Pitch of 3-component harmonic complexes


Harmonic complexes composed of 3 consecutive harmonics are among the simplest periodic sounds. Their periodicity is determined by the spacing between the harmonics. Here is such a complex, composed of harmonics 1 (the fundamental), 2 and 3 of 100 Hz. The top panel shows the spectrum of this sound, and the bottom panel shows a 30 ms long segment of the waveform, consisting of three periods (100 Hz corresponds to a period of 10 ms). The pitch of this sound is very obvious:

Vowels are not strictly periodic


One of the most important classes of sounds that have pitch in the natural environment are voiced speech sounds. However, like many other naturally-produced sounds, these sounds are not strictly periodic. In spite of this, they produce a strong sense of pitch. Sounds that are not strictly periodic but that do evoke pitch are in fact the rule, rather than the exception.

Here is a naturally-produced human vowel:

Elliot and Theunissen addressed this question by calculating the "modulation spectra" of speech as shown here:

Missing Fundamentals. Periodicity and Pitch

As explained in the section on modes of vibration. most natural sound sources will not emit pure tones, but sounds composed of many, often harmonically related frequencies. Now, some texts on hearing will tell you that the pitch of a sound is "related to the sound's frequency", but if a sound contains many (possibly harmonically related) frequencies then it may not be at all obvious which of the sound's frequencies determines the pitch. 

Pitch matching

Pitch is defined by its perceptual qualities, and therefore has to be determined by the judgment of human listeners. By convention, we use the pitch evoked by pure tones as a yardstick with respect to which we judge the pitch evoked by other sounds. In practical terms, this is performed by matching experiments: A periodic sound whose pitch we want to measure is presented lternately with a pure tone. Listeners are asked to change the frequency of the pure tone until it evokes the same pitch as the periodic sound.

How many repetitions are required to produce pitch?

The main determinant of pitch is sound periodicity. A sound is periodic when it is composed of consecutive repetitions of a single short segment (the 'period'). The following figure (fig. 3.1 "Auditory Neuroscience") shows examples of periodic sounds:

periodic sounds

Fundamental frequencies of Notes in Western Music

Chapter 3 of Auditory Neuroscience discusses the pitch intervals used western music in great detail. For convenience, a table of fundamental frequencies for equal-tempered scale is copied below from  http://www.phy.mtu.edu/~suits/notefreqs.html

By convention A4 = 440 Hz

The range of periods that evoke pitch


Regular click trains at a rate of less than about 40 Hz sound like individual regular events, perhaps a bit like machine-gun fire. Click trains with rates faster than about 40 Hz merge into a continuous "buzz", where the pitch of the buzz depends on the click rate: the faster the rate, the higher the pitch. 

Melodies and Timbre

Many different sounds have the same pitch - you can play the same melody with a flute or with a clarinet or with a horn. Here, you can hear the same melody played on three computer-generated instruments.

The melodies in these examples share the same sequence of pitches, and have about the same sound level. The property of sounds that is different between them is called 'timbre' - the timbre of the flute is different from that of the clarinet and from that of the horn.

Here are the spectra of the three versions:

Basilar Membrane Motion 4: Bach's Tocata & Fugue

This video created by the Howard Hughes Medical institute © for Prof Jim Hudspeth illustrates basilar membrane motion in response to a piece of music, (J.S. Bach's Toccata & Fugue in D-minor).


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