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. 这个喇叭嘴垫构造非常牢固。它为演奏者嘴唇的振动形成一个舒适的凹槽。 Good discussions of mouthpiece construction and function may be found in Shilke and Wolfe. The following are some of the ideas covered. 关于嘴子构造和功能的详细讨论，可参见Shilke和Wolfe。以下是一些涉及的内容。

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.
  口哨的边缘会影响灵活性和演奏力度。边缘越宽，玩家感觉越舒适，但灵活性会降低。使用较窄的边缘虽然能提高灵活性，但会使玩家更容易疲劳。
• 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.
  杯形会影响音色和攻击性。深杯形会产生更暗的音色，低音更容易演奏。浅杯形会产生更明亮的音色，高音更容易演奏。扁平的杯形能提高攻击性的精度。陡峭的杯形，如法国号，会产生更柔和的攻击性，但会改变乐器的音色。
• 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.
  口哨管的喉部（背孔）会影响音色和空气阻力。喉部直径越大，音色越柔和。较长的背孔（较短的喉部）会使高音区变平，而较短的背孔（较长的喉部）则会使高音区变尖。

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 贝尔效应

Trumpet resonance curve 小号共振曲线 Euphonium pedal tone example euphonium 踩踏音示例 Trombone pedal tone example 小号踏板音示例