Thursday, July 16, 2009

The Nuances of Timbre

There is a popular saying that usually comes up at least once when anyone is discussing anything related to the recording or reproduction of music: "Garbage in equals garbage out."

In other words, no matter what type of processing or sweetening occurs (and no matter how expensive or vibey any one piece of gear is that the audio passes through), the output will always retain something of the fundamental character of the input signal.

High-fidelity stereo enthusiasts and recordists both understand this (though the latter works tirelessly to contradict it as much as possible), but electric guitarists often seek miracles from the knobs on their equipment. It's not uncommon to hear ill-informed statements such as: "Any subtle difference between cheap thing X and expensive thing Y can be compensated for with EQ on the amp." Substitute "pickups," "wood," "strings," or virtually anything else (including the amp itself) for "thing" in the statement above, and you have a statement which has probably been made on an internet forum somewhere. I contend that this manner of thinking is fundamentally misguided as it places too much burden on something that influences but one of several factors that shape the timbre, or sound, coming from an instrument or setup.

To explain why, it helps to understand what timbre (often called "tone" by guitarists) actually is.

Timbre is influenced by three main factors: Overtone content, transient envelope, and formants. Let's discuss them one at a time.
  • Overtone content refers to frequencies that are present which are mathematically and harmonically related to the actual pitches being played. Pure sine waves excepted, all musical tones contain various overtones. Overtones are frequencies which are harmonically related to the fundamental frequency and proceed in a very specific order called the overtone series. Which overtones are present, and in what proportions relative to one another and to the fundamental, is instrumental in determining the timbre of an instrument or setup. Fourier's Theorem states that all periodic waveforms can be expressed as the sum of multiple sine waves. Here is a cool java applet that allows you to experiment with the effect of altering the ratios of harmonic overtones, and also to examine the overtone content present in various popular waveforms such as square, sawtooth, etc.
  • Transient envelope concerns the question of "what happens at the very beginning of the note?" With most instruments, there is an instantaneous burst of energy at the very beginning of a tone, often with a strong noise component, that is instrumental in determining our perception of its timbre. The precise nature of this transient is very important to the manner in which our ear parses the tone. A saxophone note with the transient removed would scarcely sound like a saxophone anymore at all-- in fact, it might be confused for a violoncello, or something else entirely.
  • Formants are frequencies present in the sound which are not directly correlated with the pitches being played. In other words, if a system has a formant at 400 Hz, it may be present whether you play a Bb, an F#, or any other tone. Formants can result from acoustic resonances such as standing waves in cabinets, rooms, or sounding chambers of instruments, or from other things. The best illustration of the effect of manipulating formants is what happens when an audio tape is played back at double speed. Vocalists, rather than sounding like humans with a higher vocal range, sound like "Alvin and the Chipmunks." This is caused by the transposition of formants to an unrealistically high range--which, of course, also accounts for both the peculiar guitar sound in Les Paul's "Lover" and the decidedly un-pianolike piano solo in the Beatles' "In My Life."
An EQ filter, particularly the type found on the average guitar amplifier or mixing console, can simply boost or attenuate spectral content which is already present. If a particular overtone or formant is present, it may be boosted or cut (usually along with several surrounding frequencies). However, an equalizer is not designed to add overtones or formants that were never in the source material to begin with, and it certainly cannot alter transient envelope.

Furthermore, hardware EQ filters are imperfect and imprecise devices. While it is beyond the scope of this article to explain in depth, suffice it to say that all hardware equalizers alter the phase of certain components of the input signal. In other words, EQ filters will delay certain components of a complex waveform by fractions of a cycle with respect to other elements, which leads to very unnatural sounds at extremes of equalization. However, even if this were not the case, trying to sculpt fine nuances of timbre out of shelving or peaking equalizers of the design typically found in guitar amplifiers would be analogous to trimming your fingernails with a chain saw.

For these reasons, their capability as shapers of timbre or as compensators for timbral deficiency is actually severely limited.

Describing sounds verbally can be elusive. There are many adjectives used ("punchy," "bright," "warm," "dark," "thin," "dull," "smoky," and "fat," etc.) which can certainly connote certain audible characteristics. This is all well and good, but it pays to beware of overly reductionist thinking.

If our ear perceives something as "bright," that does not always mean "more treble." It might mean sharp, pronounced transients that have been faithfully reproduced. "Fat" doesn't necessarily mean "more bass." It might mean "a modified/reduced transient envelope," such as what occurs when tube or tape saturation has brought up the level of a note's sustain relative to the level of its transient. If something is "boxy," the solution isn't always necessarily to turn the midrange knob all the way down. Sometimes the solution is to try a different speaker cabinet whose formants might be different, or even a different room--rooms can have formants, too!

Simply and anecdotally put, If one distortion pedal sounds 'warmer' than another as a result of having more pronounced second-harmonic overtone content, then this cannot be imitated by turning up the 'bass' knob on an amplifier. If one speaker sounds 'brighter' than another due to an ability to reproduce transients with greater fidelity, then all the "treble" in the world isn't going to imitate it.

When concerned about shaping the sound of your instrument or rig, it pays to be informed-- consider the role of each component of timbre in the equation. Don't always assume that filtering alone will get you there. In some ways, EQ filters are similar to light filters. A red gel on a spotlight might create a different atmosphere around the performer than if he was under white light alone, and it may even minimize or highlight some colors on his wardrobe, but it will not change his hairstyle or the shape of his face. Similarly, twisting the knobs of phase-mangling EQ filters on a guitar amplifier will create a perceptible difference in timbre, but it will not change the fundamental sound. For that, you have to go straight to the source-- garbage in equals garbage out, after all.

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