How are vowels formed?
As we phonate, our vocal folds produce a complex sound spectrum, made up of a wide range of frequencies and overtones. As this spectrum travels through the various differently-sized areas in the vocal tract, some of these frequencies will resonate more than others, depending on the sizes of the resonant areas in the tract. Larger spaces in the vocal tract will resonate at lower frequencies, while smaller spaces resonate at higher frequencies.
The two largest spaces in the vocal tract, the throat and mouth, therefore, produce the two lowest resonant frequencies, or formants. These formants are designated as F1 (the throat/pharynx) and F2 (the mouth). In singing or speaking, it is these two lowest formants that are controlled by shaping the resonant areas with lip and tongue movements to produce vowels. [Vocalists can also change the length of the vocal tract to modify formant frequencies; for details on this, see the tutorial on Rules for Modifying Vowels.]
Which formant frequencies result in which vowels?
The following vowel chart, adapted from the work of G.E. Peterson and H.L. Barney in 1952, shows the frequency regions for F1 and F2 which result in the 10 English vowels:
The vowels 
, [i], and [u] represent the three extremes of F1-F2 locations in the vowel chart and tongue placement. The other seven vowels are placed within these extremes. The three “corner vowels” are easy to remember by tongue placement:
- For the , or “ah” sound as in father, the tongue is low and back;
- For the [i], or “ee” sound as in keep, the tongue is high and front; and
- For the [u], or “oo” sound as in loot, the tongue is high and back.
Note, too, that the vocal tract shape 
(as in the word “us”) is located at the center of the vowel chart. It is oftened referred to as the neutral vowel because the tongue is neither high nor low, forward nor back. Make this sound. Do you see why scientists can use a tube shape to mimic the vocal tract for speech simulation research? The vocal tract is roughly uniform in cross-sectional shape from bottom (just above the larynx) to top (lips).
Individual Differences in Vowel Production
As a concluding note, a rich area of research involves the study of differences among individuals in regard to formant frequencies. These differences are attributable to differences in size, age, gender and speech habits. Differences can also be observed between speaking and singing, and between singers due to variability of training techniques. Often, the singer must balance vowel intelligibility with a beautiful quality of sound.