Welcome back, the perfect pitch is made by the sine wave, one of nature’s perfect forms. The number of times that the sine wave oscillates per second, one period, one full cycle of its perfect rolling wave defines the pitch or musical note that we hear (audio of sine wave played through human audible spectrum). Cycle 440 times a second aka 440Hz and you get a perfect A on our musical scale. Somewhere around 200Hz, 200 times a second and you get approximately a human voice’s fundamental frequency. The fundamental frequency of a human voice (video of a human voice on an oscilloscope) is the frequency at which the glottis hums into the rest of the vocal cavity. And it is on this journey out of the chest and through the mouth that the glottal frequency is distorted and shaped by a whole orchestra of vocal chords and resonant cavities into a multitude of new frequencies and phases of these frequencies which make a syllable. And all this is done with only the energy imparted by the monotonic glottis. This process of frequency generation and shaping gives the human voice its rich tamber, and dynamic. The vocal box is amazing, it has the dynamism to generate words, and not only say words but sing words too. Singing a word involves superimposing a perfect pitch or sin wave on to a complex atonal spasm of waves which form a syllable. That is if you can sing well!
BUT perfect pitch ain’t all it’s cracked up to be, it’s actually pretty boring, pretty much the worst. No serious, a single solitary frequency playing out of an electro hi-fi stereo has nothing of interest to it, B-Land. On the other hand a note played by a synthesizer, a sawtooth or square-pulse wave now that has heart, richness and an attention grabbing quality. I digress into subjectivity, but really, think of the warmest, most bounce inducing, electronic crunchy bass in your favourite dance track and it likely has a sawtooth or a square pulse, here are a few examples: Benni Benassi Satisfaction, Body ROX, Yelle Safari Disco, Dead Prez Hip Hop , Snoop Doggy Dog, check ‘em out!
The sawtooth and square pulse wave works exactly like the sine wave, the number of full cycles it make every second, the number of time it repeats graphically from tip to tail every second defines the note one hears. Except for this time the wave is as far geometrically from nature's sine wave as we can possibly be. These synthesized shapes are all sharp and jagged, perfect corners at each inflection and a rigidly straight line run from peak to peak. Quite astounding that a sawtooth or square pulse can produce a note at all without a single trace of the smooth sine in its geometry. Well the truth is the sine wave is not entirely absent, really!
So my question to you is how does one generate such an unnatural shape? A shape as diametrically opposed from the perfect natural sine wave. Really how does one synthesize such a perfect triangle or square, so rigid and straight? Well the answer is not as easy as just making a straight line with an electronic circuit. Circuits are natural things and want to operate and draw natural shapes. Sometimes/most of the time they produce crazy and sketchy vibrational spasms like the human voice box, but sometimes with some crystal magic they can form perfectly rounded waves of golden symmetry. And that’s where the magic lies, humans can, with the help of crystals and a jolt of electricity, generate an almost perfect natural sine wave, as perfect as the crystal that bore them; so in this modern age 99.99999%, that's pretty damn perfect. And depending on the species of crystal it has its own soul note or frequency which it produces. Yes! humans can draw a perfect sine wave with electricity and crystals (more info on singing crystals), which mean we can play a perfect note out of a speaker, pretty fucking cool eh!? And as we saw earlier if you can draw the shape on an oscilloscope (the monitoring/measurement tool that gave us the tv!) you can play it on a speaker.
Back to the question, how do you synthesize a sawtooth or a square wave? Well let me show you a graphic trick . Look as we superimpose harmonic waves one on top of each other, the blue line is at 1Hz and the green line is at 3Hz and 1/3 the amplitude of the blue. The red line which is the sum of the blue and green starting to take square shape. Check this website for an interactive animation, it's pretty neat!
Look as we add more and more harmonic frequencies, A-Maze-Ing :-)
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| The making of a sqaure-pulse. Summing wave at frequncies that are at multiples of eachother we begin to get a sharp square shape! |
The same trick applies for a sawtooth wave
Perfectly straight lines generated by perfectly round ones, now that’s unexpected! So despite the seemingly simple form of square-wave and sawtooth they actually contains many complex waves, many sounds made invisible by superposition and summing, and thus cancellation. Though they may be invisible to the eye they are not to invisible to the ear. If you play a sawtooth or square wave through the natural, physical and honest system which is a loudspeaker, you can still hear all those higher harmonics hidden in the dark corners of the square and sawtooth. You hear the corners and rising edges as the high pitched frequencies they are, you hear them as fuzzy noise as high as the ear can hear. still there is a powerful fundamental frequency which emerges, the graphical frequency of the shape which is also the frequency of the first harmonic, the lowest frequency wave of the sum. So now I suggest watching this video which shows the high frequency content filtered out of a sawtooth and a square waves. Perhaps a new understanding of the term 'high-frequency content' has developed for you? So as a parting thought I want to bridge this concept of wave super position to a phenomenon know as a wave packet. Wave packets are a way of visualizing fundamental particles like electrons, quarks and bosons. Here are some images of wave packets being formed by our graphical trick!
The more frequencies you sum the tighter the packet becomes and the more certain you become of its position. However this comes at the expense of the knowledge of what frequencies are included and hence the energy of the packet. From music to fundamental physics, frequency theory is a fundamental part of our Universe, use your new found knowledge wisely:)
Alectric_OFF
