Nov. 11, 2017

Every Tone A Life Unto Itself


After exploring much to do with vibrations and how they are related to the birth of the world, then delving into theories about chaos and order, fractals and Fibonacci spirals, studying various world rhythms, and finally looking at the many forms that music can take, we are now stepping into the realm of acoustics and timbre.

Acoustics is the science of sound, a branch of Physics and Engineering melded together, and timbre is the quality of that sound. Timbre is included within the smaller spectrums of form, meter and scale and is equally as important. For a singer, timbre is everything.

In 1863, a physician and physicist who had already made significant contributions to the scientific community, published his views ‘On the Sensations of Tone’, which became the foundational work on acoustics and sound perception. Hermann Von Helmholtz turned the world on its ear by opening up discussion on how we perceive different sounds, with his paper and also with his invention of a resonator machine that would help to unravel the structure of sound waves and how they travel in various frequencies or pitches.

Helmholtz’s theories and Resonator machine were the herald of modern day acoustics.  

Acoustics, derived from the Greek word ἀκουστικός, (akoustikos) is a multi-faceted science that covers the study of all sound waves found within gases, liquids and solids, and includes vibrations, sounds, ultrasounds (high frequency sounds), and infrasonics (low frequency sounds). In my past career, acoustics was often touched on from the perspective of dampening sound, or adding white noise in order to make a workplace more private. We studied the NRC ratings or Noise Reduction Coefficient properties of materials such as ceiling tiles, drywall, carpet, and panel fabrics. I’m excited now to be learning about the use of acoustical properties of spaces, as they relate to music. Since my work had involved adding fabric or absorptive materials in order to dampen sound, I never really understood the application of using these same strategies in a concert hall, mostly likely because my preferred space to perform in would be a very live one, such as a church. However, in modern days, we now must also consider other types of music and sounds, such as amplified sound; for instance, a stone church or space filled solely with hard surfaces wouldn’t be conducive to having a rock band perform in it. It is because of this that some modern concert halls are said to be acoustically superior from others for classical artists, but the opinion depends on the type of music or sounds being played and heard, and on the ears which are hearing it.

The different types of acoustic study range from those mentioned above (Ultrasonic and Infrasonic) and others:

Types of Acoustic Study & Definitions
Ultrasonic - Fast moving or high frequency sounds; most commonly known for advances in medicine which allow the capture of diagnostic images.

Infrasonic - Slow moving vibrations that the human ear cannot detect. Infrasonics are used for weather detection or to study blast waves.

Structural Vibration - This is the study of how vibrations can affect structures such as buildings and bridges. We know that hurricane force winds can cause bridges to undulate, and that earth tremors can cause buildings to sway. Now we can study the tolerances that are needed to be built in, to ensure structural integrity.

Physiological Acoustics This can be divided into three segments:
Physiological being the processing of a sound wave as it reaches our ears
Psychoacoustics: how a human interprets the sounds, such as where it is coming from, or the loudness or softness of a sound, and, part of the “Three P’s of Acoustics:
Perception, which is how we perceive a sound, as in whether it sounds bright or dark, strong or weak, etc.

Speech and Hearing - The study of sounds for human communication, used mostly in a therapeutic way to assist with deafness, stuttering and aphasia, which is the impairment of language caused by a brain injury.

Noise Measurement & Control - Studies in this area pertain to the measurement of noise in daily life and its impact on humans. Great effort is being made to understand how noises can affect us, whether they are too loud (industrial) or an underlying hum. Consider the controversy regarding wind turbines and the complaints that the noise they generate could drive one into madness.
Architectural Acoustics This involves the use of materials and structural design to either enhance sound or remove it, for spaces we live and work in, and for concert halls.

Musical Acoustics - The study of the way in which sound is produced by musical instruments, or relayed by a voice; and the study of the human perception of sound as music.
More on these definitions can be found here:

I am most fascinated by the way our human ears are built and how a sound is processed within this tiny, delicate system! It is not a simple, individual process, but rather, a string of minute processes passing through several steps and chambers or parts, and ultimately connecting with the brain.

A sound wave reaches our outer ear and is collected or absorbed into the ear canal, causing the ear drum (or tympanic membrane) to vibrate. It next travels to the middle ear, where it encounters 3 bones or ossicles, named the hammer (malleus), anvil (incus), and stirrup (stapes), which interact with each other as a lever system. It then is sent into the inner ear, where tiny fibres and an amount of fluid in the Cochlea also must be involved, to finally transmit the sound via the auditory nerve, to the brain. This passage from Scientific American describes the entire process much better than I can!

“When the eardrum vibrates as sound hits its surface, it sets the ossicles into motion. The ossicles are arranged in a special order to perform their job. Directly behind and connected to the eardrum—which is essentially, a large collector of sound—is the hammer. The hammer is arranged so that one end is attached to the eardrum, while the other end forms a lever-like hinge with the anvil. The opposite end of the anvil is fused with the stirrup (so anvil and stirrup act as one bone). The stirrup then connects with a special opening in the cochlea called the "oval window." The footplate of the stirrup—the oval, flat part of the bone that resembles the part where one would rest ones foot in an actual stirrup—is loosely attached to the oval window of the cochlea, allowing it to move in and out like a piston. The piston-like action generates vibrations in the fluid-filled inner ear that are used to signal the brain of a sound event. Without the middle ear ossicles, only about 0.1 percent of sound energy would make it into the inner ear.”

