How Well Can a Human Mimic the Sound of a Trumpet?

Ingo R. Titze – ingo.titze@utah.edu

University of Utah
201 Presidents Cir
Salt Lake City, UT

Popular version of paper 4pMU4 “How well can a human mimic the sound of a trumpet?”

Presented Thursday May 26, 2:00 pm, Solitude room

171st ASA Meeting Salt Lake City

 

Man-made musical instruments are sometimes designed or played to mimic the human voice, and likewise vocalists try to mimic the sounds of man-made instruments.  If flutes and strings accompany a singer, a “brassy” voice is likely to produce mismatches in timbre (tone color or sound quality).  Likewise, a “fluty” voice may not be ideal for a brass accompaniment.  Thus, singers are looking for ways to color their voice with variable timbre.

Acoustically, brass instruments are close cousins of the human voice.  It was discovered prehistorically that sending sound over long distances (to locate, be located, or warn of danger) is made easier when a vibrating sound source is connected to a horn.  It is not known which came first – blowing hollow animal horns or sea shells with pursed and vibrating lips, or cupping the hands to extend the airway for vocalization. In both cases, however, airflow-induced vibration of soft tissue (vocal folds or lips) is enhanced by a tube that resonates the frequencies and radiates them (sends them out) to the listener.

Around 1840, theatrical singing by males went through a revolution.  Men wanted to portray more masculinity and raw emotion with vocal timbre. “Do di Petto”, which is Italien for “C  in chest voice” was introduced by operatic tenor Gilbert Duprez in 1837, which soon became a phenomenon.  A heroic voice in opera took on more of a brass-like quality than a flute-like quality.  Similarly, in the early to mid- twentieth century (1920-1950), female singers were driven by the desire to sing with a richer timbre, one that matched brass and percussion instruments rather than strings or flutes.  Ethel Merman became an icon in this revolution. This led to the theatre belt sound produced by females today, which has much in common with a trumpet sound.

Titze_Fig1_Merman

Fig.1.  Mouth opening to head-size ratio for Ethel Merman and corresponding frequency spectrum for the sound “aw” with a fundamental frequency fo (pitch) at 547 Hz and a second harmonic frequency 2 fo at 1094 Hz.

 

The length of an uncoiled trumpet horn is about 2 meters (including the full length of the valves), whereas the length of a human airway above the glottis (the space between the vocal cords) is only about 17 cm (Fig. 2). The vibrating lips and the vibrating vocal cords can produce similar pitch ranges, but the resonators have vastly different natural frequencies due to the more than 10:1 ratio in airway length.  So, we ask, how can the voice produce a brass-like timbre in a “call” or “belt”?

One structural similarity between the human instrument and the brass instrument is the shape of the airway directly above the glottis, a short and narrow tube formed by the epiglottis.  It corresponds to the mouthpiece of brass instruments.  This mouthpiece plays a major role in shaping the sound quality.  A second structural similarity is created when a singer uses a wide mouth opening, simulating the bell of the trumpet.  With these two structural similarities, the spectrum of tones produced by the two instruments can be quite similar, despite the huge difference in the overall length of the instrument.

 

Titze_Fig2_airway_trumpet

Fig 2.  Human airway and trumpet (not drawn to scale).

 

Acoustically, the call or belt-like quality is achieved by strengthening the second harmonic frequency 2fin relation to the fundamental frequency fo.  In the human instrument, this can be done by choosing a bright vowel like /ᴂ/ that puts an airway resonance near the second harmonic.  The fundamental frequency will then have significantly less energy than the second harmonic.

Why does that resonance adjustment produce a brass-like timbre?  To understand this, we first recognize that, in brass-instrument playing, the tones produced by the lips are entrained (synchronized) to the resonance frequencies of the tube.  Thus, the tones heard from the trumpet are the resonance tones. These resonance tones form a harmonic series, but the fundamental tone in this series is missing.  It is known as the pedal tone.  Thus, by design, the trumpet has a strong second harmonic frequency with a missing fundamental frequency.

Perceptually, an imaginary fundamental frequency may be produced by our auditory system when a series of higher harmonics (equally spaced overtones) is heard.  Thus, the fundamental (pedal tone) may be perceptually present to some degree, but the highly dominant second harmonic determines the note that is played.

In belting and loud calling, the fundamental is not eliminated, but suppressed relative to the second harmonic.  The timbre of belt is related to the timbre of a trumpet due to this lack of energy in the fundamental frequency.  There is a limit, however, in how high the pitch can be raised with this timbre.  As pitch goes up, the first resonance of the airway has to be raised higher and higher to maintain the strong second harmonic.  This requires ever more mouth opening, literally creating a trumpet bell (Fig. 3).

Titze_Fig3_Menzel

Fig 3. Mouth opening to head-size ratio for Idina Menzel and corresponding frequency spectrum for a belt sound with a fundamental frequency (pitch) at 545 Hz.

 

Note the strong second harmonic frequency 2fo in the spectrum of frequencies produced by Idina Menzel, a current musical theatre singer.

One final comment about the perceived pitch of a belt sound is in order.  Pitch perception is not only related to the fundamental frequency, but the entire spectrum of frequencies.  The strong second harmonic influences pitch perception. The belt timbre on a D5 (587 Hz) results in a higher pitch perception for most people than a classical soprano sound on the same note. This adds to the excitement of the sound.

 

 

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