Vowel Acoustics

1. Vowel Acoustics November 2, 2012

2. Some Announcements • Mid-terms will be back on Monday… • Today: more resonance + the acoustics of vowels • Also on Monday: identifying vowels from spectrograms.

3. Back at the Ranch • Last time, we learned about resonance: • when one physical object is set in motion by the vibrations of another object. • In speech, the vocal tract resonates in response to… • the periodic vibrations of the vocal folds. • We can envision a resonating sound wave as a standing wave…

4. A Minor Disaster • The pressure waves of sound can set up standing waves in objects, too. • Check out the Mythbusters video online: • www.youtube.com/watch?v=PMg_nd-O688

5. Resonant Frequencies • This is important: • a standing wave can only be set up in a tube if pressure pulses are emitted from the loudspeaker at the right frequency. • What is the right frequency? That depends on: • how fast the sound wave travels through the tube • how long the tube is • Basically: • the longer the tube, the lower the frequency • Why?

6. Establishing Resonance • A new pressure pulse should be emitted right when: • the first pressure peak has traveled all the way down the length of the tube • and come back to the loudspeaker.

7. Establishing Resonance • The longer the tube, the longer you need to wait for the pressure peak to travel the length of the tube. •  longer period between pressure pulses •  lower frequency F0  F0 

8. Making the Leap • First: let’s check out the pop bottle demo • To relate resonance to speech, we need to add two elements to the theory: • It is possible for sound waves of more than one frequency to resonate in a tube at the same time. • The vocal tract is a tube that is open at one end (the mouth)… • so it behaves a little differently from a closed tube.

9. Higher Resonances • It is actually possible to set up more than one standing wave in a tube at the same time. First Resonance Second Resonance • In a closed tube, the second resonance frequency will be exactly twice as high as the first.

10. First Resonance Time 1: initial impulse is sent down the tube Time 2: initial impulse bounces at end of tube Time 3: impulse returns to other end and is reinforced by a new impulse Time 4: reinforced impulse travels back to far end • Resonant period = Time 3 - Time 1

11. Second Resonance Time 1: initial impulse is sent down the tube Time 2: initial impulse bounces at end of tube + second impulse is sent down tube Time 3: initial impulse returns and is reinforced; second impulse bounces Time 4: initial impulse re-bounces; second impulse returns and is reinforced Resonant period = Time 2 - Time 1

12. Different Patterns • This is all fine and dandy, but speech doesn’t really involve closed tubes. • Think of the vocal tract as a tube with: • one open end • a sound pulse source at the closed end • (the vibrating glottis) • The vocal tract will vibrate in response to the sound pulses… • at the particular frequencies that will set up standing waves down its length.

13. Just So You Know • A weird fact about nature: • When a sound pressure peak hits the open end of a tube, it doesn’t get reflected back. • Instead, there is an “anti-reflection”. • The pressure disperses into the open air, and... • A sound rarefaction gets sucked back into the tube.

14. Open Tubes, part 1

15. Open Tubes, part 2

16. Open Tube Resonances • Standing waves in an open tube will look like this: • 1st Resonance Frequency: F1 • 2nd Resonance Frequency: • F2 = 3 * F1 • 3rd Resonance Frequency: • F3 = 5 * F1 tube length

17. An Evenly Spaced Spectrogram • Go to Praat and check out: • My neutral vowel

18. My “Open Tube” Vowel formants

19. Spectral Analysis: Vowels • Remember: Fourier’s theorem breaks down any complex sound wave (e.g., speech) into its component sinewaves. • For each component sinewave (harmonic), this analysis shows us: • its frequency • its amplitude (intensity) • In vowels: • resonating harmonics have higher intensity • other harmonics will be damped (have lower intensity)

20. A Vowel Spectrum F1 F2 F4 F3 Note: F0  160 Hz

21. Different Vowels,Different Formants • The formant frequencies of resemble the resonant frequencies of a tube that is open at one end. • For the average man (like Peter Ladefoged or me): • F1 = 500 Hz • F2 = 1500 Hz • F3 = 2500 Hz • However, we can change the shape of the vocal tract to get different resonant frequencies. • Vowels may be defined in terms of their characteristic resonant frequencies (formants).

22. Artificial Examples • The characteristic resonant frequencies (formants) of the “corner” vowels: “[i]” “[u]” “ ”

23. Real Vowels

24. Real Vowels

25. What we need to worry about • There are 8 contrastive monophthong vowels in Canadian English: • [i] “heed” • “hid” cap-i • “head” • [æ] “had” ash • “hod” / “hawed” • “hud” wedge • “hood” upsilon • [u] “who’ed”

26. More Vowels • There are also five diphthongs: • “bayed” • “bode” • “bide” • “bowed” • “Boyd” • Diphthongs change vowel qualities within a syllable • Each of these vowels/diphthongs has characteristic resonant frequencies (i.e., formants)… • which are related to their articulatory properties.

27. Vowel Articulations • We learned (a long time ago) that vowels are articulated with characteristic tongue and lip shapes

28. 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 = distance from center of vowel space.

29. The Vowel Space

30. Vowel Acoustics • But it turns out that we can get to the same chart a different way... • 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

31. Reality Check • Let’s check out the formant values for Bruce Hayes’ vowels in Praat. • And plot them on the board.

32. Things to Keep in Mind • Resonant frequencies (formants) are primarily based on the length of the speaker’s vocal tract. • (the length of the open tube) • The longer the vocal tract, the lower the formant frequencies. • Thought Question #1: • What effect might lip rounding have on formant frequencies?

33. Things to Keep in Mind • Thought Question #2: • How might formant frequencies differ between men and women?

34. [i] [u] [æ]

35. [i] [u] [æ]

37. Women and Men • The acoustics of male and female vowels differ reliably along two different dimensions: • Sound Source • Sound Filter • Source--F0: depends on length of vocal folds • shorter in women  higher average F0 • longer in men  lower average F0 • Filter--Formants: depend on length of vocal tract • shorter in women  higher formant frequencies • longer in men  lower formant frequencies

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

39. 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.

40. 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

41. In Praat • Check out: • Andre • Goldie • Julia • Popeye • Low-to-high F0 • Pitch Shifting

42. In Conclusion • Everybody’s vowel space is different. • A vowel space is defined by a speaker’s range of first formant (F1) and second formant (F2) frequencies. • We identify vowels on the basis of the patterns formed by their formants within that acoustic space. • F1 determines the height of vowels. • F2 determines the front/backness of vowels. • Questions?