Perturbation Theory Vowels (again)

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Perturbation Theory Vowels (again)
March 15, 2012
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On The Docket

• Today (and next Tuesday)
• more Perturbation Theory!
• the Tube model of vowel production
• Also on Tuesday Course Project 4 is due
• Homework assignments will be handed back after
  the weekend
• And I owe you a mystery spectrogram, too.
• In the meantime dogs playing the piano!

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The Big Idea, part 2

• Idea 2 constriction at (or near) a velocity
  anti-node decreases frequency
• The constriction slows the velocity down
• ? constriction at a pressure node decreases
  frequency
• Idea 3 constriction at (or near) a velocity
  node increases frequency
• The constriction increases the pressure
• This enhances airflow
• ? constriction at a pressure anti-node increases
  frequency

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Heres the goal

• Lets figure out how we can perturb the airflow
  in the articulatory tract to get to the corners
  of the vowel space.
• We need to
• Lower F1 and raise F2 --gt high, front vowels
• Lower F1 and lower F2 --gt high, back vowels
• Raise F1 and raise F2 --gt low, front vowels
• Raise F1 and lower F2 --gt low, back vowels
• Lets consider them each in turn

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F1

• Velocity node at glottis
• Velocity anti-node at lips
• To lower F1
• make a constriction closer to the lips than to
  the glottis
• To raise F1
• make a constriction closer to the glottis than to
  the lips

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F2

• Velocity nodes at
• palate
• glottis
• Velocity anti-nodes at
• lips
• pharynx

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F2

• To raise F2, make a constriction at the
• palate
• glottis
• To lower F2, make a constriction at the
• lips
• pharynx

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3. Low, Front Vowels

• Raise F1 and raise F2
• Where should we make constriction(s)?

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3. Low, Front Vowels

• Raise F1 and raise F2
• Where should we make constriction(s)?
• To raise F1

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3. Low, Front Vowels

• Raise F1 and raise F2
• Where should we make constriction(s)?
• To raise F1
• constrict close to glottis

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3. Low, Front Vowels

• Raise F1 and raise F2
• Where should we make constriction(s)?
• To raise F1
• constrict close to glottis
• To raise F2

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3. Low, Front Vowels

• Raise F1 and raise F2
• Where should we make constriction(s)?
• To raise F1
• constrict close to glottis
• To raise F2
• constrict close to glottis
• constrict at palate

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4. Low, Back Vowels

• Raise F1 and lower F2
• Where should we make constriction(s)?

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4. Low, Back Vowels

• Raise F1 and lower F2
• Where should we make constriction(s)?
• To raise F1

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4. Low, Back Vowels

• Raise F1 and lower F2
• Where should we make constriction(s)?
• To raise F1
• constrict near glottis

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4. Low, Back Vowels

• Raise F1 and lower F2
• Where should we make constriction(s)?
• To raise F1
• constrict near glottis
• To lower F2

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4. Low, Back Vowels

• Raise F1 and lower F2
• Where should we make constriction(s)?
• To raise F1
• constrict near glottis
• To lower F2
• constrict at pharynx

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Summary
palatal
labial
glottal
pharyngeal
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A Note About F3

• What about F3 distinctions?
• Theyre unusual.
• For acoustic reasons
• Intensity of voicing harmonics drops off at the
  higher end of the frequency scale
• (spectral tilt)
• And also auditory reasons
• Sensitivity to frequency distinctions drops off
  in the higher frequency regions
• Note F2 and F3 often merge for i

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Decreasing F3

• If we wanted to decrease F3...
• Where we would make constrictions?

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Decreasing F3

• If we wanted to decrease F3...
• Where we would make constrictions?
• Constrict at
• lips
• velum
• pharynx

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English

• English is distinctive because it has a
  very low F3.
• It has labial, post-alveolar (retroflex), and
  pharyngeal constrictions.

