A Few Notes on Pitch

After 2,500 years of contemplation, musical pitch is as much an issue as ever. Musicians may have finally agreed on standardized 'concert pitch', but there is still no scientific consensus on what percentage of the population possesses 'perfect pitch', whether the skill is inherited or learned, or even how perception of pitch is achieved by the brain. Douglas Page surveys contemporary pitch research.

by Douglas Page, © 1998

The Rev. Sir Frederick Ouseley (1825-1889), Professor of Music at Oxford University, while attending a philharmonic concert at the age of eight, contended the Mozart's Symphony in G Minor to which he was listening was actually being performed in A-flat minor. Upon investigation it was found that, the great heat in the hall having sharpened the wind instruments, the strings had been advised to tune up a semitone.

Ouseley possessed the uncommon ability to identify absolutely the pitch of a musical note without the help of first hearing a reference note, a talent known as perfect, or absolute, pitch (AP). (Scientists generally call the phenomenon "absolute pitch", while musicians tend to refer to it as "perfect pitch". The terms are used interchangeably here.)

Pitch is the definition given for the frequency of vibrations of a particular object; the more vibrations in a given period the higher the sound. Here the certainty ends. Scientists may agree on what pitch is, but the specific mechanisms involved in pitch perception remain unclear. Nor is there a consensus on what percentage of the population possess perfect pitch or why.

Music adds an almost infinite complexity to the discussion of pitch. "Our perception of pitch depends on a number of things," says music professor William Alves, Harvey Mudd College, Claremont, Calif. "Most obviously, it maps to frequency fairly well. Thus, we often speak of pitches relating to specific frequencies in terms of Hertz: A is 440, C is 263, and so on. However, it's more complicated than that, because loudness, among other things, can affect our perception of pitch. Even trained musicians tend to judge slightly sharp octaves as 'in tune'."

Defining pitch, therefore, is a complex question that has to do with the relative presence of harmonics versus non-harmonic partials or overtones in the sound spectrum. "When does a collection of frequencies become a spectrum of a perceptually distinct tone, when do they become a chord and when do they become mere noise?" Alves asks rhetorically. "Psychoacousticians are still studying the mysterious process by which the brain makes these distinctions."

Pitch itself is a purely psychological phenomenon, says Daniel J. Levitin, a research scientist at Interval Research Corporation, Palo Alto, Calif., and Stanford University lecturer. "Sound waves exist in the real world; they have frequency and amplitude, but pitch is created entirely in the brain of the perceiver."

According to Levitin, sound waves are perceived similar to the way light waves are perceived. "Light waves have no color," he says. "All they are is electromagnetic radiation with differing wavelengths. A 680 nm wavelength excites certain neurons and not others, and sets off a chain of chemical and electrical activity in the brain which then 'interprets' the 680 nm wavelength in a certain way - giving rise to the experience of red. There is no red in the world. So it is with pitch. Air molecules vibrate at certain frequencies, and our ears interpret this as a psychological quality we call pitch."

When a note is sounded, such as middle A (440 Hz) on a piano, a complex set of oscillations of air is transmitted to the 30,000 or so auditory nerve fibers in each human ear, the frequencies of which consist of the lowest, fundamental frequency (440 Hz) and its corresponding higher frequencies (the 'harmonics' of 880, 1,320, 1,760 2,200 Hz, etc). The auditory receptors forward the frequency information to neurons in the brain stem and, ultimately, to the auditory cortex - where the sensation of 'hearing' the tone is formed.

Interestingly, when experimentally deleting the fundamental frequency while keeping the harmonics, the ear nevertheless perceives the missing fundamental, suggesting the brain computes what the fundamental frequency would have been - and then plugs it in. "In fact," says Levitin, "we can remove a number of lower harmonics and still believe that the pitch of the tone is that of the missing fundamental. This is one of the principles exploited by the telephone: its bandwidth is not large enough to reproduce the fundamental of a male speaker's voice, although we have little difficulty distinguishing males from females over the phone. This is due to the restoration of the fundamental." Levitin believes the missing fundamental, also called 'periodicity pitch', occurs at a relatively high level of processing, probably in the superior olivary nucleus, a wavy band of grey matter within the brain's medulla oblongata.

There is no general agreement, however, about how any of this perception is accomplished. There are two competing theories.

Some believe that the basilar membrane (that part of the cochlea containing the collection of auditory nerves) processes pitch below about 5 KHz based on the so-called "place theory" of pitch perception. That is, different regions of the membrane are excited by different frequencies and pitch is extracted that way. "According to this theory," Levitin explains, "pitches above 5 KHz, because they exceed the phase-locking capabilities and resolution of the basilar membrane, are processed based on temporal features at structures higher up, probably in the auditory cortex."

