Terms and concepts:
5.Hammer, anvil, stirrup
Modes of vibration
Sine wave graphs are useful for explaining a basic wave, but they are merely monotones: a mathematical approximation of a musical sound. The sine wave’s intensity and duration is constant and unending and says nothing about decay or other factors that create musical waves.
Music is far more complex. Musical sounds rely on our own intuition – the subjective judgments we make with our ears and our minds. We then develop a scale based on the tones and sounds that we have selected from a nearly infinite variety.
This applies to personal and communal Indigenous music as much as it does to Western classical music. In fact, the European-based scale is merely an elaborate, documented and institutionalized form of the same intuitive choices that a skilled indigenous musician makes. This section will outline some of the mysteries of how all of us – Indigenous or not – hear, organize and arrange those sounds.
To know how we make these choices, we must first understand the ear, the instrument that conducts those sounds to our minds. The human ear has three sections – the outer, middle, and inner. Let’s discuss these.
The Outer Ear
The outer section is the auricle, or pinna, the part we see. This funnels sound waves into the auditory canal. This is a tube about three centimeters long. At its inner end is the tympanum, or eardrum, a membrane that does what its name suggests. It vibrates like a drum when sound hits it.
The Middle Ear
Inside the eardrum, a short passage, the eustachian tube, runs to the back of the throat. This equalizes air pressure changes inside and outside the ear, which keeps the eardrum from distorting.
The middle ear contains the ossicles, which are three tiny bones. Scientists name them after what they look like: the hammer, anvil and stirrup. Doctors often like to use their Latin forms: malleus, incus and stapes. The stirrup and its muscle, the stapedius, are the tiniest bone and muscle in the body. Flexible joints connect the three bones. The hammer also attaches to the eardrum and vibrates with it, while the stirrup, at the other end, connects to another membrane, the oval window that leads to the inner ear region.
The Inner Ear
Passing through the oval window, we enter the cochlea, a coiling, snail-shell shaped cavity in the inner skull filled with a fluid, the perilymph. The all-important basilar membrane divides the cochlea into two long chambers. This membrane is about 35 millimetres long and coils 2½ times in a spiral. The organ of corti sits on top of this membrane for its full length. Tiny sensory hair cells with nerve endings, stereocilia, carpet this organ. We hear sounds because the membrane passes its vibrations to the hairs, which convert the sounds into signals the auditory nerve sends to the brain.
The oval window connects the upper chamber to the eardrum, while another membrane, the round window, connects the lower chamber to the middle ear. At the cochlea’s far end, the sound-sensitive basilar membrane ends with a small opening called the helicotrema that funnels the two chambers into one.
Transmission of Sounds Through the Ear
The pinna channels sound waves down the auditory canal, which makes the eardrum and the tiny bones vibrate. The bones act like levers, and focus the larger eardrum’s vibrations onto the oval window’s much smaller surface. This concentrates and increases the pressure on the window.
The oval window moves sound pressure to the cochlea and its perilymph fluid. The fluid must be free to move, or the basilar membrane and the organ of corti cannot pick up the vibrations. The lower chamber’s round window makes this possible. When the oval window moves inward, the round window moves outward – just enough to give the fluid room to move. This sends sound sensations to the basilar membrane, next the organ of corti’s sensory hairs pick up these vibrations and carry the signals to the brain.
The organ of corti’s sensory hair cells signal different tones and sound qualities. The oval window sends vibrations down the basilar membrane toward the helicotrema at the other end. Each individual wave gains in amplitude as it moves along. When it reaches a certain point it quickly dwindles.
Different frequencies do this at different places along the membrane. Higher frequencies reach their greatest amplitude and then decline closer to the oval window. Low frequencies do the same, but closer to the helicotrema at the cochlea’s other end. The brain interprets the drop-off points along the basilar membrane and organ of corti as either high tones or low tones. Scientists understand the basics, but they are still learning how the brain can separate and distinguish tens of thousands of tones.
