Transcript 17-Sonorant-Acoustic.. - The Bases Produced Home Page

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 major chord: A4 - C#5 - E5
(a “minor second”)
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.
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.
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
t
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
• Damping by the nasal cavities decreases the overall
amplitude of the sound coming out through the nose.
[m]
[m]
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.
Here’s Why
100 Hz sinewave
+
90 Hz sinewave
+
110 Hz sinewave
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
F3 of [m]
F3 of
The formants in nasals have increased bandwidth,
in comparison to the formants in vowels.
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
fn =
(2n - 1) * c
4L
L = 21.5 cm
c = 35000 cm/sec
F1 = 35000
86
9 cm
= 407 Hz
F2 = 1221 Hz
F3 = 2035 Hz