1. Physics 1251 The Science and Technology of Musical Sound
Unit 3
Session 32 MWF
The Singing Voice

2. 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.

3. Physics 1251 Unit 3 Session 32 The Singing Voice
A Little Q&A

4. Physics 1251 Unit 3 Session 32 The Singing Voice
Luciano Pavarotti
Andrea Bocelli
What is the difference?

5. 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.

6. Physics 1251 Unit 3 Session 32 The Singing Voice
The Vocal Apparatus
Nasal cavity
2&3. Pharynx
4. Vocal folds
5. Tongue
8. Epiglottis
9. False v.c.
10. Trachea
The Vocal Tract is the organ of speech and
the instrument
of the Voice.

7. 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

8. 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
Closed
Open
Larynx
fvocal = 1/2π √k/ m

9. 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
k = fold stiffness m = effective mass
For a cord:
f = 1/2L√T/ μ T = σ (t‧d) μ = ρ(t‧d) f = 1/2L√ σ / ρ
Stress σ
Length L
fvocal = 1/2π √k/ m

10. 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
f = √ σ / (4L2 ρ)
k = fold stiffness m = effective mass
k = π2 σ m/ L2 ρ = π2 T/ L m = ρ L(t‧d)
For a cord:
f = (1/2L)√T/ μ T = σ (t‧d) μ = ρ(t‧d) f = (1/2L)√ σ / ρ
L ≈ m ρ ≈ 1040 kg/m σ ≈ 12 kPa f ≈ 100 Hz m ≈ 200 mg; T≈ 0.14 N

11. 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

12. Physics 1251 Unit 3 Session 32 The Singing Voice
Vocal Range – Fundamental Pitch ♩ ♩
1175 Hz ♩
880 Hz ♩
587 Hz ♩
523 Hz ♩
392 Hz
329 Hz
196 Hz
165 Hz
147 Hz
131 Hz
98 Hz
82 Hz
Tenor C2 – C5
SopranoG3 – D6 ♂: ♀:
Mezzo-SopranoE3 – A5
Baritone G2 – G4
Bass E2 – E4
ContraltoD3 – D5

13. 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 lengthen at puberty
f1 = √ σ / (4L2 ρ)
f1 = 1700/L (mm)
Pitch lowers at puberty.

14. 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
Body
Epithelium
Lamina Propria (3 layers)
Thyroarytenoid Muscle

15. Physics 1251 Unit 3 Session 32 The Singing Voice
Video of
Laryngoscopy
Tenor, Baritone and Soprano

16. 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.

17. Physics 1251 Unit 3 Session 32 The Singing Voice
80/20Vocal Registers:
f1 = (1/2L)√ σ / ρ
σ =σexternal + σinternal
Terminology
Speaking: Pulse Modal Falsetto
Singing: Chest Head Falsetto
(alternative) Fry Middle Whistle Stohbass flageolet

18. Physics 1251 Unit 3 Session 32 The Singing Voice
80/20The shape of the Vocal Tract determines the frequency of the Formants.
“ah”
“eh”
“oh”
“oo”

19. Physics 1251 Unit 3 Session 32 The Singing Voice
Spectrogram of Human Speech

20. 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

21. 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 I ε æ e
Second formant frequency Λ D U u c
First formant frequency

22. 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 i u A A A f f f

23. 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.

24. 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.