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Draw a diagram of the vowel triangle, giving the approximate position of the basic English vowels

Subject: Speech Processing

Topic: Speech Production, Acoustic Phonetics and Auditory Perception

Difficulty: Low

1 Answer
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(i) The plot F$_1$ vs F$_2$ for the vowel triangle is shown in figure or rather a vowel quadrilateral would represent the English vowels better as shown in figure. The vowel |i| can be seen on the top left corner (upper vertex of the triangle), which indicates a high second format (F$_2$) and very low first format (F$_1$)

(ii) Similarly the vowel |u| can be seen at the lower left corner (lowest vertex), indicating a low F$_1$ and F$_2$.

(iii) The vertex on the extreme right corner (the third vertex) of the triangle contains the vowel |a| which has a considerably high F$_1$ but a low F$_2$.

(iv) Therefore, we can say that the vowels |(i,a,u)| have extreme values for the formats F$_1$ and F$_2$.

(v) And it can also be observed that most of the other vowels have formant values near.

(vi) One of the sides of the triangle mainly the |i| - |a| axis and the |u| - |a| axis; the front vowels lie near the |i| - |a| axis and the back vowels lie near |u| - |a| axis.

The Vowel Triangle

(vii) There is an acoustic as well as articulation angle for interpreting the vowels, please refer figure, the tongue hump is raised to the roof of the mouth for |i| leaving a small cavity and is found on the top of the vowel quadrilateral, and the tongue is lowered for |a| leaving a large cavity and is placed at the bottom of the quadrilateral.

(viii) It should also be noted simultaneously that as the tongue height increases, the F$_1$ decreases, and when the tongue is shifted backwards the F$_2$ decreases, hence the vowel |i| that is position at the top has lowest F$_1$ and highest F$_2$ among all the other vowels.

(ix) The vowel |a| has the highest F$_1$ since the tongue position is the lowest.

(x) For producing the back vowels lips are required to be rounded where as the front vowels do not required anything of that sort.

(xi) As the tongue height, it is more likely that the vowels would have a more central tongue position laterally.

(xii) Therefore the difference in the F$_2$ for the lower vowels like |ae| and |a| is quite less when compared with the F$_2$ differences between higher vowels like |i| and |u|.

(xiii) As the height of the tongue increases the intensity of the vowel decreases over a range of 4 to 5 dB.

(xiv) There is a wide separation between F$_1$ and F$_2$ and also there is a -6 dB per octave fall-off for the high vowels, due to which they have little energy outside F$_1$.

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