2. Source/Filter Theory and Vowels February 4, 2010

3. Some Lab Notes

8. Also: the whisper video One point: ranges Check out the EGG audio recording, too.

9. Open Tube Resonances For the first three resonances in an open tube, the standing waves will look like this: = 4L L = 4L / 3 = 4L / 5 closed endclosed end open endopen end

10. Open Tube Resonances Last time, we learned that, for open tubes, the frequency of the nth resonance of the tube was determined by the following equation: f n = (2n - 1) * c 4L For an open tube of length 17.5 cm, this would yield formant frequencies of: F1 = 500 Hz F2 = 1500 Hz F3 = 2500 Hz Important: vowel formants correspond to the resonant frequencies of the vocal tract “tube”

11. My “Open Tube” Vowel formants Note: the vowel produced by an unperturbed human vocal tract sounds like /schwa/

12. 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)

13. My Open Tube Profile Note: F0  160 Hz F1 F2 F3 F4

14. Source/Filter Theory The combination of harmonics + resonances in the vowel /schwa/ lays the foundation for the source-filter theory of vowel production. Developed by Gunnar Fant (1960) The shape of the vocal tract filters this complex wave to amplify the intensity of some harmonics and diminish the intensity of others. For speech, the source of sound = complex waves created by periodic opening and closing of the vocal folds

15. “Filters” For any particular vocal tract configuration, certain frequencies will resonate, while others will be damped. analogy: natural variation/environmental selection This graph represents how much the vocal tract would resonate for sinewaves at every possible frequency.

16. Source + Filter = Output + =

17. Schwa at different pitches 100 Hz120 Hz 150 Hz

18. “Filters”? A filter is a tool used in both electronic engineering and digital signal processing to shape the spectrum of a complex sound. A filter removes harmonic components of certain frequencies in the signal. There are different types of filters: 1.Low-pass filters Allow low frequencies to pass through the filter. And remove high frequencies from the signal. 2.High-pass filters: Allow high frequencies to pass through filter. And remove low frequencies.

19. Low-Pass Filter in Action Power spectrum of 100 Hz + 1000 Hz combo: Filter passes 100 Hz component, but not 1000 Hz component. Demo: Low-pass filter some noisy EGG waveforms.

20. Band-Pass Filters A band-pass filter combines both high- and low-pass filters. It passes a “band” of frequencies around a center frequency.

21. Band-Pass Filtering Basic idea: components of the input spectrum have to conform to the shape of the band-pass filter.

22. Bandwidth Filters can differ not only in terms of which frequencies they allow to pass, but also in terms of their bandwidth. Bandwidth is the range of frequencies over which a filter will respond at.707 of its maximum output. bandwidth Half of the acoustic energy passed through the filter fits within the bandwidth. Bandwidth is measured in Hertz.

23. Different Bandwidths narrow band wide band

24. Your Grandma’s Spectrograph Originally, spectrographic analyzing filters were constructed to have either wide or narrow bandwidths.

25. Narrow-Band Spectrogram A “narrow-band spectrogram” clearly shows the harmonics of speech sounds. …but the formants are less distinct. harmonics Also: temporal resolution is not very good.

26. Wide-Band Spectrogram By changing the parameters of the Fourier analysis, we can get a “wide-band spectrogram” This shows the formants better than the harmonics. formants

27. Wide-Band Spectrogram By changing the parameters of the Fourier analysis, we can get a “wide-band spectrogram” This shows the formants better than the harmonics. formants F1 F2 F3 voice bars (glottal pulses) Also: temporal resolution is better.

28. The Other Half Source-filter theory holds that: Resonance effectively creates a series of band-pass filters in our mouths. += Wide-band spectrograms help us see properties of the vocal tract filter.

29. Formants Rather than filters, though, we may consider the vocal tract to consist of a series of resonators. With center frequencies And particular bandwidths The characteristic resonant frequencies of a particular articulatory configuration are called formants. Questions to answer: What formant frequencies are characteristic of each vowel? How can we change the resonant frequencies of the vocal tract? (i.e., make spectral changes)

30. 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).

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

32. Real Vowels

34. Vowel Acoustics If you look at enough of these, you will start to notice a pattern. The first formant (F1) of “high” vowels tends to be lower than the F1 of /schwa/. …while the first formant of “low” vowels tends to be higher than the F1 of /schwa/. The first formant (F2) of “front” vowels tends to be higher than the F2 of /schwa/. The second formant (F2) of “back” vowels tends to be lower than the F2 of /schwa/. So…what should the F1 and F2 values of my [æ] be?

35. 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?

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

37. [i] [u] [æ]

38. [i][u] [æ]

40. Women and Men The acoustics of male and female vowels differ reliably along two different dimensions: 1.Sound Source 2.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

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

42. F0/Formant mismatches Source and filter characteristics are independent of each other...and can sometimes “mismatch” in men and women: Julia Child: high F0, low formant frequencies Popeye: low F0, high formant frequencies