hz)
The vowel for "who'd", ooooooo or [u]
Container 1 (behind the tongue) is large.
Container 2 (in front of the tongue) is large.
The pitch of the air in Container 1 (Formant 1) is low.
The pitch of the air in Container 2 (Formant 2) is low.
/u/ has a low F1 (@ 250 Hz) and a low F2 (@ 800 Hz)
We use the @ symbol for formant frequencies for two reasons.
1) formants are mobile and move around, and are wider than a single frequency
2) the exact vowel color of all complex vowels (which is most vowels) is made up of a number of variables.
This means that any one formant can change its position a little and the complex vowel color will still be understood. An [u] can have a first formant of 250Hz or 400Hz and still be understood as [u]. In most cases, however, the center of the [u] first formant will be close to 250Hz.
Another variable to formants is that they can be wider and more diffuse (e.g. ranging from 250-350Hz with less power) or more narrow and concentrated (e.g. ranging from 250-275Hz with more power). This "Q factor" plays an important role in harmonic/formant interaction, but isn't discussed often. For most purposes, we can get enough out of realizing that formants are measured by a single frequency (e.g. 250Hz), but are actually wider than a single frequency. Harmonics have a fundamental that can be more or less a single frequency. The caveat to that point is that all voices waiver pitch a little, and intentional wavering in the form of vibrato can be quite wide, even up to dozens or hundreds of Hertz wide. We still say that the person is singing a single frequency.
in summary
Containers of air vibrate at certain pitches.
The pitch of the air changes if the container changes size, shape, or size of opening.
Small containers of air have higher pitches, large containers of air have lower pitches.
The size of the vocal tract's air containers can change shape when altered by the
jaw, tongue, lips, soft palate, pharynx and larynx.
When the vocal tract's air containers change shape, the pitch they vibrate at changes.
Each formant is mobile within about a thousand Hertz range. Some more narrow, some a little wider.
The first formant, for example, can range from around 250Hz-1000Hz.
Formants will never cross one another.
Even though the range of the first and second formants overlaps (1st=@250-1000Hz, 2nd=@800-2200Hz), the second formant can never cross below the first.
The pitch of the air changes if the container changes size, shape, or size of opening.
Small containers of air have higher pitches, large containers of air have lower pitches.
The size of the vocal tract's air containers can change shape when altered by the
jaw, tongue, lips, soft palate, pharynx and larynx.
When the vocal tract's air containers change shape, the pitch they vibrate at changes.
Each formant is mobile within about a thousand Hertz range. Some more narrow, some a little wider.
The first formant, for example, can range from around 250Hz-1000Hz.
Formants will never cross one another.
Even though the range of the first and second formants overlaps (1st=@250-1000Hz, 2nd=@800-2200Hz), the second formant can never cross below the first.
How to discern the difference between harmonics and formants in a spectrogram?
Harmonics are measured by their frequency. Frequency means the number of times something vibrates per second. Sound is measured in Hertz (Hz). A frequency of 100Hz (G2) means that the sound vibrates 100 times per second. A frequency of 400Hz (G4) means that the sound vibrates 400 times per second.
Perhaps the primary confusion when discussing harmonics and formants lies in the fact that formants are also measured by their frequency in Hertz (Hz). Learning to see the difference between harmonics and their mathematical series and formants with their radical mobility can be challenging at first. Here are some pointers:
Perhaps the primary confusion when discussing harmonics and formants lies in the fact that formants are also measured by their frequency in Hertz (Hz). Learning to see the difference between harmonics and their mathematical series and formants with their radical mobility can be challenging at first. Here are some pointers:
A typical spectrogram image is full of information. Look at the one below in Voce Vista and notice the following. On the far left, the numbers articulate the frequency. To the right of those numbers you can see a full harmonic series for a G2 at 100Hz. Notice that the lowest line aligns with 100Hz. Each harmonic is a different color and width. The color and width represent the amplitude (relative loudness) of the frequencies. In this color scheme, the wider, darker, redder ones are loudest. The thinner, bluer/blacker ones are softest.
To the right of the full harmonic series, you see the same harmonic series filtered to show the locations where formants occur, thereby boosting the harmonics near them. Remember that without the vocal tract, each harmonic would get equally softer to the previous one. The frequency at 1000Hz would be 10 times softer than the frequency at 200Hz. But you can tell that's not the case. The 1000Hz 10th harmonic in this example is darker red (e.g. louder) than even the fundamental frequency. That's the result of the second formant from the vocal tract aligning with the frequency at 1000Hz.
