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Sonorant Acoustics

Sonorant Acoustics. March 20, 2013. On the Horizon. Today: acoustics of sonorants Friday: more sonorant and stop acoustics plus an introduction to the motor theory of perception. Extremes. Not all music stays within a couple of octaves of middle C. Check this out:

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Sonorant Acoustics

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  1. Sonorant Acoustics March 20, 2013

  2. On the Horizon • Today: acoustics of sonorants • Friday: more sonorant and stop acoustics • plus an introduction to the motor theory of perception

  3. Extremes • Not all music stays within a couple of octaves of middle C. • Check this out: • Source: “Der Rache Hölle kocht in meinem Herze”, from Die Zauberflöte, by Mozart. • Sung by: Sumi Jo • This particular piece of music contains an F6 note • The frequency of F6 is 1397 Hz. • (Most sopranos can’t sing this high.)

  4. Implications • Are there any potential problems with singing this high? • F1 (the first formant frequency) of most vowels is generally below 1000 Hz--even for females • There are no harmonics below 1000 Hz for the vocal tract “filter” to amplify • a problem with the sound source •  It’s apparently impossible for singers to make F1-based vowel distinctions when they sing this high. • But they have a trick up their sleeve...

  5. Singer’s Formant • Discovered by Johan Sundberg (1970) • another Swedish phonetician • Classically trained vocalists typically have a high frequency resonance around 3000 Hz when they sing. • This enables them to be heard over the din of the orchestra • It also provides them with higher-frequency resonances for high-pitched notes • Check out the F6 spectrum.

  6. more info at: http://www.ncvs.org/ncvs/tutorials/voiceprod/tutorial/singer.html How do they do it? • Evidently, singers form a short (~3 cm), narrow tube near their glottis by making a constriction with their epiglottis • This short tube resonates at around 3000 Hz • Check out the video evidence.

  7. Overtone Singing • F0 stays the same (on a “drone”), while singer shapes the vocal tract so that individual harmonics (“overtones”) resonate. • What kind of voice quality would be conducive to this?

  8. Vowels and Sonorants • So far, we’ve talked a lot about the acoustics of vowels: • Source: periodic openings and closings of the vocal folds. • Filter: characteristic resonant frequencies of the vocal tract (above the glottis) • Today, we’ll talk about the acoustics of sonorants: • Nasals • Laterals • Approximants • The source/filter characteristics of sonorants are similar to vowels… with a few interesting complications.

  9. Damping • One interesting acoustic property exhibited by (some) sonorants is damping. • Recall that resonance occurs when: • a sound wave travels through an object • that sound wave is reflected... • ...and reinforced, on a periodic basis • The periodic reinforcement sets up alternating patterns of high and low air pressure • = a standing wave

  10. Resonance in a closed tube t i m e

  11. Damping, schematized • In a closed tube: • With only one pressure pulse from the loudspeaker, the wave will eventually dampen and die out. • Why? • The walls of the tube absorb some of the acoustic energy, with each reflection of the standing wave.

  12. Damping Comparison • A heavily damped wave wil die out more quickly... • Than a lightly damped wave:

  13. Damping Factors • The amount of damping in a tube is a function of: • The volume of the tube • The surface area of the tube • The material of which the tube is made • More volume, more surface area = more damping • Think about the resonant characteristics of: • a Home Depot • a post-modern restaurant • a movie theater • an anechoic chamber

  14. An Anechoic Chamber

  15. Resonance and Recording • Remember: any room will reverberate at its characteristic resonant frequencies • Hence: high quality sound recordings need to be made in specially designed rooms which damp any reverberation • Examples: • Classroom recording (29 dB signal-to-noise ratio) • “Soundproof” booth (44 dB SNR) • Anechoic chamber (90 dB SNR)

  16. Spectrograms classroom “soundproof” booth

  17. Spectrograms anechoic chamber

  18. Inside Your Nose • In nasals, air flows through the nasal cavities. • The resonating “filter” of nasal sounds therefore has: • increased volume • increased surface area •  increased damping • Note: • the exact size and shape of the nasal cavities varies wildly from speaker to speaker.

  19. Nasal Variability • Measurements based on MRI data (Dang et al., 1994)

  20. Damping Effects, part 1 • Damping by the nasal cavities decreases the overall amplitude of the sound coming out through the nose. [m] [m]

  21. Damping Effects, part 2 • How might the power spectrum of an undamped wave: • Compare to that of a damped wave? • A: Undamped waves have only one component; • Damped waves have a broader range of components.

  22. Here’s Why 100 Hz sinewave + 90 Hz sinewave + 110 Hz sinewave

  23. The Result 90 Hz + 100 Hz + 110 Hz • If the 90 Hz and 110 Hz components have less amplitude than the 100 Hz wave, there will be less damping:

  24. Damping Spectra light medium

  25. Damping Spectra heavy • Damping increases the bandwidth of the resonating filter. • Bandwidth = the range of frequencies over which a filter will respond at .707 of its maximum output. •  Nasal formants will have a larger bandwidth than vowel formants.

  26. Bandwidth in Spectrograms F3 of F3 of [m] The formants in nasals have increased bandwidth, in comparison to the formants in vowels.

  27. Nasal Formants • The values of formant frequencies for nasal stops can be calculated according to the same formula that we used for to calculate formant frequencies for an open tube. • fn = (2n - 1) * c • 4L • The simplest case: uvular nasal . • The length of the tube is a combination of: • distance from glottis to uvula (9 cm) • distance from uvula to nares (12.5 cm) • An average tube length (for adult males): 21.5 cm

  28. The Math 12.5 cm • fn = (2n - 1) * c • 4L • L = 21.5 cm • c = 35000 cm/sec • F1 = 35000 • 86 • = 407 Hz • F2 = 1221 Hz • F3 = 2035 Hz 9 cm

  29. The Real Thing • Check out Peter’s production of an uvular nasal in Praat. • And also Dustin’s neutral vowel! • Note: the higher formants are low in amplitude • Some reasons why: • Overall damping • “Nostril-rounding” reduces intensity • Resonance is lost in the side passages of the sinuses. • Nasal stops with fronter places of articulation also have anti-formants.

  30. Anti-Formants • For nasal stops, the occlusion in the mouth creates a side cavity. • This side cavity resonates at particular frequencies. • These resonances absorb acoustic energy in the system. • They form anti-formants

  31. Anti-Formant Math • Anti-formant resonances are based on the length of the vocal tract tube. • For [m], this length is about 8 cm. 8 cm • fn = (2n - 1) * c • 4L L = 8 cm AF1 = 35000 / 4*8 = 1094 Hz AF2 = 3281 Hz etc.

  32. Spectral Signatures • In a spectrogram, acoustic energy lowers--or drops out completely--at the anti-formant frequencies. anti-formants

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