HARMONICS & TIMBRE: Theoretical Aspects of Trumpet Design © Part 2 of 21

“When a note is played very softly, the lips vibrate simply and only the fundamental tone is produced.  When the note is played at a higher dynamic level, the lips vibrate in a more complex manner, and a disturbance is produced that contains harmonics.  The number of harmonics present in the tone varies inversely with the fundamental frequency and increases with the playing volume.  The frequency of each harmonic is an integer multiple of the fundamental frequency.  Ordinarily, the relative amplitude of each higher frequency harmonic successively decreases.

French physicist, Henri Bouasse, (1929 and 1930) declared that the energy production in woodwind and brass instruments was not associated solely with the frequency of the fundamental, but also with the frequencies of the harmonics.

Benade’s graduate student, Walter Worman, (1971) found that the total acoustic energy was distributed between the frequencies of all the harmonics (the fundamental and partials) and interacted with a set of air column impedance maxima (resonance modes).  He found that when woodwinds and brasses were played softly, the fundamental frequency interacted with the impedance maximum associated with such frequency.  However, when the instrument was played louder, harmonics interacted with the maxima associated with the harmonic frequencies.  When played louder, each successive harmonic grew in strength much faster than the fundamental.  At full volume, the strengths of the harmonics in the tone were in direct proportion to the height of the various impedance maxima that cooperate to generate the tone.

The timbre is the direct result of the relative amplitude of the harmonics.  The relative amplitude of the harmonics depends upon the player’s unique lip physiology, oral cavity and playing technique.  When several trumpeters play the same trumpet, each produces a unique timbre.

Nevertheless, the timbre also depends upon the design of the trumpet air column and the trumpet structure.  The mouthpiece cup volume and the design of the lead pipe affect the magnitude of the input impedance peaks, which affects the relative amplitude of the harmonics.  The trumpet wall thickness, the metal wall acoustic velocity, and the trumpet mass affect the relative amplitude of the harmonics.”