Producing a harmonic sequence of notes with a trumpet

A closed tube produces only odd harmonics, but it is desirable for a brass instrument to produce all harmonics - a full harmonic sequence. This is accomplished by forcing the resonant frequencies toward the harmonic frequencies with the acoustic effects of the bell and mouthpiece. The mouthpiece forces the upper resonances down (the mouthpiece effect) and the bell forces the lower resonances up (the bell effect). The result is close to a harmonic sequence, but the lowest resonance is discarded and an extra pedal tone can be played as the fundamental of the sequence.

Producing an exact harmonic sequence of notes has its problems, as may be seen from the values of harmonics in cents. The upper harmonics are not exactly in tune with equal temperament, and the seventh harmonic is particularly troublesome.

The Mouthpiece Effect

The mouthpiece of a brass instument contributes to bringing the resonances into a harmonic sequence by bringing the high resonances down with respect to the resonances of a closed tube. The mouthpiece acts like a cavity resonator, and as the played frequency approaches this resonant frequency, the effective length of the tube becomes greater (approaching the tube length which would give that same resonant frequency. This increases the effective length for high frequencies lowering the high resonant frequencies.

This trumpet mouthpiece is very solidly constructed. It forms a comfortable cup for the vibration of the players lips. Good discussions of mouthpiece construction and function may be found in Shilke and Wolfe. The following are some of the ideas covered.

The mouthpiece can be divided into three parts:

• The rim of the mouthpiece affects flexibility and attack. The wider the rim, the more comfortable it feels to the player, but flexibility is reduced. With narrower rims, enhanced flexibility comes at the expense of tiring the player more quickly.
• The cup of the mouthpiece affects tone and attack. A deep cup gives a darker tone and low notes are easier to play. A shallow cup produces a brighter tone and the upper notes are easier to play. A flatter shape improves the precision of attack. A steep shape like the French horn provides gentler attacks, but changes the timbre of the instrument.
• The throat/backbore throat of the mouthpiece affects tone and air resistance. A larger diameter throat gives a mellower tone. Longer backbore (shorter throat) can make the higher register flat and shorter backbore (longer throat) can make it sharp.

The Pedal Tone

The pedal tone is a unique characteristic of brass instruments. It is the note which is at the fundamental frequency of the harmonic sequence of the instrument, but it is not a resonant frequency of the air column. When the bell effect raises the lower resonances of the closed tube, the lowest resonance is actually not used, being out of tune with the rest of the notes. However, if the player's lips are vibrated at the pedal tone frequency, all the harmonics above it contribute and produce a tone at this pedal tone pitch. It is sometimes called a fictitious fundamental, but for the bass brass instruments, it is quite strong and useful.

Bell effect

Trumpet resonance curve Euphonium pedal tone example Trombone pedal tone example