From Resonance to Vowels March 8, 2013

Friday Frivolity Some project reports to hand back… Mystery spectrogram reading exercise: solved! We need to plan ahead: Who wants to give a class presentation for their final course project report? Who would like to be our speaker for the static palatography demo? The final exam has been scheduled, by the way: Monday, April 22 nd, 3:30 – 5:30 pm. Science Theater 055

The Big Picture The fundamental frequency of a speech sound is a complex periodic wave. In speech, a series of harmonics, with frequencies at integer multiples of the fundamental frequency, pour into the vocal tract from the glottis. Those harmonics which match the resonant frequencies of the vocal tract will be amplified. Those harmonics which do not will be damped. The resonant frequencies of a particular articulatory configuration are called formants. Different patterns of formant frequencies = different vowels

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 More 21 st Century (and more Canadian): YTV’s “Pretty Tiffany”

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