A Single Note

What is a note?

 

A note is actually a multidimensional thing.  It has both pitch and duration.

It’s like how a vector has direction, and magnitude.  The magnitude might be zero, but it’s there.

In the case of a note, the pitch might be zero but the note still has duration as the vector maintains its direction.

The duration of a note might be forever, but it cannot be without duration at all.  The instance of a note duration with zero pitch is called a rest-note, or simply a “rest.”

Sound, as we hear it, is about the exchange of kinetic energy.  Some sound “source” jostles the air at a sufficient velocity and the jostling is detected by tiny hairs in our ears which transduces the kinetic energy into electrical impulse, interpreted via nerves by our cerebral cortex.

I believe the use of the word “note,” in any language, puts the sound in question squarely into a musical context.  Described musically, the sound could quite possibly be considerted “out of tune.”

We tune, musically, to a thing called “A 440.”  This is short for “440 Hertz(Hz), which is called ‘A.'”  Our society has simply chosen to call the frequency of 440 Hz  “A,” and everything else is tuned from that pitch.

What is pitch? What is Hertz? What is frequency?

These terms are related.  When a sound source, such as a guitar string, vibrates it jostles the air around it.  The rippling waves created by these jostlings propagate longitudinally through the air.  If you can imagine a transverse wave vibrating and oscillating through the air in three dimensional spheres of undulating positive and negative pressure then you start to get the picture.  Oh yeah, and the oscillations can happen many times per second.  For human hearing we’re talking 20 vibrations per second minimum, to be heard as sound.  We as humans can detect very many more vibrations per second, however.  The top end of human hearing is 20,000 oscillations per second.  I try to imagine visually the many wrigglings that the longitudinal wave worm would have to perform per second to create the effect of even 8,000 oscillations.  It’s difficult.

Hertz was a guy.  The measure of oscillations that pass through a given point in a second at the speed of sound is named after him.  The more Hertz (Hz), the higher the pitch.  The exact number of oscillations per second in Hertz is referred to as a sound’s frequency.

Waves can take on different forms, but there is a fundamental wave form against which all others are compared.  It is called a sine wave.

This wave form is the building block.

A guitar string playing a note seems like a single sound, but it’s actually lots of sine waves at different frequencies sounding all at once.

Most sound sources are not capable of reproducing a perfect sine wave.  Things like animals, cars, humans, instruments create what are called complex waveforms.  They’re complex because they’re made up of multiple sine waves sounding at once.  The waves interfere with one another both constructively and destructively to create a sound signature that we perceive in amalgam.

To imagine this, ask yourself “how can two people sing the same note, but sound different from one another at the same time?”

The answer is that a single note, unless it’s a sine wave, is not just a single not but the combination of many sine waves sounding simultaneously.  When a person sings a note a whole series of notes sound in resonance with the lowest, fundamental note.  The lowest, loudest sounding note is called the “fundamental” and is what we would call the pitch of the note being sung.  However, every multiple of that fundamental frequency actually sounds, just much more quietly, simultaneously with the fundamental.  Although the higher multiples of the fundamental frequencies are much quieter they still impact the overall sound enough to create an audible signature.  This series sounding in harmony with fundamental is eponymously called the “harmonic series.”  The relative volumes of the upper harmonics as compared to the fundamental is what gives a sound it’s recognizeable signature; it’s timbre.

 

Read more at hobbylocal.com.

About Kiv

art - math - music

07. January 2012 by Kiv
Categories: Math, Music | Tags: , , , , , , , , , , , , , , , , , , | 2 comments

Comments (2)

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