1. Perturbation Theory, part 2
March 20, 2014

2. Life’s Persistent Questions
Let’s step back and review what our standing wave patterns look like in an open tube…
And where they come from, exactly.

3. Back to Perturbation Theory
Basic idea #1: vocal tract resonances (formants) are the result of standing waves in the vocal tract
These standing waves have areas where velocity alternates between high and low (anti-nodes), and areas where velocity does not change (nodes)

4. Perturbation Principles
Basic Idea #2: constriction at a velocity anti-node decreases a resonant frequency
anti-node
anti-node

5. Perturbation Principles
Basic Idea #3: constriction at a velocity node increases a resonant frequency
node
node

6. Labial
Constrictions in the labial region are at anti-nodes for both F1 and F2.
 Labial constrictions decrease both F1 and F2

7. Palatal
Labial
Constrictions in the palatal region are at an F2 node and near an F1 anti-node
 F1 decreases; F2 increases

8. Velar
Palatal
Labial
Constrictions in the velar region are at an F2 anti-node and near an F1 anti-node
 F1 decreases; F2 decreases

9. Pharynx
Velar
Palatal
Labial
Constrictions in the pharyngeal region are at an F2 anti-node and near an F1 node
 F1 increases; F2 decreases

10. Larynx
Pharynx
Velar
Palatal
Labial
Constrictions in the laryngeal region are at an F2 node and an F1 node
 F1 increases; F2 increases

11. Different Sources
For a particular articulatory configuration, the vocal tract will resonate at a certain set of frequencies…
no matter what the sound source is.
Let’s check out what Peter Frampton can do with a talk box…
and the “Sonovox”
Now let’s see what happens when we change our sound source to a duck call…

12. Duck Call Vowels
Now let’s filter the duck call with differently shaped plastic tubes….
Care to make any predictions?
duck call is placed here

13. Another View
[i]

14. Duck Call Spectrograms
[i]

15. Duck Call Spectra
[i]

16. How About These?
duck call is placed on this side

17. [i] vs. [e]
[i] [e]

18. [u] vs. [o]
[u] [o]

19. Philosophical Fragments
Consider the Cardinal Vowels, again.
An age-old question:
Why are the high, back vowels rounded…
And everything else unrounded?
Rounding back vowels takes advantage of an acoustic synergy…
which lowers both F1 and F2.
But is there anything wrong with rounding the other vowels?

20. Five Vowel Spaces
Many languages have only three or five vowels, separated evenly in the vowel space in a triangle
Here’s a popular vowel space option:
i u
e o a

21. Five-Vowel Spaces

22. Gujarati Vowel Space

23. A “Bad” Vowel Space
Five vowels in a vowel system are rarely, if ever, distributed thusly:
[i]
[e]
[æ]
Why?

24. Adaptive Dispersion Theory
Developed by Bjorn Lindblom and Johan Liljencrants
(Swedish speakers)
Adaptive Dispersion theory says:
Vowels should be as acoustically distinct from each other as possible
(This helps listeners identify them correctly)
So…languages tend to maximize the distance between vowels in acoustic space
Note: lack of ~ distinction in Canadian English.

25. Swedish

26. Unrounded Vowel Stats
Number of languages with the following unrounded vowels (out of 316, from the UPSID database):
i: : : 4
: 54
e: : 4
(e: 113) : 77 ( : 6)
: : : 4
æ: 38
a: 14 (a: 274) : 22

27. Rounded Vowel Stats
Number of languages with the following rounded vowels (out of 316, from the UPSID database):
y: : 6 u: 254
: : 48
ø: o: 88
: 5 (o : 133)
œ: : 100
: : 5

28. Rounded/Unrounded
Ratio of number of languages with rounded vowels divided by number of languages with unrounded vowels, for particular parts of the vowel space:
.056
.065 (22.2)

29. The Good, the Bad and the…
High, front region of the vowel space:
Unrounded vowels are preferred (good) (271)
Rounded vowels are dispreferred (bad) (21)
High, back region:
Unrounded vowels are bad (4)
Rounded vowels are good (254)
Low, back region:
Unrounded vowels are better (22)
Rounded vowels are worse (5)
Low, front region: Rounded vowels are really bad. (0)

30. Bad Vowel #1: [y] [y] has both labial and palatal constrictions
Why is this bad?

31. Bad Vowel #2: [ ]
[ ] has only a velar constriction
Why is this bad?

32. Bad Vowel #3: [ ] [ ] has a pharyngeal and a labial constriction
Why is this bad?

33. Really Bad Vowel #4: [ ]
[ ] has both laryngeal and labial constrictions
Why is this bad?

34. Advanced Tongue Root
Some languages have an added articulatory feature for vowels, called advanced tongue root
found in a lot of West African languages
What are the acoustic consequences of advancing the tongue root?

35. Ultrasound This is a speaker of Kinande. Kinande is spoken in Congo.
(from Gick, 2002)

36. Ultrasound: +ATR vs. -ATR
advanced (+ATR) retracted (-ATR)

37. ATR vowels in Akan
Akan is spoken in Ghana

38. +ATR vs. -ATR

39. ATR Vowel Spaces
DhoLuo is spoken in Kenya and Tanzania

40. F3 and , revisited
English has pharyngeal, palatal and labial constrictions
These constrictions conspire to drastically lower F3

41. F3 and , revisited

42. Retroflex Vowels
Retroflexion is a feature which may be superimposed on other vowel articulations.
Retroflexion is contrastive in vowels in Badaga, a language spoken in southern India.

43. Retroflex Vowel Spectrograms
[be]

44. F3 and [y] [y] has both labial and palatal constrictions
What effect would these constrictions have on F3?

45. [i] vs. [y]
[li] [ly]

46. Overrounded Vowels
Note: there is typically more rounding on [u] than [o]
and on [o] than
all the way down the line...
It is possible to have [u]-like rounding on lower vowels
“over-rounding” in Assamese
Assamese is spoken in Bangladesh.

47. Overrounded Vowel Spectrograms

48. Overrounded Vowel Spectrograms