2. Parametric Trombone Synthesis by Coupling Dynamic Lip Valve and Instrument Models Tamara Smyth (tamaras@cs.sfu.ca) Frederick Scott (fss3@cs.sfu.ca) 8 th Sound and Music Computing Conference (SMC), Thursday July 7, 2011, Padova, Italy

3. Outline Trombone instrument model Measuring bell reflection and transmission Generalized pressure-controlled valve Mouthpiece Sound examples

4. Trombone Instrument Model (no mouthpiece) Reed Pulse Instrument Signal + + F3nmp B3nmp D3nmp F4nmp

5. Measurement System microphone speaker Cylinder, closed Cylinder, bell terminated 2 meters 7 cm

6. Model of Measurement System Speaker output signal at exterior mic signal at interior mic + +

7. Measured Impulse Responses (interior mic)

8. Obtaining the Reflection Closed tube arrivals : Bell terminated tube arrivals: Take the ratio of second arrivals to obtain the bell reflection.

9. Measured Impulse Response (exterior mic)

10. Alternate Representation (convolutional synthesis) Reed Model Reed Model Blowing pressure

11. Lumping Round-Trip Loss in Transfer Function Denote round-trip losses from the mouthpiece to the bell and back again as The model transfer functions may be written as

12. Generalized Pressure-Controlled Valve Swinging (vocal systems, lip reeds) Blown closed (woodwind) Blown open (vocal systems, lip reed)

13. Generalized Pressure-Controlled Valve (trombone configuration) Parameters : QuantityVariableValue Radius of exhaust8 mm Equilibrium pos.0.01 mm Valve mass.3 g Valve width*2.3 mm Valve length*23.2 mm Valve thickness*6 mm Valve stiffness*

14. Valve Area Functions

15. Mouthpiece Enclosed volume Constriction Acoustic compliance InertanceDissipative element F3 Bb3

16. Mouthpiece Model QuantityVariableValue Volume5 X 10 -6 m 3 Choke length48 cm Choke radius4.5 mm

17. Valve Area Functions (with Mouthpiece)