Vowels (yet again)

February 25, 2010

Housekeeping• Term project prospectuses?

• Today we’ll lay the groundwork for lab exercise #3.

• Due next Thursday.

• Wrap up Perturbation Theory

• And start in on the tube model of vowel production.

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.

Liljencrants + Lindblom (1972)• Attempted to quantify “contrast” in the vowel space.

• to emphasize the importance of perception in the formation of phonological structure.

• They start with an articulatory model of the limits of the vowel space:

• note: space is plotted in three formants…

• and in mels (auditory equivalent of frequency)

Liljencrants + Lindblom (1972)• Quantification of contrast in the space:

• Given m pairs of n vowels,

• Where m = (n * (n-1)) / 2

• And ri2 = the Euclidean distance between the ith pair of

vowels, in formant space.

• The perceptual goal of the system is:

• I.e., the more formant space between vowels,

• the easier they will be to distinguish from one another.

• Note: floating magnets analogy

• Also: crowded elevator analogy

An Auditory Interlude• In the 1920s, psychophysicists noticed that:

• listeners can more accurately distinguish between pure tones of low frequency than between pure tones of high frequency.

• (there are interesting physiological reasons for this)

• To capture this fact, they developed the mel scale of frequency.

• A Mel = auditory analogue of Hertz (acoustic frequency)

• Twice the number of mels = twice as high of a perceived frequency.

Quiz Time• Let’s try the Mel scale test!

• Match this tone:

• To the tone that is twice its frequency:

• Now try it for a higher frequency tone:

• Which tone is twice the frequency?

• Mels = 1127.01048 * ln (1 + F/700)

• where acoustic frequency (F) is expressed in Hertz.

The Mel Scale

Masking• Another scale for measuring auditory frequency emerged in the 1960s.

• This scale was inspired from the phenomenon of auditory masking.

• One sound can “mask”, or obscure, the perception of another.

• Unmasked:

• Masked:

• Q: How narrow can we make the bandwidth of the noise, before the sinewave becomes perceptible?

• A: Masking bandwidth is narrower at lower frequencies.

Critical Bands• Using this methodology, researchers eventually determined that there were 24 critical bands of hearing.

• The auditory system integrates all acoustic energy within each band.

• Two tones within the same critical band of frequencies sound like one tone

• Ex: critical band #9 ranges from 920-1080 Hz

• F1 and F2 for might merge together

• The auditory system consists of 24 band-pass filters.

• Each critical band 0.9 mm on the basilar membrane.

• Each filter corresponds to one unit on the Bark scale.

Bark TableBand Center Bandwidth Band Center

Bandwidth

1 50 20-100 13 1850 1720-2000

2 150 100-200 14 2150 2000-2320

3 250 200-300 15 2500 2320-2700

4 350 300-400 16 2900 2700-3150

5 450 400-510 17 3400 3150-3700

6 570 510-630 18 4000 3700-4400

7 700 630-770 19 4800 4400-5300

8 840 770-920 20 5800 5300-6400

9 1000 920-1080 21 7000 6400-7700

10 1170 1080-1270 22 8500 7700-9500

11 1370 1270-1480 23 10500 9500-12000

12 1600 1480-1720 24 13500 12000-15500

Bark Scale of Frequency

• The Bark scale converts acoustic frequencies into numbers for each critical band

Liljencrants & Lindblom (1972)• In perceptually optimal systems…

• vowels tend to spread out around the edges of the available space.

• There is also a trend for more high vowel contrasts than are normally found in language.

• Possible fixes:

1. A better quantification of contrast

2. Articulatory factors

• In particular: “ease of articulation”, or a principle of “least effort”

3. Syntagmatic aspects

• Conclusion: phonetics (and perception) are relevant to the study of language

• = it is not a strictly formal object.

H & H Theory• In later work, Lindblom recognized the need to temper the needs of the listener with speaker-based articulatory constraints.

• “Unconstrained, a motor system tends to default to a low-cost form of behavior.”

• = Speakers tend to be lazy (or efficient), for biological reasons.

• For similar biological reasons, speech is adaptive.

• = responds to changing conditions and listener needs.

• “If the speech system operates so as to minimize 'articulatory effort', we should expect it to undershoot phonetic targets quite often, but not necessarily in every single instance. The key point is: Speakers have a choice.”

H & H Theory• The articulatory result: speech can vary between hypo- and hyper-articulation.

• Hypoarticulation: speakers undershoot phonetic targets

• Energy is conserved speakers are happy

• Speech quality is reduced listeners job is tougher

• Hyperarticulation: speakers exert greater effort to reach phonetic targets

• Sounds are more distinct listeners’ job is easier

• More energy is consumed speakers are less happy

• "Clear speech is not merely normal speech produced louder. It also involves reorganization of articulatory gestures and acoustic patterns."

The Upshot• “…our story conforms with accounts of speech production that view it as a continual tug-of-war between demands on the output on the one hand and system-based constraints on the other…”

• Lindblom’s approach is a novel way of dealing with the problem of invariance.

• “there is simply no way to define a phonetic category in purely acoustic terms.” --Liberman and Mattingly

• In H&H Theory, variance is a natural extension of the adaptive demands of the speech communication task.

• (i.e., it’s not really a problem)

• “…adaptive behavior is the reason for the alleged lack of invariance in the speech signal.”

Cost/Benefit• In the production of vowels, a lip rounding gesture always comes at an articulatory cost.

• (it’s an extra gesture)

• H & H Theory predicts:

• Vowels will only be rounded if rounding improves the vowel’s contrastiveness.

• “Bang for your buck”

• Let’s check out some numbers…

Raw Numbers• 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

Raw Numbers• 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?

Bad Vowel #3: [ ]

• [ ] has a pharyngeal and a labial constriction

• Why is this bad?

Really Bad Vowel #4: [ ]

• [ ] has both laryngeal and labial constrictions

• Why is this bad?

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?

Ultrasound

This is a speaker of Kinande.

Kinande is spoken in Congo.

(from Gick, 2002)

Ultrasound: +ATR vs. -ATR

advanced (+ATR) retracted (-ATR)

ATR vowels in Akan• Akan is spoken in Ghana

+ATR vs. -ATR

ATR Vowel Spaces

• DhoLuo is spoken in Kenya and Tanzania

F3 and , revisited

• English has pharyngeal, palatal and labial constrictions

• These constrictions conspire to drastically lower F3

F3 and [y]

• [y] has both labial and palatal constrictions

• What effect would these constrictions have on F3?

[i] vs. [y]

[li] [ly]

Lab Exercise!• Let’s walk through it…