From Resonance to Vowels

1. From Resonance to Vowels March 8, 2013

2. 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 22nd, 3:30 – 5:30 pm. • Science Theater 055

3. 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

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

5. “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

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

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

8. Schwa at different pitches 100 Hz 120 Hz 150 Hz

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

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

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

12. The Vowel Space The Vowel Space o

13. 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

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

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

16. (From some old phonetics class data)

17. 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

18. Prototypical Voices • Andre the Giant: (very) low F0, low formant frequencies • Goldie Hawn: high F0, high formant frequencies More 21st Century (and more Canadian): YTV’s “Pretty Tiffany”

19. 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.

20. 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

21. 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?

22. 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

23. 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?

24. 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. glottis lips