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The Fundamentals of Signal Processing - Part 4
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Harmonics are an interesting study. On a guitar, if you pick a single note, that note will have a fundamental frequency with various overtones. Feed that into an amplifier which then distorts that input, and you will get harmonic distortion in various odd or even multiples of the fundamental frequency. Exactly what kind of harmonic distortion will occur depends on the circuitry involved, how much gain is applied and what kind of components are in the signal chain. Generally speaking, signals that get distorted in tube gear will have different characteristics and the harmonic distortion will be different than that which is created by solid state devices such as transistors, diodes and opamps (this was discussed in a little more detail in Part 1 of this series). Below is an interactive Javascript Fourier Synthesizer created by G. Tranter which you can use to see the relationship between harmonics and waveforms. The sliders on the right add sine waves, and the ones on the left add cosine waves (these are sine waves that line up with each other at the peaks instead of the zero crossings). |
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The primary sound "color" of an instrument is determined by the strength of the first few harmonics. Each of the lower harmonics produces its own characteristic effect when it is dominant or it can modify the effect of another dominant harmonic if it is prominent. The lower harmonics are divided into two tonal groups: even and odd. The odd harmonics (third and fifth) produce a "stopped" or "covered" sound. The even harmonics (second, fourth, and sixth) produce "choral" or "singing" sounds. The second and third harmonics are the most important ones to consider when speaking about the quality of sound in guitar distortion tones, and how it compares with the tube sound. Musically, the second is an octave above the fundamental and is almost inaudible; yet it adds body to the sound, making it fuller. The third is the musical twelfth. It produces a sound many musicians refer to as "blanketed." Instead of making the tone fuller, a strong third actually gives the sound a "metallic" quality that gets more annoying in character as its amplitude (loudness) increases. A strong second with a strong third tends to open the "covered" effect. Adding the fourth and fifth to this changes the sound to an "open horn" like character. The higher harmonics, above the seventh, give the tone "edge" or "bite." Provided the edge is balanced to the basic musical tone, it tends to reinforce the fundamental, giving the sound a sharp attack quality. Many of the edge harmonics are musically unrelated pitches such as the seventh, ninth, and eleventh. Therefore, too much edge can produce a raspy dissonant quality. Since most people's ears seem to be very sensitive to the edge harmonics, controlling the amount of these harmonics is important if one wants a pleasant sounding distortion. As mentioned in Part 1 of this series, solid state devices generally produce a very strong third harmonic and many of the odd harmonics above that. There are very little even order harmonics to be found after the sound goes thru a solid state device such as a transistor or an opamp. JFETs and MOSFETs seem to be a little more tube-like in the quality of sound, which I suspect is due to more even order harmonics being present in the signal as a result of their very nature. I have yet to see any papers or data showing proof of this, but maybe one will appear one day to show the world what is going on in those types of devices. What is covered here is a very basic overview of harmonic distortion. For a much more in depth explanation of what is covered here in terms of how it affects guitar tone, check out the Distortion 101 page at the Blackstone Appliances website (which is where I got this cool java applet) and this more general Tubes vs Transistors article for more info on the characteristic differences in harmonics between tubes and transistors. |