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Synergy

• The labial, retroflex and pharyngeal
  constrictions all work together to lower F3.
• Similarly, both labial and velar constrictions
  lower F1 and F2 in high, back (round) vowels
• Synergy
• Interestingly, labial-velar vowels are far more
  common in the languages of the world than either
• labial vowels
• velar vowels

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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)

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Perturbation Principles

• Basic Idea 2 constriction at a velocity
  anti-node decreases a resonant frequency

anti-node
anti-node
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Perturbation Principles

• Basic Idea 3 constriction at a velocity node
  increases a resonant frequency

node
node
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Labial

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

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Labial
Palatal

• Constrictions in the palatal region are at an F2
  node and near an F1 anti-node
• ? F1 decreases F2 increases

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Labial
Palatal
Velar

• Constrictions in the velar region are at an F2
  anti-node and near an F1 anti-node
• ? F1 decreases F2 decreases

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Labial
Palatal
Velar
Pharynx

• Constrictions in the pharyngeal region are at an
  F2 anti-node and near an F1 node
• ? F1 increases F2 decreases

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Labial
Palatal
Velar
Pharynx
Larynx

• Constrictions in the laryngeal region are at an
  F2 node and an F1 node
• ? F1 increases F2 increases

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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.
• Lets check out what Peter Frampton can do with
  a talk box
• Now lets see what happens when we change our
  sound source to a duck call

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Duck Call Vowels

• Now lets filter the duck call with differently
  shaped plastic tubes.
• Care to make any predictions?

duck call is placed here
http//www.exploratorium.edu/exhibits/vocal_vowels
/vocal_vowels.html
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Another View
i
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Duck Call Spectrograms
i
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Duck Call Spectra
i
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How About These?
duck call is placed on this side
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i vs. e
i e
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u vs. o
u o
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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?

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Five Vowel Spaces

• Many languages have only three or five vowels,
  separated evenly in the vowel space in a triangle
• Heres a popular vowel space option
• i u
• e o
• a

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Five-Vowel Spaces
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Gujarati Vowel Space
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A Bad Vowel Space

• Five vowels in a vowel system are rarely, if
  ever, distributed thusly
• i
• e
• æ

• Why?

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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)
• Solanguages tend to maximize the distance
  between vowels in acoustic space
• Note lack of distinction in
  Canadian English.

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Swedish
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Unrounded Vowel Stats

• Number of languages with the following unrounded
  vowels (out of 316, from the UPSID database)
• i 271 46 4
• 54
• e 83 4
• (e 113) 77 ( 6)
• 116 6 4
• æ 38
• a 14 (a 274) 22

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Rounded Vowel Stats

• Number of languages with the following rounded
  vowels (out of 316, from the UPSID database)
• y 21 6 u 254
• 3 48
• ø 15 o 88
• 5 (o 133)
• œ 7 100
• 0 5

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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
• .077 .130 63.5
• .056
• .077 22.0
• .065 (22.2)
• .060 25.0
• .000 .227

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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)

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Bad Vowel 1 y

• y has both labial and palatal constrictions
• Why is this bad?

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Bad Vowel 2

• has only a velar constriction
• Why is this bad?

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Bad Vowel 3

• has a pharyngeal and a labial constriction
• Why is this bad?

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Really Bad Vowel 4

• has both laryngeal and labial
  constrictions
• Why is this bad?

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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?

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Ultrasound
This is a speaker of Kinande. Kinande is spoken
in Congo. (from Gick, 2002)
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Ultrasound ATR vs. -ATR
advanced (ATR) retracted (-ATR)
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ATR vowels in Akan

• Akan is spoken in Ghana

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ATR vs. -ATR
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ATR Vowel Spaces

• DhoLuo is spoken in Kenya and Tanzania

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F3 and , revisited

• English has pharyngeal, palatal and labial
  constrictions
• These constrictions conspire to drastically
  lower F3

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F3 and , revisited
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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.

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Retroflex Vowel Spectrograms
be
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F3 and y

• y has both labial and palatal constrictions
• What effect would these constrictions have on F3?

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i vs. y
li ly
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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.

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Overrounded Vowel Spectrograms
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Overrounded Vowel Spectrograms