Brass instruments are a family of musical instruments that produce sound through the vibration of the player’s lips as they blow air into a metal mouthpiece. These instruments are typically made of brass or other metals and include instruments like trumpets, trombones, tubas, and French horns. The sound produced by brass instruments is shaped by the length and shape of the tubing, the player’s embouchure (the way they position their lips), and the manipulation of valves or slides that alter the pitch.
Naada Brass, currently, is a collection of two instruments, the Trumpet and the French Horn. The ensemble versions of these instruments are also present. In the future, we plan to increase this collection to all the popular instruments in the family.
Articulations and playing options
Tremolos, falls, wah-wah, and mutes are all controlled through parameters, while vibratos and shakes are managed via MIDI modulation messages. The pressure at the mouth is modeled using MIDI expression messages.
Physics
The lip and its embouchure, the bore, the mouthpiece, and the interaction between the lips and mouthpiece all play crucial roles in sound production.
Lip and embouchure: The lip is modeled as a spring with mass, in contrast to the reeds used in woodwinds, and it oscillates in response to pressure fluctuations in the mouthpiece. Unlike traditional reeds, the lip functions as a reed that is “blown open,” making it non-dissipative only within a narrow frequency range just above its natural frequency, exhibiting negative impedance. Consequently, the natural frequency of the lip spring must be slightly below that of the bore [1]. This results in the stiffness of the lip being dynamically altered throughout playing. The flow through the mouth is dependent on the overall area of the lip opening. This area depends non-linearly on the position of the lip when it is considered as a spring and is nearly elliptical [3].
Bore and mouthpiece: The propagation of pressure waves in the bore is modeled using a Digital Waveguide, while the mouthpiece modifies the signal, represented as a filter. The speed of sound increases with the square root of pressure, causing waveform distortion at higher pressures. This distortion contributes to the characteristic “brassy” sound of all brass instruments, a phenomenon that is also accounted for in the model.
Lip-Mouthpiece interaction: As the lips oscillate, they come into contact, causing a temporary cessation of airflow. This behavior is modeled by dynamically adjusting the lip spring properties. At each synthesis time step, the pressure at the mouthpiece must be recalculated. In Naada, this computation follows the method proposed by Vergez and Rodet [2]. The key phenomena considered in this process include:
- The lip oscillates as a spring described by a second order differential equation.
- The flow through the mouthpiece satisfies Bernoulli’s equations
- The flow into the mouthpiece is proportional to the difference of the outgoing and incoming pressure waves.
References
- [1] “The Physics of Musical Instruments”, Fletcher and Rossing, Springer-Verlag.
- [2] “Air Flow Related Improvements for Basic Physical Models of Brass Instruments” , Vergez and Rodet, International Conference on Mathematics and Computing, 2000
- [3] “Blowing Pressure, Power and Spectrum in Trumpet Playing“, Fletcher and Tamopolsky, J. Acoust. Soc. Am. Feb 1999