Transcript Physics 1251 The Science and Technology of Musical Sound

Physics 1251
The Science and Technology
of Musical Sound
Unit 3
Session 32 MWF
The Singing Voice
Physics 1251
Unit 3 Session 32
The Singing Voice
Foolscap Quiz:
•
What produces the vibrations in the
human voice?
The vocal folds produce the vibrations required
for phonation of the human voice.
Physics 1251
Unit 3 Session 32
The Singing Voice
A Little Q&A
Physics 1251
Unit 3 Session 32
The Singing Voice
The Singing Voice
What is the difference?
Luciano Pavarotti
Andrea Bocelli
Physics 1251
Unit 3 Session 32
The Singing Voice
1′ Lecture:
•
The pitch range of the singing voice is
determined by the properties of the vocal folds.
•
The intelligibility of words is due to the
relationship of the first two formants.
•
Modification of the shape of the vocal tract
significantly affects the timbre of the singing
voice.
Physics 1251
Unit 3 Session 32
The Singing Voice
The Vocal Apparatus
1. Nasal cavity
The Vocal Tract is
the organ of speech
and
the instrument
of the Voice.
2&3. Pharynx
4. Vocal folds
5. Tongue
8. Epiglottis
9. False v.c.
10. Trachea
Physics 1251
Unit 3 Session 32
The Singing Voice
The Mechanics of the Vocal Folds
80/20The
properties of the vocal folds determine their
vibration frequency.
Larynx
Larynx
Physics 1251
Unit 3 Session 32
The Singing Voice
The Mechanics of the Vocal Folds
80/20The
properties of the vocal folds determine their
vibration frequency.
Vocal Folds
Larynx
Closed
Open
fvocal = 1/2π √k/ m
Physics 1251
Unit 3 Session 32
The Singing Voice
The Mechanics of the Vocal Folds
80/20The
properties of the vocal folds determine their
vibration frequency.
fvocal = 1/2π √k/ m
Vocal Folds
Density ρ
Stress σ
Length L
k = fold stiffness
m = effective mass
For a cord:
f = 1/2L√T/ μ
T = σ (t‧d)
μ
= ρ(t‧d)
f
fvocal = 1/2π √k/ m
= 1/2L√ σ / ρ
Physics 1251
Unit 3 Session 32
The Singing Voice
The Mechanics of the Vocal Folds
80/20The
properties of the vocal folds determine their
vibration frequency.
fvocal = 1/2π √k/ m
2
f = √ σ / (4L ρ)
k = fold stiffness
k = π2 σ m/ L2 ρ = π2 T/ L
m = effective mass
m = ρ L(t‧d)
For a cord:
L ≈ 0.017 m
f = (1/2L)√T/ μ
ρ ≈ 1040 kg/m3
σ
T = σ (t‧d)
μ
≈ 12 kPa
f
= ρ(t‧d)
f
≈ 100 Hz
m
= (1/2L)√ σ / ρ
≈ 200 mg; T≈ 0.14 N
Physics 1251
Unit 3 Session 32
The Singing Voice
The Mechanics of the Vocal Folds
80/20The
properties of the vocal folds determine their
vibration frequency.
f1 = (1/2L)√ σ / ρ
80/20Conclusions:
• Resting length, stress and density set voice range
• Stress (tension) can be increased external to the
vocal fold or internal to it.
• Overall, increased tension increases stiffness, pitch
Physics 1251
Unit 3 Session 32
The Singing Voice
Vocal Range – Fundamental Pitch
♩ 329 Hz ♩392 Hz
♩ 82 Hz ♩98 Hz
♩523 Hz
♩131 Hz
♩587 Hz
♩147 Hz
♩880 Hz ♩1175 Hz
♩165 Hz ♩196 Hz
Tenor
Soprano
Mezzo- G – D
♂:
C2 – C5 ♀:
6
Soprano 3
Baritone
E3 – A5
Bass G2 – G4
Contralto
E2 – E4
D3 – D5
Physics 1251
Unit 3 Session 32
The Singing Voice
Anatomy of the Human Voice
80/20During
adolescent the vocal folds grow longer and the
voice lowers in pitch.
Vocal Folds
f1 = √ σ / (4L2 ρ)
f1 = 1700/L (mm)
Pitch lowers at
puberty.
lengthen at
puberty
Physics 1251
Unit 3 Session 32
The Singing Voice
Anatomy of the Human Voice
80/20The
vocal folds comprise muscle, lamina propria and
epithelium.
Cover
Epithelium
Lamina Propria
(3 layers)
Thyroarytenoid
Muscle
Body
Physics 1251
Unit 3 Session 32
The Singing Voice
Video of
Laryngoscopy
Tenor, Baritone and Soprano
Physics 1251
Unit 3 Session 32
The Singing Voice
80/20Pitch
is raised by increasing tension on
vocal folds, both external to the vocal fold
(Cricothyroid muscle) and internal to it
(Thyroarytenoid muscle).
f1 = (1/2L)√ σ / ρ
The nature of the stress in the vocal fold
(internal or external tension) permits
phonation in different registers.
Physics 1251
80/20Vocal
Unit 3 Session 32
The Singing Voice
Registers:
f1 = (1/2L)√ σ / ρ
σ =σexternal + σinternal
Terminology
Speaking:
Pulse
Modal
Falsetto
Singing:
Chest
Head
Falsetto
Middle
Whistle
flageolet
(alternative) Fry
Stohbass
Physics 1251
80/20The
Unit 3 Session 32
The Singing Voice
shape of the Vocal Tract
determines the frequency of the
Formants.www.exploratorium.edu/exhibits/vocal_vowels/vocal_vowels.html
“ah”
“eh”
“oh”
“oo”
Physics 1251
Unit 3 Session 32
The Singing Voice
Spectrogram of Human Speech
Physics 1251
Unit 3 Session 32
The Singing Voice
Speech
80/20The
individual units of speech are called
phonemes.
The classes of (English) phonemes are:
•
•
•
•
•
•
•
•
•
•
Unvoiced Plosives‒ p, t, k (c, q, x)
Voiced Plosives‒ b, d, g
Fricatives‒ unvoiced/voiced: f/v, th/th,
Sibilants‒ unvoiced/voiced: s(c)/z, sh/zh (j), h/kh
Liquids‒ l, r
Nasals‒ m, n, ng
Semi-vowels‒ w, y
Vowels‒ a, e, i, o, u
Physics 1251
Unit 3 Session 32
The Singing Voice
Vowels and Formants
80/20The
relative frequency of the 1 st and 2 nd vowels
formants are unique to various vowels.
i
ε
I
æ
U
D
Λ
u
First formant frequency
Physics 1251
Unit 3 Session 32
The Singing Voice
Control of Formants
80/20Tongue
and lip placement and the shape of the
pharanx are most important in vowel formation.
“Corner Vowels”
D
A
A
A
f
f
f
Physics 1251
Unit 3 Session 32
The Singing Voice
Formants and Singing
Harmonics align
with Formants
Singers’
Formant
•Vowel modification shifts formats.
•Alignment of formants with harmonics
intensifies pitch.
•Dilation of vocal tract causes Singer’s Formant.
Physics 1251
Unit 3 Session 32
The Singing Voice
Summary:
•
•
The pitch range of the singing voice is
determined by the size, tension, and density
of the vocal folds.
Vocal registers and breaks in the voice result
from changing modes of oscillation of the
vocal folds.
•
Vowels are distinguished by the frequency
relationship of the first two formants.
•
Modification of the vocal tract shape sets the
timbre of the singing voice.