Others, such as Malcolm Slaney, a perception modeler at Interval Research Corp., believe that all pitch processing is temporal, and none is based on location - the so-called "rate theory" or "periodicity theory" of pitch perception. With this theory, pitch is determined by the rate at which excited hair cells in the cochlea fire.

"So far there is evidence for and against both theories and no one has yet crafted a combination of the two that fits all the evidence," says Alves.

NATURE OR NURTURE

Scientists also don't know how many people possess AP ability. A recent University of California San Francisco study claims perhaps 10 percent of musicians possess the musical gift of perfect pitch, 200 times more than the rate in the general population. Neurologist and author Oliver Sacks says that perfect pitch, though common in musicians, occurs only in about one person in 10,000 in the general population.

Nor is it completely understood why some people possess absolute pitch and some don't. Some theories hold that AP capability is inherited, that it cannot be acquired or learned at any time in one's life. Others believe AP can be learned, but only before age 5 or 6, while others think AP can be learned anytime by anyone. Advocates of the theory that anyone can be taught perfect pitch at any time maintain that AP is not the result of memorizing the actual pitches of notes, rather, that each note has an individual "color", or characteristic quality, which can be learned and recognized by anyone with a decent ear. Levitin has done work in this area of mental codes and memory, with collaborators Michael Posner, Roger Shepard and Perry Cook.

"A great many people are able to remember musical pitches absolutely. I would claim that nearly everyone has something akin to absolute pitch," says Levitin, who lectures to Stanford psychology, computer science and music classes. "If I ask a musician with AP to sing a G-sharp, they can do so. Until eight years ago, all AP tests were carried out only with musicians, because they were the only ones with the [musical] vocabulary necessary to complete the test."

There are reasons to believe, however, that people who succeed in music are less likely to have AP than others. "In particular," Levitin says, "most musicians are trained to recognize patterns in music. In music, the ability to transpose is highly valued, so one could argue that those who succeed in music have learned to suppress AP, or never had it to begin with."

"HOTEL CALIFORNIA" ON DEMAND

Levitin devised a means to test non-musicians for AP, whereby subjects are simply asked to sing a few notes of their favorite pop or rock song.

(It has to be a pop or rock song because these songs have a canonical 'correct key", whereas songs like "Happy Birthday" do not. The identity of any song, or melody, is determined by distances between successive notes, not by the pitch of the notes themselves, he says. That is, melody is a function of relative pitch information, not absolute pitch information. Because of this, any song can be sung in any key - which would cause a problem in doing an experiment on key recognition. Songs like "Happy Birthday" and "Twinkle, Twinkle, Little Star" are commonly sung in a variety of keys, so there is no objective standard to decide what the "correct" key for such a song is. By contrast, songs like "Hotel California" generally exist only in the original key as recorded by the original artists, so they have a "correct" key.)

"When asked to do this," he says, "most people sing at or very near the correct pitch. This indicates that they have encoded in memory the absolute pitch information of this song." He maintains that if a non-musician can sing "Hotel California" on demand that is just as convincing as being able to sing an F-sharp on demand, that "it's only their labels (or mental codes) that differ".

Moreover, he says, AP ability, in its original sense of naming or producing specific musical notes, is different than many people thought. "First, people with AP are no more accurate at pitch matching or pitch memory than those without it, so 'absolute pitch' is not by any means 'perfect pitch'.

"Second, AP is not an all-or-none ability. It occurs in greater or lesser degrees in different people; pitch memory forms a continuum, not a bi-modal distribution.

"Finally, pitch is not perceived by anyone we know of in a categorical sense, the way that color is. In other words, if you look at a rainbow, a broad patch of it is seen as red, another orange, and so on. Despite the fact that there are continuously changing wavelengths in the rainbow, we see the colors in discrete categories. This is not the case with pitch, which is perceived more or less continuously."

The recent UCSF study suggests both genes and early training are necessary to achieve AP. Scientists there reported in early 1998 that genes are not enough, that acquiring the skill also requires early musical training. Perfect pitch, the researchers concluded, is a model trait for investigating both the nature and nurture of human behavior.

The authors suggest that early musical experience literally shapes the brain's ability to perfectly perceive pitch, and that this window of opportunity may close before school age is reached. The suggestion that specifically timed environmental influence may be necessary to initiate the potential of a genetic predisposition is not new. Earlier research has shown there is a critical period in the development or reinforcement of certain neural circuits in the brain for singing behavior in song birds, and for language development in humans.

