From Resonance to Vowels March 13, 2012

Fun Stuff (= tracheotomy) Peter Ladefoged: “To record the pressure of the air associated with stressed as opposed to unstressed syllables we need to record the pressure below the vocal folds. A true recording of the subglottal pressure can be made only by making a tracheal puncture.This is a procedure that must be performed by a physician. A local anesthetic is applied both externally and inside the trachea by means of a fine needle. A larger needle with an internal diameter of 2 mm can then be inserted between the rings of the trachea as shown in figure 3.3”

Figure 3.3 “As you can see from my face it is not at all painful. But it is not a procedure that can be carried out in fieldwork situations.”

Somewhat Less Fun Korean stops homework to hand back… Mystery spectrogram reading exercise #2!

Stopping by woods on a snowy evening Whose woods these are I think I know. His house is in the village though. He will not see me stopping here To watch his woods fill up with snow. My little horse must think it queer To stop without a farm house near Between the woods and frozen lake The darkest evening of the year. Robert Frost ( )

He gives his harness bells a shake To ask if there is some mistake. The only other sound’s the sweep Of easy wind and downy flake. The woods are lovely, dark and deep. But I have promises to keep, And miles to go before I sleep-- And miles to go before I sleep. Stopping by woods on a snowy evening Robert Frost ( )

Vowel Resonances The series of harmonics flows into the vocal tract. Those harmonics at the “right” frequencies will resonate in the vocal tract. f n = (2n - 1) * c 4L The vocal tract filters the source sound lipsglottis

“Filters” In speech, the filter = the vocal tract This graph represents how much the vocal tract would resonate for sinewaves at every possible frequency: The resonant frequencies are called formants

Source + Filter = Output + = This is the source/filter theory of speech production.

Source + Filter(s) Note: F0  160 Hz F1 F2 F3 F4

Schwa at different pitches 100 Hz120 Hz 150 Hz

More Than Schwa Formant frequencies differ between vowels… because vowels are produced with different articulatory configurations

Remember… Vowels are articulated with characteristic tongue and lip shapes.

Vowel Dimensions For this reason, vowels have traditionally been described according to four (pseudo-)articulatory parameters: 1.Height (of tongue) 2.Front/Back (of tongue) 3.Rounding (of lips) 4.Tense/Lax = amount of effort? = muscle tension?

The Vowel Space o

Formants and the Vowel Space It turns out that we can get to the same diagram in a different way… Acoustically, vowels are primarily distinguished by their first two formant frequencies: F1 and F2 F1 corresponds to vowel height: lower F1 = higher vowel higher F1 = lower vowel F2 corresponds to front/backness: higher F2 = fronter vowel lower F2 = backer vowel

[i] [u] [æ] (From some old phonetics class data)

[i][u] [æ] (From some old phonetics class data)

Women and Men Both source and filter characteristics differ reliably between men and women F0: depends on length of vocal folds shorter in women  higher average F0 longer in men  lower average F0 Formants: depend on length of vocal tract shorter in women  higher formant frequencies longer in men  lower formant frequencies

Prototypical Voices Andre the Giant: (very) low F0, low formant frequencies Goldie Hawn: high F0, high formant frequencies

F0/Formant mismatches The fact that source and filter characteristics are independent of each other… means that there can sometimes be source and filter “mismatches” in men and women. What would high F0 combined with low formant frequencies sound like? Answer: Julia Child.

F0/Formant mismatches Another high F0, low formants example: Roy Forbes, of Roy’s Record Room (on CKUA 93.7 FM) The opposite mis-match = Popeye: low F0, high formant frequencies

Back to Vowels A vowel space is defined by a speaker’s range of first formant (F1) and second formant (F2) frequencies. …but everybody’s vowel space is different. Vowels contrast with each other in terms of their relationships within that acoustic space. F1 determines the “height” of vowels. F2 determines the “front/backness” of vowels. Question: How does the way that vowels are produced… Determine their acoustic characteristics?

Articulation to Acoustics Last time, we calculated the formant values for “schwa”, or a neutral vowel. Theoretical values (vocal tract length = 17.5 cm) F1 = 500 Hz F2 = 1500 Hz F3 = 2500 Hz My values: F1 = 500 Hz F2 = 1533 Hz F3 = 2681 Hz F4 = 3498 Hz

With a neutral vowel, we’re somewhere in the middle of the acoustic vowel space. Q: How do we get to the corners of the space?

Perturbation Theory There are two important theories that answer this question. The first of these is Perturbation Theory. Remember: formants are resonances of the vocal tract. These resonances are the product of standing waves in the resonating tube of the articulatory tract. lipsglottis

What’s the Big Idea? Chiba and Kajiyama (1941): Formant frequencies can be changed by perturbing the airflow of the standing waves in the vocal tract Idea #1: velocity of standing waves is inversely related to pressure Sort of like the Bernoulli Effect

Standing Waves in the Vocal Tract Remember: Vocal tract is a tube with one open end at the lips. So: Pressure node at the lips Pressure anti-node at the glottis …for all potential standing waves This translates into: Velocity anti-node at the lips Velocity node at the glottis

Standing Waves in the Vocal Tract F1F2 Diagrammed in terms of velocity:

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

Here’s the goal Let’s 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--> high, front vowels Lower F1 and lower F2--> high, back vowels Raise F1 and raise F2--> low, front vowels Raise F1 and lower F2--> low, back vowels Let’s consider them each in turn…

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

F2 Velocity nodes at: palate glottis Velocity anti-nodes at: lips pharynx

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

1. High, Front Vowels Lower F1 and raise F2 Where should we make a constriction(s)?

1. High, Front Vowels Lower F1 and raise F2 Where should we make a constriction(s)? To lower F1:

1. High, Front Vowels Lower F1 and raise F2 Where should we make a constriction(s)? To lower F1: constrict close to lips

1. High, Front Vowels Lower F1 and raise F2 Where should we make a constriction(s)? To lower F1: constrict close to lips To raise F2:

1. High, Front Vowels Lower F1 and raise F2 Where should we make a constriction(s)? To lower F1: constrict close to lips To raise F2: constrict at palate

2. High, Back Vowels = Lower F1 and lower F2 Where should we make a constriction(s)?

2. High, Back Vowels = Lower F1 and lower F2 Where should we make a constriction(s)? To lower F1:

2. High, Back Vowels = Lower F1 and lower F2 Where should we make a constriction(s)? To lower F1: constrict at lips

2. High, Back Vowels = Lower F1 and lower F2 Where should we make a constriction(s)? To lower F1: constrict at lips To lower F2:

2. High, Back Vowels = Lower F1 and lower F2 Where should we make a constriction(s)? To lower F1: constrict at lips To lower F2: constrict at lips constrict at “pharynx” Note: these vowels are usually rounded