The structure of the ear is fascinating to explore, and the parts are extremely delicate. What I noticed first in the diagrams was the similarity of the Cochlea to a Fibonacci spiral, so I went looking to see if it was indeed a perfect Golden Ratio. It turns out that it is close, but not perfect, but it was interesting to read about it.

Let’s take a look at sound waves and try to understand their structure. If we picture a tightened string, when it flexes and is bent or curved upwards, this is called displacement, and the height it reaches is the amplitude. At its median, this is called equilibrium. When it moves below the median, and then back to the centre, this is called the restore point. The amplitude is the maximum displacement from equilibrium.

The above illustration depicts a Transverse Wave, and there are other types of waves, discernible by the direction in which the wave is traveling. Transverse waves look very similar to Sine (Sinusoidal) Waves, but a Sine wave is completely linear. Here is the best description that I could find, that compares the two. Ultimately, it is mathematics that defines their properties.

“A Sinusoidal wave is a wave that can be described by a single sine or cosine function.

A Transverse wave is a wave where the displacement of an element is perpendicular to the direction of travel. If you get your hands on a slinky, a transverse wave goes up and down or side to side, and it kind of looks like how a snake might move.
A longitudinal wave goes backwards and forwards along the direction of travel; there is a stretching and squeezing in the slinky that travels along it, looking more like an earthworm.
You can also get circular or elliptical waves, which spiral around the direction of travel; I was amazed when I first discovered this while playing around with a garden hose.

A transverse wave is usually sinusoidal, but it could be any shape it damn well pleases; this is achieved by adding a lot of sinusoidal waves on top of each other in what's called a Fourier* series. You can make straight lines that slope up and down, you can make sawtooth waves, you can even make exact square waves.”

This is Joe Gedge’s response to the question, on

*So how does all of this relate to music and pitch? Well, Mr. Jean-Baptiste Joseph Fourier (1768-1830) and his work with Spectrum helps us with this. Fourier’s analysis tore apart the Sine Wave and thus identified the various frequencies. His work investigated the spectrum of pitches and found the harmonic content therein, or the ‘fingerprint’ of pitch.

Tying in with this fingerprint, we can then correlate pitches to a series governed by ratio. The Harmonic Series ratio is 1 : 2 : 3 : 4 : 5 : 6.

We know that our tuning note of “A” is considered to be A440 pitch, which means that the sound is vibrating at 440 cycles per second or 440 Herz.

If we therefore start at the lowest A, which would be A110, we then multiply it by 2 we arrive at A220, a 2:1 ratio; and we are given the Octave.

When we start with A110 and multiply by 3, we are given E330, or 3:2 and this is the Perfect 5th.
A multiple of 4 gets us to A440 and now we have Perfect 4ths with a 4:3 ratio, and so on.

Here’s what the ratio looks like, relative to Sine Waves and actual Notes on a C-based progression, on the staff. It works starting on any note.

This is known as the Chord of Nature – each note that we add is an ‘overtone’ and these overtones can be found in natural sounds in these exact same intervalic or harmonic relationships. How cool is that?! Never before has there been more meaning to the phrase “It’s all relative”. 

Cooler still is to look at it through the lens of a Fibonacci spiral and associate to colours!

Now, relating to those colours and even more interesting is that each musical instrument has its own set of harmonics, which brings us to TIMBRE, an important part of the Perception of music.

Timbre is the quality of sound, and what makes A440 sound different on a flute than it does on a violin. For this we should be very thankful indeed! We are given the painter’s palate of music, mixing primary tonal material.

Once again I’m brought around to the voice, and how each voice is its owner’s unique vocal fingerprint. No two voices are the same. We can use our voices to paint in different colours and therefore we use many descriptive words to help a singer find these sounds, or feelings of sounds. Some descriptors would be rich versus thin, or bright versus dark, warm or cold, and in particular ‘round’ is a very good descriptor. In making our sound round, we can then add varying degrees of colour or cover or darkness or brightness. I believe that round is the ‘key’…., but that achieving a nice, round sound is very challenging.

Noise is all a part of this too. For many musicians, ‘noise’ can be intolerable, since it consists of clusters of frequencies without Whole Integer Relations. There are different kinds of noise, based on filters, but all noise together is chaos, when all pitches are produced at once. The Acoustics industry has done work filtering frequencies for instance, to create ‘white noise’, which is a blend of sound that is piped into the workplace to create an overarching hum, the purpose of which is to bring a little more acoustical privacy to conversations that are happening in the environment. Some believe that this is not necessary, because the building systems themselves, the equipment in our offices, and the chatter of voices already provides a white noise. I have found myself breathing an audible sigh of relief when the ‘sound masking’ is turned off at the end of the day!

Interference is considered to be part of Noise. An example given in class was the interference of a very close tone next to another, and how the two sounds together can seem to generate a beat or a shimmer, a ‘chorus effect’. It is essentially a micro-dissonance.

Resonance is a transfer of vibrational energy ~ it is a sympathetic vibration or coupling of a sound. A good example of this would how when a drum is sounded, the wave travels across the room and reaches a bell, which chimes on its sympathetic tone.

Resonance and vibration are what give sound its life and colour. The description of noise uses the words Envelope, Onset, Body, and Decay. Each tone is a life unto itself; a Birth, a Lifetime, and a Decay or death. Every part of our brain is in use when we listen to or perform music. It’s no wonder that music can bring so much life to us.