Table of Contents:  Background  Introduction  Procedure Data Analysis  Conclusion  Bibliography  Return To Research Page

Background 

The source of any sound is a vibrating object. 

Sounds may be characterized by pitch, loudness, and quality. 

Sound is carried through space in the form of waves 

The quality of sound refers to different timbre or tone color

Sound quality depends on the presence of overtones (their number and amplitude)

When a note is sung, the fundamental (lowest resonant frequency) as well as the overtones are heard all at the same time

A waveform is the composite of all overtones

An overtone is any resonant frequency above the fundamental

A formant is a favored frequency produced by some sort of resonance which stays the same even if the fundamental changes

The formant frequencies are distinctly different for the three vowel sounds (EE, AH, OO)

Pitch of a sound is determined by the frequency, the higher the frequency, the higher the pitch

Articulation determines the vowel, which determines the frequency of the formant

Beat frequencies occur when there are two simultaneous frequencies which create interference, which make the sound of beats 

Constructive interference means that the frequencies are the same, so the sound heard is louder

Destructive interference means the frequencies are different, creating beats

Jake and Joe are amazing students.

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Introduction: 

We wanted to discover to what extent vocal overtones changed their frequency as different variables were changed. The variables we tested were vowel shape (ah, ay, ee, oh, oo), volume, and gender.  

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Procedure: We will be using a computer program called LoggerPro to measure the overtone frequencies and magnitudes. We will have a microphone connected to a computer which will record our voices and display the prominent overtones as frequencies on a graph. Using this data we will analyze the overtones and see which variables made significant changes in the overtone patterns.  

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Data Analysis  

Our first data comparison will be between Jake and Kaley. This will show the difference in sound of the male and female voice. The variable is gender; the control is the pitch (the A above middle C, which is 440 hertz). We will look at how the overtones vary between male and female voices as the vowel shape is changing. We will use a Venn diagram to show the differences and similarities. Here, the A (440 hertz) that Jake and Kaley sang on an Ah had an Octave overtone (880hertz) in common. Kaley had two E’s as overtones. So here, the A (440hertz) is mostly comprised of an octave overtone, and fifths. This is why a different sound is heard when Kaley and Jake sing the same note. The prominent Overtones here are the Octave, and the fifth.  The eee was very rich in overtones for both Kaley and Jake. The common overtones here were the 880hertz A, and the 1757hertz A (two octaves above the fundamental). Jake’s note had two E’s (1318hertz and 2636hertz) and an even higher A. (Something interesting to note was Kaley’s D# overtone. It is not quite a fifth, so I thought that it could be an experimental error. But the same overtone showed up on Jake’s 440hertz A that was sung on an aay vowel. It doesn’t sound like much, but sometimes when people sing an aay vowel they do what is called a diphthong, which means they attach an eee sound on to the end. So this could be another part of what makes an eee). Again, the octave and the fifth above the octave are the prominent overtones. When Kaley and Jake sung an oh vowel, they had an 880hertz octave and the 1318hertz fifth above that in common. Kaley had two other octaves above the fundamental creating her tone. Kaley and Jake have very different sounding voices. During the experiment, they sang on the same exact note, with the same vowel shape. While their overtones were similar each time, there was always something different. The differences in the overtones account for the differences in tone that is heard from a male or female voice. The next variable we tested is vowel shape. We will compare and contrast the difference between the five vowels, and what makes them sound different. Jake sang the five vowels on the A above middle C. We will use a chart to show the differences in overtones.  

 
All of the vowels are different in fundamental ways, except for the oh and ooh, but they were even different in how intense each overtone was. The ah is the least rich in overtones. This may be because I was slightly flat (below pitch), so most of the visible overtones on the computer program were too random to record. The aay had the standard overtones of 880hertz and 1318hertz, but it also had a D#, which could account for an obnoxiously sung eee (because of the diphthong) vowels hectic sound. The eee was the richest in overtones, which is most likely why it has the most distinct sound. The most common overtone intervals in this part of the experiment were the Octave and the fifth above the octave, the same as the Gender experiment. The third and final variable we tested was voice placement. Jake sang falsetto, head, and chest voices. The control was the vowel and the note (I had to sing the A an octave lower on 220Hz for chest voice, otherwise it wouldn’t be chest voice). 

There wasn’t a lot of difference in the intervals of the overtones. The octave and the fifth above the octave were present in each note. The head voice had the most overtones because I had to sing louder in order for it not to be in falsetto. 

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Conclusion:  As the variables changed, the number of overtones changed. This is why they each have a unique sound. However, the overtones were generally the same intervals above the fundamental. The most common partials were unanimously the fifth and the octave (varying octaves of each). These differences in overtones are interesting because they determine the tones of notes that we hear. Our uncertainties were closeness to the microphone, how loud we sung for each recording, sound disturbances in the room, and the pixels in the computer program didn’t allow for 100% accurate readings.   

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                                                                                                    Bibliography:

1. Physics, Giancoli 1998
2.World Book Encyclopedia, Field Enterprises Educational Corporation 1967
3.hyperphysics.phy-astr.gsu.edu/hbase/music/harmon.html , Georgia State University4.World Dictionary FEEC 1967
5.Useful Mathematical and Physical Fornulae, Matthew Watkins 2000

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Useful Sites

http://www.spectralvoices.com/secondpg.htm - this website helped us in discovering some of the properties behind vocal overtones.

http://exhibits.pacsci.org/music/MusicPhysics.html - this was a basic background site for our research on music and physics.

http://www.numbera.com/musictheory/mechanics/physics.aspx - another technical site with information on the voice, overtones, and sound quality.

http://www.physicsforums.com/archive/index.php/t-19009.html - this website helped us get information on the physics of sound and its properties.
 


 

happy picnicking….