Sonorant Acoustics November 13, 2014

Playing Catch Up! I graded lots of homework over the break! You also owe me the Formant measuring homework now. On Tuesday, the next course project report is due. Also on Tuesday, I’ll give you: Guidelines for the course project report #5 Guidelines for the final course project report Oh yeah: we need a volunteer for the palatography demo! In the meantime, let’s take a look at our second mystery spectrogram!

Some Notes on Music The lowest note on a piano is “A0”, which has a fundamental frequency of 27.5 Hz. The frequencies of the rest of the notes are multiples of 27.5 Hz. F n = 27.5 * 2 (n/12) where n = number of note above A0 There are 87 notes above A0 in all

Octaves and Multiples Notes are organized into octaves There are twelve notes to each octave  12 note-steps above A0 is another “A” (A1) Its frequency is exactly twice that of A0 = 55 Hz A1 is one octave above A0 Any note which is one octave above another is twice that note’s frequency. C8 = 4186 Hz (highest note on the piano) C7 = 2093 Hz C6 = Hz etc.

Frame of Reference The central note on a piano is called “middle C” (C4) Frequency = Hz The A above middle C (A4) is at 440 Hz. The notes in most western music generally fall within an octave or two of middle C. Recall the average fundamental frequencies of: men ~ 125 Hz women ~ 220 Hz children ~ 300 Hz

Harmony Notes are said to “harmonize” with each other if the greatest common denominator of their frequencies is relatively high. Example: note A4 = 440 Hz Harmonizes well with (in order): A5 = 880 Hz (GCD = 440) E5 ~ 660 Hz(GCD = 220)(a “fifth”) C#5 ~ 550 Hz(GCD = 110)(a “third”).... A#4 ~ 466 Hz(GCD = 2)(a “minor second”) A major chord: A4 - C#5 - E5

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.)

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...

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.

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. more info at:

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?

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.

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

Resonance in a closed tube timetime

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.

Damping Comparison A heavily damped wave will die out more quickly... Than a lightly damped wave:

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

An Anechoic Chamber

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)

Spectrograms classroom “soundproof” booth

Spectrograms anechoic chamber

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.

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

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

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.

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

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

Damping Spectra light medium

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.

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

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. f n = (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

The Math 12.5 cm 9 cm f n = (2n - 1) * c 4L L = 21.5 cm c = cm/sec F1 = = 407 Hz F2 = 1221 Hz F3 = 2035 Hz