Loud sounds could damage our hearing, but the eardrum’s tensioning muscle and the stirrup’s tiny stapedius muscle contract in response to loud sounds. This affects the eardrum and interrupts the way the specially shaped hammer, anvil and stirrup vibrate together, which reduces sound pressure on the oval window. That doesn’t mean people can safely listen to earsplitting music and noise. The muscles cannot stop chronically loud sounds. Hearing damage starts at a sustained 85 to 90 decibels or so, but a typical rock concert blasts ears at a constant 100 decibels. Also, painful sounds such as gunshots, explosions and some industrial noises are dangerous because the tensioning muscles cannot react quickly enough. The damage can be permanent.
Pure and Complex Tones
The basilar membrane and organ of corti can detect tiny tonal and sound-quality differences. The brain’s ability to interpret these is extraordinary.
Tone is the primary musical unit. A tone is any steadily vibrating pressure changes in the air that endure long enough for the human ear to interpret them as sound. About the lowest rate a human ear can is 20 vibrations per second (20 hertz). People usually feel frequencies lower than 20 hertz as vibrations. The highest rate that people who have exceptionally good ears can hear is about 20,000 vibrations per second (20,000 hertz). A steady frequency gives a person the sensation of a musical tone of constant pitch. A low hertz number indicates a low pitch. A high number indicates a high pitch.
A pure tone is a sound wave of a single frequency, but no musical instrument produces a pure tone. Rather, each instrument is unique because it vibrates in several ways at once. These different vibrations are the instrument’s modes. Pure tones themselves would be monotonous and uninteresting.
Let’s review the basics of sound, only we will consider their effects upon human hearing. Complex sounds have more than one vibration. The lowest mode, the fundamental frequency is the simplest vibration and thus the one with the lowest frequency. All the other modes, with all their varying tones, combine into partial frequencies, or to put it simply, partials.
The partial tones are harmonics, but only if they have frequencies that are integral multiples of the fundamental frequency. Interestingly, the human ear perceives only these precise mathematical multiples as being “in tune” or melodious.
The fundamental frequency is also the first harmonic. For example, if the fundamental frequency is 100 Hz, then the first harmonic is the same (100 Hz). The next mode, the second harmonic, is twice that frequency: In this example, two times 100 Hz would be 200 Hz. The third harmonic is three times the fundamental frequency: Three times 100 Hz would be 300 Hz. The fourth harmonic would be four times the fundamental frequency and so forth.
Harmonics (mathematically precise multiple frequencies) are useful musical organizers, We include them as overtones, but many overtones are not harmonic. Overtones include all the system’s other higher-frequency vibrational modes, too.
Even non-harmonic overtones can be important to music. For example, the overtones in drums, bells, and rods or bars are not harmonic. Also, strings normally have harmonic overtones. But, significant stiffness (as, say, found in piano wires) can causes the higher partials to deviate from harmonic frequencies. Piano tuners work with this, of course. These differences are part of the tonality we call “piano string sound.”
When we classify harmonic overtones, we do not count the first harmonic, which is the lowest tone, namely, the fundamental frequency. This means the second harmonic is also the first overtone.
The ways in which all these partials combine into a single, steady tone is complex. The mathematician, Jean Baptiste Joseph Fourier (1768-1830), came up with a way to understand this. Fourier’s theorem allows us to put waves together or take them apart. The theorem says that any combined sound of a periodic waveform vibration, however complicated, comes from a series of simple vibrations whose frequencies are harmonics of a fundamental frequency.
Fourier’s analysis allows us to separate an existing complex sound into its various harmonics’ amplitudes and phases. Fourier’s synthesis does the opposite. It allows us to create a complex tone using the harmonics of the fundamental frequency.
A Fourier diagram graphs vibrations and includes all their complex waveforms. It plots where different frequencies rise and dwindle along the way. This is similar to how the basilar membrane does its job. In fact, researchers say the membrane plots tones using the same physics as Fourier’s analysis.
