The Trumpet

The modern trumpet has three valves and a bore that is partly cylindrical, partly conical. The standard orchestral trumpet, built in B-flat, has a range of about three octaves extending upward from the F-sharp be extending upward from the F-sharp below middle C(F3 sharp = 185 Hz). Models in D, C, and other pitches also exist.

Music for all models is written as if they were C trumpets (written C sounds B-flat for a B-flat trumpet). This allows players to switch instruments without learning new fingerings.

Those models other than the C are said to be transposing instruments.

The cornet is very similar to the trumpet except that it has a conical bore throughout its length while most of the trumpet's bore is cylindrical. Another relative of the trumpet is the flugelhorn , sometimes dubbed the "valved bugle" . It has a mellower sound than the trumpet.

Use of valvesProducing a harmonic seriesResonance curve
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Trumpet Valves

The three valves of the trumpet add lengths of tubing to the instrument to lower the pitch. The first valve lowers it by a whole tone, the second by a semitone, and the third by a minor third.

Based on a length of 148 cm, valve 1 would have to add 17.9cm, valve 2 8.6 cm, and valve 3 would need to add 27.8 cm. Note that valves 1 and 2 depressed together lengthen the tube by 26.5 cm and are not equivalent to a minor third.

When a trumpet valve is up, the air goes straight through, and when it is depressed, a different air path is opened which adds a section of tubing. The length to add for the three valve intervals is calculated by using the fact that the frequency of an air column is inversely proportional to length.

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Reference
Backus
 
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Trumpet Resonance Curve

A trumpet exhibits natural resonant frequencies which follow a harmonic sequence fairly closely up to the tenth harmonic. This harmonic sequence is obtained with the help of the bell effect and the mouthpiece effect on the resonances. A unique pedal tone can be played inaddition to the resonant frequencies.

Trumpet resonance data
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Backus
 
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Trumpet Resonance Data

The data for the trumpet resonance curve reported by Backus were obtained by what he calls the capillary excitation method. The air column is excited by a loudspeaker type driver through a capillary tube into the air column near the mouthpiece end. The mouthpiece is closed off by a response microphone which measures the resulting mouthpiece pressure in response to the excitation. Note that the resonant peaks increase until about the 7th harmonic. This increase is attributed to approaching the helmholtz resonant frequency of the mouthpiece.
Above that peak, the amplitude diminishes rapidly. Backus attributes this to the fact that the wavelength of the 10th harmonic at about 1170 Hz is about equal to the circumference of the bell. Above that frequency, most ofthe wave energy is radiatedrather than being reflected tocontribute to the standingwaves necessary for resonance.

Trumpet resonance curveTrumpet discussion
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Reference
Backus
 
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