The UCSF research found that 40 percent of 600 musicians who began musical training before age 4 claimed to possess perfect pitch, whereas 27 percent of those who began music lessons between age 4 and 6 acquired the trait. The percentage dropped dramatically to 4 percent for those who started between ages 9 and 12, and to 2.7 percent among those who did not begin music training until after age 12.

"There is very clear evidence that what happens to you early can profoundly affect your perception later," says one of the authors, Siamak Baharloo, Center for Neurobiology and Psychiatry, UCSF.

Self-reported AP possessors are four times more likely to report another AP possessor in their families than are non-AP possessors. The family of Thom Ritter George, music director, Idaho State Civic Symphony, is an example. "My grandfather had perfect pitch. His daughter (my mother) has it. I have it, and my three children all have it," says "As you might expect, we are all musicians." (How does one know if they possess perfect pitch? Testing oneself against an instrument, or pitch pipe is conclusive, but usually not necessary; people with perfect pitch are already aware of their skill - some call it a curse - from 'knowing' the fly on the window is buzzing around in B-flat.) Estimates of what percentage of musicians possess perfect pitch range between three and 15.

A 1995 finding by neurologist Gottfried Schlaug, Beth Israel Deaconess Medical Center, Boston, reported in Science (267:699-671, 1995), is consistent with the UCSF work. Schlaug found that the planum temporale, a thumb-sized structure in the left hemisphere of the brain responsible for processing auditory input, is 25 to 30 percent larger in the brains of musicians with AP than in musicians without.

The question, then, is whether genetics leads to a larger planum temporale, predisposing a child to perfect pitch, or does early music training expand that region of the brain through mental exercise?

PITCH THROUGH HISTORY

The measurement of pitch, especially with regard to a musical tuning system, has been an issue of concern since antiquity when the philosopher Pythagoras, who established the idea that numbers provided the means for understanding the universe, first proposed a tuning system. "While the Pythagorean system is flawed, we still use it to tune string instruments because the system is based on pure fifths," says conductor Thom Ritter George.

The Pythagorean system exhibits an audible difference between the interval of a semitone and the interval resulting from the subtraction of the semitone from the whole tone. Over time, other systems emerged to address this flaw, including Mean Tone tuning, a system that generates the scale with fifths just flat enough to eliminate this difference, producing a scale containing acoustically perfect thirds. While these systems have certain attractive features and are still used (orchestras use Mean Tone tuning to produce very resonant chords), they are all flawed in one way or another, George says. In Mean Tone tuning, for instance, the discrepancy between chromatic notes (semitones) renders this system unsuitable for successive modulations (a shift in the key center of a composition).

"The whole matter of conflicting tuning systems was resolved by J.S. Bach. He solved the problem by writing a musical work, 'The Well Tempered Clavichord', or in his case, the harpsichord. It was impossible to get good results in his set of 48 Preludes and Fugues without resorting to a tuning system known as 'Equal Temperament', which is based on half steps."

In Equal Temperament, every semitone is the same frequency ratio, so all keys sound the same. Each tone is derived from the preceding chromatic scale tone by multiplying the frequency of the starting tone by the 12th root of two. "For example, A = 440 Hz," George explains. "To derive A-sharp, multiply 440 Hz by 1.059463, which is 466.16 Hz. In Western music, the octaves must be pure, so, if A = 440 Hz (the oboe tuning note), then an octave higher must be exactly twice that frequency (A one octave higher = 880 Hz)."

The earliest successful attempt to standardize pitch was made in 1858, when a commission at the Paris Academy composed of musicians and scientists appointed by the French government agreed upon A of 435 cycles per second. Thirty-one years later, in 1889, the 435 Hz standard, now called international pitch or diapason normal, was adopted by an international conference in Vienna. However, the standard was raised to 440 Hz by the International Standards Association in London in 1939.

The advantage of having an international standard was that musicians could more easily travel and that instruments themselves could be more easily sold abroad.

Orchestras and conductors, however, routinely deviate even from these standards. "I like to tune the orchestra at A = 442 Hz to achieve extra brilliance," George says. "Other conductors want a lower tuning note (A = 438 Hz, for example) for the purpose of getting more sonority from the strings."

Likewise, says Harvey Mudd's Alves, many groups performing early music prefer A = 415 Hz because it gives a more mellow, less tense sound, and probably also because modern makers of reproductions of early instruments have used models closer to 415 than 440. ----------------------------------------------------------