Parametric Trombone Synthesis by Coupling Dynamic Lip Valve and Instrument Models Tamara Smyth Frederick Scott 8 th Sound and Music Computing Conference (SMC), Thursday July 7, 2011, Padova, Italy

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

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

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

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

Measured Impulse Responses (interior mic)

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

Measured Impulse Response (exterior mic)

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

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

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

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*

Valve Area Functions

Mouthpiece Enclosed volume Constriction Acoustic compliance InertanceDissipative element F3 Bb3

Mouthpiece Model QuantityVariableValue Volume5 X m 3 Choke length48 cm Choke radius4.5 mm

Valve Area Functions (with Mouthpiece)