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.

• Fn = 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 = 1046.5 Hz

• etc.

Frame of Reference• The central note on a piano is called “middle C” (C4)

• Frequency = 261.6 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: http://www.ncvs.org/ncvs/tutorials/voiceprod/tutorial/singer.html

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

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i

m

e

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] [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 +

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:

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.

• 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

The Math

12.5 cm

9 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