Do Harmonics Determine Vowel Sounds?

Have you ever heard the sound of dogs barking, a door slam, or an audience applauding? These, along with all other sounds, have one thing in common. They have their own set of harmonics, also known as overtones, that when heard at the same time create what we call that certain sound.

Now there are two parts to sound. There is noise and there is music. The sounds I gave for examples would be placed in the noise category because the harmonics that make up that sound are so disorganized that no real pitch can be heard. This is why the noise sounds unorganized and sometimes unpleasant. In music the harmonics are organized in such a way that a definite pitch can be made out. Harmonics play a part in what the pitch is and also how the pitch sounds to the human ear. How it sounds is called the tone color or timbre, and cannot be defined quantitatively only in qualitative terms such as bright, warm, ringing, hollow, or brassy (Kerman 11). The differences in the relative amplitudes of the various harmonics that make up the pitch cause the differences in musical instruments (Giancoli 361). This is what makes an oboe sound different than a clarinet or a piano different than an organ (Lampton 36).

However, the most distinctive tone color of all is the human voice (Kerman 11). The human voice is fascinating. While all man made instruments with the same name sound alike, no human voice sounds like another. As with the differences in instruments, this is caused by the differences in harmonics between each person. Everyone creates their own set of harmonics that is unique to them, just like fingerprints (Berger 24).

I have noticed, while observing Tualatin High School’s Treble Choir, that when the choir is singing a unison pitch on the same vowel, a vowel is defined as a sound that is the result of the acoustical properties of one’s vocal tract that is also governed by the position of one’s lips, jaw, tongue, and velum (Wall 3), and one person is singing a slightly different vowel then that person sticks out even though they would normally be drowned out. This leads me to my question. Harmonics make a difference in pitch and timbre. In my research I will answer the question as to whether or not harmonic structure makes a difference in vowel sounds as well. I hypothesize that each vowel sound will have its own harmonic structure.

Setup:

Here is a diagram of my setup-

Method:

To get the harmonic structure of each vowel I used FFT which analyzes the voice and gives the amplitude of each overtone in volts. Each singer sang a given pitch, which was an A at 440 Hz for the girls and at 220 Hz for the guys, for a sustained time. The note was given from the same pitch pipe each time. After I made sure they were singing the pitch correctly and steadily I took the data. The program records about one-tenth of a second of the person singing. After I took all the data points I printed out the graphs and laid them out side by side to see if I could see any similarities or differences.

Results:

by participant | by vowel

Because of the nature of the data the analysis is mostly qualitative.

Graphs organized by participant

Participant 1 | Participant 2 | Participant 3 | Participant 4

It might take a couple seconds for the graphs to load.

Participant #1

Raw Data

Ah Eh

Ee Oh

Participant #2

Raw Data

Ah Eh

Ee Oh

Participant #3

Raw Data

Ah Eh

Ee Oh

Participant #4

Raw Data

Ah Eh

Ee Oh

Graphs organized by vowel

Ah Vowel|Eh Vowel|Ee Vowel|Oh Vowel|Oo Vowel

It might take a couple seconds for the graphs to load.

Ah Vowel

Raw Data

Participant #1 Participant #2

Participant #3 Participant #4

Eh Vowel

Raw Data

Participant #1 Participant #2

Participant #3 Participant #4

Ee Vowel

Raw Data

Participant #1 Participant #2

Participant #3 Participant #4

Oh Vowel

Raw Data

Participant #1 Participant #2

Participant #3 Participant #4

Oo Vowel

Raw Data

Participant #1 Participant #2

Participant #3 Participant #4

Discussion:

My data supported my thesis that each vowel has its own harmonic structure. The ah vowel was typically dominated by the fundamental and first two harmonics. The eh vowel had many of the harmonics mixed together. The ee vowel was dominated by the fundamental with little from any of the other overtones. The oh vowel had many of the overtones but the fundamental, first and second harmonics were the most prominent. Finally, the oo vowel, like the ee vowel, was dominated by the fundamental but had more assistance from other harmonics.

With these comparisons made I can see now why each vowel sounds as it does. The ee and oo vowels have a somewhat hollow sound at times which can be attributed to the fact that the majority of their harmonic structure is made up of the fundamental. Also the rest of the vowels tend to sound fuller and their structures are more split equally among the other overtones, how they are split depends on the singer.

My actual lab did not have many difficulties I had to face in making sure it worked right or finding hidden variables I might not have overlooked. There were a few problems I ran into which caused me to discard some data. One set was incomplete and some parts were mislabeled, so I could not properly analyze all the vowels because I was not sure which were which. The other had sung to low, for the graphs to make out any clear harmonic structure. Overall they all sung on pitch, which should be expected seeing that all of the participants are in this school’s chamber group, and at the relatively same volume.

While analyzing the data I noticed that I could not successfully analyze the graphs quantitatively. Each person has their own harmonic structure that is unique to them. This was already known from the background research. I tried to use the actual values for each of the overtones to find things like the percentage of the structure each harmonic took up. In the end I found this step to be quite redundant. Firstly, the numbers did not match up closely because of the different structures. Also, it came up with the same qualitative results that I could get from the original graphs from the fft.

It would be interesting to go further on the analyzing of these graphs to see if we could quantitatively map a persons harmonic structure. What would have to be done is when the data is taken a person educated on the subject of voice quality would write down what they hear on each vowel. For example, they would see if a person was singing loud or soft and what the timbre sounded like. These qualitative descriptions of the voice itself would then be compared to the graphs of the singer’s voice to see if any patterns could be made. It would also be nice to do this experiment on more people to see if the pattern continues.

Bibliography:

Berger, Milton. The Science of Music. New York: Harper Collins, 1989.

Giancoli, Douglas C. Physics: principles with applications. Fifth Edition. New Jersey: Prentice-Hall, 1998.

Kerman, Joseph. Listen. Third Brief Edition. New York: Worth, 1996.

Lampton, Christopher F. Sound: more than what you hear. New Jersey: Enslow, 1992.

Wall, Joan, Robert Caldwell, Tracy Gavilanes, and Sheila Allen. Diction for Singers. Dallas: Pst...Inc.,1990.

Links:

"Fundamental Frequency and Harmonics"- From "The Physics Classroom." A good introduction to harmonics and frequency. Explains nodes and anti-nodes. Also has information on wavespeed in relation to wavelength and frequency.

"Natural Frequency"- Also from "The Physics Classroom." Begins to connect harmonics in musical terms. Defines timbre and how harmonics cause the timbre that is heard.

"Understanding Harmonics"- Starts from the beginning. Defines pitch and the wave thoery. Also explains how to play harmonics and how to calculate them.

"Vocal Tract Resonance"- Illustrates the human vocal chords and how sound is resonated in the human body.

"Vowel Sounds"- Explains how vowel sounds are formed by humans.

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