Look at the full harmonic spectrum. Notice that there are pockets that are softer (more yellow/orange/blue) and places that are louder (more red). The louder places aren't next to one another, and they occur across the harmonic spectrum. That's because the formants can move around due to the fact that the vocal tract can change shape. Notice the filtered harmonic spectrum. We've used filters in Voce Vista to show where the formant locations of five formants for this note are. You call the lowest frequency one the first formant. In this example the first formant is at 500Hz, the second formant at 1000Hz, the third formant at 2100Hz, and the fourth and fifth formants cluster at 2800Hz, meaning they align closely enough to create an extra boost in sound.
For the first, lowest formant, you would say that it lies around 500Hz, and amplifies the fifth harmonic of the 100Hz harmonic series. You can see that the harmonics immediately above and below 500Hz are softer. So, in this case, the first formant (the lowest frequency formant) is amplifying one harmonic that happens to be the 5th one. It, therefore, has a narrow Q factor. If the vocal tract shape remained the same, and the singer lept to a note that is 500Hz (C5), their first formant would amplify their first harmonic. That's because the first formant would remain at 500Hz if the vocal tract shape didn't change, but the new fundamental frequency would be 500Hz.
Because both the sung frequency that creates harmonics from the vocal folds, and the formants that increase energy in certain harmonics are both mobile, it can be confusing to sort out which is doing what.
Spend some time puzzling out the fact that formants and harmonics are both measured by frequency in Hertz (Hz), and that the goal of discovering where formants lie in relationship to a given sung note has to do with looking for areas of amplification. Get Voce Vista and try to find the areas that are amplified. Listen to the filtered sound and notice that you're hearing the color of the whole sound, even with only a few filters. That's how formants work. They choose focused aspects of the overall sound to amplify and make most dominant in the sound.
To the right of the full harmonic series, you see the same harmonic series filtered to show the locations where formants occur, thereby boosting the harmonics near them. Remember that without the vocal tract, each harmonic would get equally softer to the previous one. The frequency at 1000Hz would be 10 times softer than the frequency at 200Hz. But you can tell that's not the case. The 1000Hz 10th harmonic in this example is darker red (e.g. louder) than even the fundamental frequency. That's the result of the second formant from the vocal tract aligning with the frequency at 1000Hz.
Look at the full harmonic spectrum. Notice that there are pockets that are softer (more yellow/orange/blue) and places that are louder (more red). The louder places aren't next to one another, and they occur across the harmonic spectrum. That's because the formants can move around due to the fact that the vocal tract can change shape. Notice the filtered harmonic spectrum. We've used filters in Voce Vista to show where the formant locations of five formants for this note are. You call the lowest frequency one the first formant. In this example the first formant is at 500Hz, the second formant at 1000Hz, the third formant at 2100Hz, and the fourth and fifth formants cluster at 2800Hz, meaning they align closely enough to create an extra boost in sound.
For the first, lowest formant, you would say that it lies around 500Hz, and amplifies the fifth harmonic of the 100Hz harmonic series. You can see that the harmonics immediately above and below 500Hz are softer. So, in this case, the first formant (the lowest frequency formant) is amplifying one harmonic that happens to be the 5th one. It, therefore, has a narrow Q factor. If the vocal tract shape remained the same, and the singer lept to a note that is 500Hz (C5), their first formant would amplify their first harmonic. That's because the first formant would remain at 500Hz if the vocal tract shape didn't change, but the new fundamental frequency would be 500Hz.
Because both the sung frequency that creates harmonics from the vocal folds, and the formants that increase energy in certain harmonics are both mobile, it can be confusing to sort out which is doing what.
Spend some time puzzling out the fact that formants and harmonics are both measured by frequency in Hertz (Hz), and that the goal of discovering where formants lie in relationship to a given sung note has to do with looking for areas of amplification. Get Voce Vista and try to find the areas that are amplified. Listen to the filtered sound and notice that you're hearing the color of the whole sound, even with only a few filters. That's how formants work. They choose focused aspects of the overall sound to amplify and make most dominant in the sound.
next steps
- Learn how Harmonics and Formants interact together on our Resonance page
- Learn about the way Formants and Harmonics interact to determine vocal style on our Acoustic Strategies page
- Learn about ways of hearing predictable Harmonic/Formant interaction for practical vocal training on our Filtered Listening Of Vocal Regions page
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