Physics 4830 Notes Tues 11/13/01

 

Last time: Flute-type, percussion instruments

Next time: Resonant tube lab

Today: Voice
Read: Chapter 15, 17 (17 is optional)

Outline

- Vocal folds

- Vocal tract

- Singer's formant

- Raised formants

- Throat singing

The human voice is quite a remarkable instrument. It has the capability of changing timbre and has an enormous variety of sounds and articulations, or so called "Phonemes".

The voice allows human beings to communicate in ways well beyond that of other animals and scientists speculate this is what sets the human being apart in the evolutionary process. At some point, man's vocal tract developed to a point to where it could communicate efficiently. If you look at the anatomy of other animals, they do not have the long vocal tract humans have. In fact, most mammals have the capability to eat and breathe at the same time, which is a big advantage for survival. Adult humans do not, because their larynx is open to provide a resonant cavity for making vowel sounds, as we will see.

Vocal Tract

The vocal tract is an open cavity including the nasal cavity, mouth cavity, pharynx and larynx. It ends at the vocal folds, which are made of soft skin-like tissue. The voice is like other wind instruments. There is a sound generating device and a resonant cavity. Air is forced from the lungs up through the trachea. The air stream passes through the vocal cords, which vibrate. The sound generation mechanism for the human voice is very similar to brass player's lips buzzing in a mouthpiece. The vocal folds are about 2 cm long. Frequency depends on the tension supplied by small muscles attached to the vocal folds and supporting cartilage. The Frequency range of vocal cord vibrations is approximately 70-200 Hz for men and approximately 140-400 Hz for women. There is an important physical effect called the Bernoulli's effect, which says that when a fluid speeds up, the pressure drops. This makes sense since if a small volume of fluid increases in speed something must be pushing on it so there must be a force on the fluid element, hence a pressure drop. The Bernoulli effect is important in the vocal tract because air flows faster through the folds causing a pressure drop and hence a force pulling the folds together. When, the folds come together, the flow is blocked and the air pressure from the lungs then pushes them apart. This is a simple explanation for how the vocal folds vibrate (especially for large amplitude vibrations of the vocal folds).

The sound resonates in the throat cavity, and mouth cavity. The resonances are weak however, since the tissue is soft and absorbing and the cavity shape is complicated. The tongue, jaws, lips and soft palate, help shape the resonant cavity to form different sounds. The difference between the voice and a musical instrument such as the clarinet for example, is that the resonant cavity is less selective than the long narrow pipe of the clarinet. This causes the perceived pitch to be determined by the vocal cords themselves. The buzz of the vocal cords would have the same vibrational frequency with or without the vocal tract attached. This is different then brass-players lips or a reed.

One can approximate the effect of the vocal tract on the amplitude of the harmonics by

total amplitude of a harmonic = (source) x (filter function)

Formants

There are many types of sounds or phonemes generated when we speak. You may have heard of the categorization of various consonant sounds studied in speech and hearing science as well as in the field of linguistics. For example, the difference between a plosive sound "p" and a fricative sound "f". We will not cover these consonant sounds, because they do not generate the sensation of a distinct pitch. On the other hand, vowel sounds are steady sounds with a definite pitch. a, ah, ee, oo. Vowel sounds are complex periodic waveforms.

How are these different vowel sounds made?

A vowel held steady, has a frequency spectra, which forms a harmonic series. It is the strength of the various harmonics that determines the particular vowel sound. Different vowel sounds are somewhat like different timbres.

The Formants are the natural modes or resonances of the vocal tract. The vocal tract can be crudely approximated as a pipe closed at one end. (The vocal cords cause pressure pulses at one end.) This means that the frequency location of the peak of the formants are at f, 3f, 5f, For example, if the first formant is at 500 Hz, then the second formant is at 1500 Hz and the third formant is at 2500 Hz. This corresponds to a vocal tract of 17.5 cm, this corresponds pretty well with the "ea" sound in head that has formants at 1500, 1800, 2500 Hz. It is typically the first two formants that are important for recognizing vowel sounds. However, trained singers have 4 or more distinct formants.

These resonances (called formants) are broad. The vocal tract is made up of soft walls and a complicated geometry. The vocal chords generate a harmonic series. These resonances enhance the harmonics a given frequency range. This is in many ways like subtractive synthesis. It is also like a clarinet in that it is approximately a pipe closed at one end. However, it is very different than a clarinet in that the resonances are broad, or not vary distinct.

Figure showing vocal tract and formants handed out in class.

One can approximate the effect of the vocal tract on the amplitude of the harmonics by

total amplitude of a harmonic = (source) x (filter function)

Singer's Formant

Professional male singers have an extra formant slightly higher in frequency than the third formant. This is done by lowering the larynx and widening the pharynx (cavity above the larynx). This high frequency peak allows the voice to be heard over an orchestra and is associated with a voice that "projects" well. This frequency (around 2600Hz) is above where the energy spectrum peaks for an orchestra.

Raised Formants

Sopranos frequencies are often higher than the first formant. So a trained singer will raise her first formant to be in resonance with the fundamental frequency being sung. This often makes the high note lines sung by an opera singer difficult to understand. This must be taken into account in the composition by having the words repeated elsewhere in the composition. Or by making the content of the words unimportant.

Throat Singers of Tuva

There is very interesting vocal music, called "throat singing" which originated in Tuva (officially now called Tyva) which borders Russia and Mongolia. Tuvan throat singers have the capability to hold a low tone, while simultaneously singing a higher tone to carry a melody. The higher tone is a formant that has a very narrow resonance. The lower tone is the fundamental frequency of the vocal cord vibrations. It is perceived as fairly loud through the phenomena of virtual pitch that we just studied.

From Track 9: Music of the (Former) Soviet Union, Music Library

Summary

Vowels are steady periodic sounds, pitch determined by the fundamental frequency of the vocal cords.

Enhanced frequency ranges due to vocal tract resonances are called formants.

The vocal tract crudely behaves as a pipe closed at one end.