Frequency

Frequency, in the context of this course, is a measure of a cycle of vibration per unit time. For voice, it is equal tothe number of times the vocal folds open and close per second. The vibration of a tuning fork results in a pure tone, as the fork vibrates at only one frequency. The vibration of the vocal folds is much more complex, due to the structure of the vocal folds. Vibration of the vocal folds produces a complex tone, one that is composed of several frequencies of vibration. Fundamental frequency is the lowest frequency component of the complex tone. Frequency relates directly to pitch, which is perceptual.

 

simple.complex.wave.png harmonic spectra.png

 

The image on your left is from your textbook, page 27. It illustrates two waveforms. The top is a sinusoidal wave of a sound that may be produced by a tuning fork--a pure tone. The bottom waveform is that of a complex wave, with more than one frequency component.

 

 

We judge pitch to correspond to the fundamental frequency of a harmonic series. The image on the right, from your textbook, page 80, illustrates harmonic series produced by an adult and a child. A complex tone of 600, 900, and 1,200 Hertz (Hz) is judged to have a pitch of a 300-Hz tone. This is the rate at which the basic pattern of the complex wave repeats itself.

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Looking at the image on the right, what is the pitch of the adult?

 
 
 
 

 

 

 

Frequency and voice: a look at the musical scale and voice registers

singing.voice.jpg The rate of vocal fold vibration is described either in terms of fundamental frequency (cycles per second or Hz), or in terms of musical notes (pitch). In either case the scale is on a continuum ranging from less than 60 Hz (B1 on the musical scale) in the basso voice to over 1588 Hz (G6 on the musical scale) in the soprano voice.

Looking at the picture on the left (from Zemlin, W. R. (1998). Speech and Hearing Science: Anatomy and Physiology (4th ed.), p. 166.  Boston: Allyn & Bacon), you can see that there are five registers (numbered 1-5) covering a range of notes, and the registers are different for males and females. The registers overlap. No one person has all 5, and good singers have 3 registers. The concept of registers is controversial in singing, with some authors designating 4 registers. But in speech pathology, register is associated with vocal fold vibration.

 

The names of the registers vary. In singing, the "head" voice is associated with the position and use of the vocal folds and larynx. It is used in singing and found in all voice types, from bass to soprano. In the "head" register (number 4 on the picture), vocal folds are thin, and there is no firm glottal closure. The cricothyroid muscles are active. Singers say the sound vibrates in their in their heads rather than chest. "Chest" register (number 4 on the picture) is the range of notes below midle C (C4 on the picture). This is the lower half of a person's vocal range. The pitch is said to resonate throughout the chest cavity.

 The musical scale is organized into octaves, with a fequency ratio of 2 to 1. So, for example, 1 octave above a 500-Hz tone is a 1,000-Hz tone. C4 is middle C, and you can see on the picture to the left that it is 256 Hz. Actually, the "standard" for Middle C is 261.63 Hz. If we want to find an octave below middle C, we divide by 2 to get 130.81 Hz, or C3. The note A4 is an international standard at 440 Hz. If we have a tuning fork set at this standard, it will vibrate at 440 Hz. If we tune a piano precisely to this value, everything else is in proportion to that.

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One octave below a 2,000 Hz tone is a

 
 
 
 

  For the speaking voice, there are three registers. Modal register is commonly used when speaking, and corresponds to the singing "chest" register. Pulse register is the lowest register. You could technically speak in pulse register, but it would be difficult. Pulse register typically occurs at the end of an utterance, and has a double vibratory pattern. It is a "creaky" voice, also known as glottal or vocal fry. The vocal folds in this register are short and thick. The highest register is the loft register. This register is also called falsetto. The vocal folds are long, stiff, and very thin along the edges, and somewhat bow-shaped. The vocalis and cricothyroid muscles are stiff, and the vocal folds may not be completelly closed. In singing, the loft register corresponds to the "head" voice.

  

Factors that affect frequency

The size of the vocal folds determines fundamental frequency. A greater length and higher mass lower frequency. Men have vocal folds that are approximately 17-24 millimeters (mm) in length, and women's vocal folds are 13-17 mm.

The fundamental frequency for males averages 130 Hz, for females, 220Hz, and for children, 300 Hz.

Mutations are voice changes, which are due to the rapid growth of the larynx that occurs during puberty. Before puberty, both boys and girls have fundamental frequencies of aproximately 270-300 Hz. Voice changes are more recongnizable in males than females. Changes in the boy's voice are approximately 1 octave, from approximately 270 to 120 Hz, as the vocal folds grow longer and thicker. The boy's singing ability is not as good after the change. In females, the change is about 2-3 tones, rather than 1 octave, with a change from 270 to 220 Hz.

 

Frequency is proportional to tension, stiffness, and elasticity over mass. The relationship can be depicted in this equation:

f α k/m

f = frequency

k = tension, stiffness, elasticity

m = mass

α = is proportional to

 

This relationship helps us compare the speaking voice between people, for example, an adult male and a small child. The larger the vocal folds, the lower the frequency. This formula holds within an individual, too--if a person chooses to vary his frequency, he is going to manipulate the variables of tension, stiffness, elasticity, and mass.

 

Raising Frequency

We raise frequency through the action of the laryngeal muscles. Even before we make a sound, the vocal folds get shorter--the arytenoid cartilages come together medially and anteriorly. The vocal folds are shorter during phonation than at rest breathing. Remember that the cricothyroid muscle contracts to lengthen the vocal folds. The cricothyroid is the most important muscle in raising frequency. As the vocal folds are stretched, their mass per unit length decreases. The stretching also increases the stiffness factor. It can be represented in this way:

k↑  

m↓ The net result is that frequency is increased.

 

We can also increase the internal tension of the vocal folds. The most medial part of the vocal folds (the thyroarytenoid muscle) is the vocalis muscle. If the vocalis contracts, it increases the internal tension of the vocal folds, and increases the stiffness. In the equation, it is represented like this:

k↑  

m Note that mass does not decrease, and the net result is that frequency is increased.

 

Frequency can be increased through the lateral cricoarytenoid muscle. Remember that the lateral cricoarytenoid attaches to the cricoid and attaches to muscular processes for medial compression. The medial compression restricts the vibrating mass to more of the anterior position of the vocal folds. The action is similar to putting frets on a guitar--it reduces the vibrating mass, which is one way to increase frequency. The formula is depicted here:

 

Lowering Frequency

Whereas the cricothryoid muscle raises frequency, there's not much evidence that points to one muscle to lower frequency. If you think about the thyroarytenoid muscle in its broadest sense, as it contracts, it draws the vocal folds together. As it contracts, it draws the vocal folds together, and they become shorter, thicker, and more relaxed. The formula is depicted here:

 

k_↓  

m↑  The net result is that frequency is decreased.

 

The extrinsic muscles of the larynx have at best a secondary role in frequency change. Professional singers do lower their larynx, which opens the lower pharyngeal cavity for what is called "singer's formant."

 

Now that you have learned about frequency, take a short quiz to test your knowledge. The last question is a challenge question.

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