Physics 1251 The Science and Technology of Musical Sound

1. Physics 1251The 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. Luciano Pavarotti Andrea Bocelli Physics 1251 Unit 3 Session 32 The Singing Voice The Singing Voice 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. Closed Open 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 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 = π2σ 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 ≈ 0.017 m ρ ≈ 1040 kg/m3 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 1175 Hz Vocal Range – Fundamental Pitch 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.www.exploratorium.edu/exhibits/vocal_vowels/vocal_vowels.html “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 Harmonics align with Formants Singers’ Formant Formants and Singing • 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.