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 Luciano Pavarotti Andrea Bocelli What is the difference?

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 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.

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 Closed Open Larynx 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 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

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 ≈ 0.017 m ρ ≈ 1040 kg/m3 σ ≈ 12 kPa f ≈ 100 Hz m ≈ 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 ♩ ♩ 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

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.

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

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 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

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”

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