Consequently, humans have astoundingly sensitive abilities to tell musical tones and non-musical sounds apart. For example, if a sound has any components that do not line up with the harmonics, the ear will perceive that sound either as non-musical, or as an off-key note with an unclear tone or pitch. What science achieved mathematically, Nature, over millennia, had already achieved organically. The two ocean currents, science and the Aboriginal worldview, converge once again.
Tonal Perception: Pitch, Timbre, Intensity
Science explores mathematically why musical tones sound like they do. But, the traditional Aboriginal musician does the same using the ear alone. Both know that a single sound can vary in many ways. Both creatively organize musical tones from the vast array of possible sounds.
As the scientific method exists, so does an Indigenous method. The two disciplines begin with intuition and follow experimental patterns, but that is where they separate.
Like scientists, Indigenous people observe, synthesize, experiment, record, analyze and predict. As Elders who teach the next generations they also share with others who can replicate what they have done. But, unlike scientists, the Indigenous goal is more directly spiritual. Scientists observe but do not subjectively identify with the phenomena. In contrast, Indigenous people, in this case, musicians, seek to discover the knowledge to become one with their instruments, their communities, their ancestors and the natural world.
Yet, the ultimate goal of both scientists and Indigenous people is the deepest possible knowledge of the Universe. Put simply, scientists and Indigenous musicians are two canoes painted differently, but in the same stream.
To return to music, whether scientific or Indigenous, people identify and select desirable tones in three basic ways. The most important characteristic is pitch, the quality that makes a sound higher or lower. Human cultures use pitch to create musical scales. Yet pitch is seldom exact. Many factors, especially temperature, can affect a tone’s pitch. For example, in 1938 (or some say 1939), the British Standards Institute set the A note at 440 Hz and 68 degrees Fahrenheit. Before and after that conference, nations for generations had argued vigorously but have never achieved a lasting consensus.
No one has documented any Indigenous dispute over pitch (which is not to say that we haven’t disagreed). A speech that scholars have attributed to a 19th century Native American, Talatawi tribal Chief White Cloud, said people should never argue over God. Perhaps the same wisdom should apply to the physics of music.
Music follows external mathematical rules. Scientists seek universally replicable results, but Indigenous music will always be both intuitive and subjectively experiential. As the debate over the 440 Hz A-tone shows, Europeans and their North American offspring have aimed for precise pitch. Thus, they have attempted to quantify an ability that is equally relevant to Indigenous music: the ability to pinpoint subtle tones with the human ear.
Both world cultures have identified people who can do this precisely. These are the ones who have developed absolute pitch, also known as perfect pitch. In the Indigenous world, pitch preferences vary widely across communities and peoples. Many scholars have abandoned the usual scales when studying Native music and instead opted for the term inventory: an open method that documents tonal preferences across cultures. Perhaps these scholars could apply the North American inventory to their own peoples. This might be more respectful than heated arguments over pitch.
Timbre refers to the unique tonal qualities that different musical instruments produce. For example, a pure sine wave and a Native flute can have the same tone (periodicity), but the likeness stops there. Mathematically, all instruments produce different waveforms. Some will be triangular and others will be square, jagged (sawtooth), or simply a series of sound pulses that we call a pulse train. Put simply, every tonal signature is unique.
This is due to the fact that each instrument or voice produces a sound that favours certain harmonics over others because of its particular harmonically related modes. In other words, each musical source mixes its sounds differently. Thus a wind instrument that emphasizes the second harmonic will sound strikingly different from an instrument in which a different harmonic is strongest.
Intensity is the instrument’s basic loudness or power. Technically, source intensity depends mostly on oscillation amplitude rather than frequency. We measure sound power in watts (W), which equals how much sound-energy per second a source releases into the air.
As we move away from the sound source, the loudness changes. Sound pressure, or relative intensity, depends on three qualities: how much power the sound source has, a room’s (or other area’s) characteristics and how far the listener is from the sound source. Most commonly we use the decibel scale (dB) to measure sound pressure at a particular position. People named the decibel in honour of Alexander Graham Bell, the telephone’s inventor.