Perturbation Theory, part 2

November 4, 2014

Before I forget• Course project report #3 is due!

• I have course project report #4 guidelines to hand out.

• I’m still working on the grading of the Korean stops lab exercise.

• Let’s check out the mystery spectrogram!

SummaryMale Formant Averages

200

300

400

500

600

700

800

900

1000

10001500200025003000

F2

F1

palatal

glottal

labial

pharyngeal

A Note About F3• What about F3 distinctions?

• They’re 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]

Decreasing F3

• If we wanted to decrease F3...

• Where we would make constrictions?

Decreasing F3

• If we wanted to decrease F3...

• Where we would make constrictions?

• Constrict at:

lips

“velum”

pharynx

English • English is distinctive because it has a very low F3.

• It has labial, post-alveolar (retroflex), and pharyngeal constrictions.

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

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.

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)

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

anti-node

anti-node

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

node

node

Labial

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

• Labial constrictions decrease both F1 and F2

Labial

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

• F1 decreases; F2 increases

Palatal

Labial

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

• F1 decreases; F2 decreases

PalatalVelar

Labial

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

• F1 increases; F2 decreases

PalatalVelarPharynx

Labial

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

• F1 increases; F2 increases

PalatalVelarPharynxLarynx

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…

Duck Call Vowels

http://www.exploratorium.edu/exhibits/vocal_vowels/vocal_vowels.html

duck call is placed here

• Now let’s filter the duck call with differently shaped plastic tubes….

• Care to make any predictions?

Another View

[i]

Duck Call Spectrograms

[i]

Duck Call Spectra

[i]

How About These?

duck call is placed on this side

[i] vs. [e]

[i] [e]

[u] vs. [o]

[u] [o]

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?

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

Five-Vowel Spaces

Gujarati Vowel Space

A “Bad” Vowel Space• Five vowels in a vowel system are rarely, if ever, distributed thusly:

[i]

[e]

[æ]

• Why?

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.

Swedish

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

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

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

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)

Bad Vowel #1: [y]

• [y] has both labial and palatal constrictions

• Why is this bad?

Bad Vowel #2: [ ]

• [ ] has only a velar constriction

• Why is this bad?