CSD 232 Home

Fundamental Frequency and the Glottal Pulse

If you look at the time domain representation of a human speech, you will find that voiced sounds, such as voiced obstruents ([b], [d], [g] etc.), sonorant consonants ([n], [m], [l], etc.), and all vowels, you will find a periodic pattern. That is, you will see a repeating pattern.
periodic_wave

Each of the identifiable repeating patterns is called a cycle. The duration of each cycle is called the (duration of the) glottal pulse or pitch period length.  We represent the length in time of the glottal pulse or pitch period length by the Greek letter tau, τ.  When the
pitch period length is measured in milliseconds, we customarily represent it by τms. If the pitch period length is measured in seconds, we represent it as τs or simply as τ.

The fundamental frequency (also called the fundamental) of a periodic signal is the inverse (reciprocal) of the pitch period length. We represent the fundamental frequency as F0 ("F-zero", or "F-sub-zero").

We can represent the relationship between the fundamental frequency and the duration of the glottal pulse as follows:
F0 = 1/τs    or as   F0 = 1000/τms
The fundamental frequency is a measure of how high or low the frequency of a person's voice sounds. Its psychological correlate is pitch. It is the frequency of vocal fold vibration and correlates with changes in vocal fold tension and subglottal air pressure. A bass voice has a lower fundamental frequency than a soprano voice. A typical adult male will have a fundamental frequency of from 85 to 155 Hz, and that of a typical adult female from 165 to 255 Hz. Children and babies have even higher fundamental frequencies. Infants show a range of 250 to 650 Hz, and in some cases go over 1000 Hz.  A 10-year-old boy or girl might have a fundamental frequency around 400 Hz. When we speak, it is natural for our fundamental frequency to vary within a range of frequencies. This is heard as the intonation pattern or melody of natural speech.  When we sing a song, we are controlling the fundamental frequency of our voice according to the melody of that song.  Since a person's voice typically varies over a range of fundamental frequencies, it is more accurate to speak of a person having a range of fundamental frequencies, rather than one specific fundamental frequency, Nevertheless, a person's relaxed voice usually can be characterized by a "natural" fundamental frequency that is comfortable for that person.


How would you calculate the fundamental frequency,
F0 , to the nearest integer, from a given glottal pulse duration of 4.5 milliseconds?

Here's the forumula, given here in terms of τms, since we are dealing with milliseconds.

    F0 = 1000/τms
Now, plugging in 4.5ms for τms we get
F0 =1000/4.5ms     , which yields
F0 =222.222 Hz, rounding off to
F0 222 Hz.

Going the other way, let's say you know the fundamental frequency. How would you calculate the duration of the glottal pulse?  Let's say we are given the fundamental frequency as being 180 Hz. The formula is
τms = 1000/F0
Now, plugging in 180 Hz for F0, we get
τms = 1000/180 Hz   , which yields
τms = 5.555 ms   , which rounds off to
τms = 5.56 ms

Exercise:

Calculate the fundamental frequency to the nearest integer or glottal pulse period to the nearest tenth of a millisecond in these six cases. Also, in each case, give your guess about the probable gender of the speaker with this F0 (feedback here):

Case Number
Fundamental Frequency
Glottal Pulse Period
Probable Gender of Speaker
1
125 Hz


2
202 Hz

3
88 Hz

4

4.7 milliseconds
5

0.0087 seconds
6

10 milliseconds