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Inside Music:
"A Musical Approach to Equalization"
by Richard Middleton

First published in Victory Review, June 2001.

More and more musicians are doing their own recording and mixing these days, and many soon discover there's more to producing a good recording than just capturing a good performance. Of the many technical issues that come up, one that can prove particularly frustrating is learning how to use equalization (EQ) effectively. EQ can be confusing because it reduces music to seemingly abstract numbers and "frequencies," with no apparent musical frame of reference. Let's see if we can demystify EQ a little bit by taking a more musical approach.

First, some definitions. A sound is a vibration, and "frequency" is the speed of that vibration. We measure frequency in cycles per second, or Hertz (Hz). 100 Hz means "100 cycles per second." For higher frequencies, we use the term kiloHertz (or kHz), which means "1,000 Hz." 2.5 kHz means "2,500 Hz." The range of human hearing is roughly 16 Hz to 20 kHz (for most adults, the upper limit is about 16 kHz).

Now, a few Useful Facts:

  1. Every musical tone has its own "fundamental" frequency, which determines its pitch. For example, middle "C" is 261.6 Hz; the "A" above that is 440 Hz; the lowest tone on a bass is low "E," or 41.2 Hz; and so on.

  2. The higher the pitch, the higher the frequency: 200 Hz is a higher pitch than 100 Hz.

  3. Every musical tone also contains other frequencies which are much less prominent than the fundamental but contribute to the overall sound; these are called "harmonics" or "overtones," and are always higher than the fundamental.

  4. If you double the fundamental frequency of a tone, you go one octave higher. For example, 880 Hz is an octave above 440 Hz . The reverse is also true: cut the frequency in half and you go one octave lower. 220 Hz is an octave below 440 Hz.

  5. Any musical interval (e.g. octave, fifth, fourth, etc.) can be viewed as a ratio between two frequencies. For example, since an octave is a doubling of frequency, its ratio is two to one, or 2:1. A perfect fifth is 3:2, therefore 300 Hz is a fifth above 200 Hz; a perfect fourth is 4:3, therefore 800 Hz is a fourth above 600 Hz. At the low end of the frequency spectrum, a small increase in frequency can produce a large musical interval, but at higher frequencies, a much greater increase in frequency is required to produce the same interval. In other words, the interval ratio remains constant, but the corresponding difference in frequency gets larger the higher you go. (More on this below.)

Let's see how these Useful Facts relate to EQ.

Many people use EQ a bit like the "treble" and "bass" controls on their stereos. If the music sounds thin, they turn up the low end. If the vocals have too many sizzling "esses," they turn down the high end. This approach can work sometimes, but it often creates more problems than it solves, due to two mistakes that novices often make:

- First, they use too much frequency boosting, when cutting would be more effective. Most professional engineers use EQ primarily to reduce or remove unwanted frequencies that are cluttering the mix; they work by subtraction rather than addition. For a single track, they may cut quite a few frequencies to shape the sound. They rely very little on boosting, and only when a little added clarity or color is needed. This is because too much boost can lead to unwanted noise and phase problems, and make your mix sound less natural. When you find yourself using lots of boost, try thinking "backwards" for a moment: instead of boosting something, see if you can get what you want by cutting something else.

- The second common mistake is to apply EQ across broad frequency ranges rather than targeting specific frequencies. Most professional engineers use very narrow frequency bands, specifically cutting problem frequencies but leaving adjacent frequencies relatively unaffected. This requires more precise listening and EQ adjustment, and numerous, selectable bands of EQ, but it produces a more natural sound. In order to make such narrow, specific frequency cuts, you need to be able to hear which frequencies are causing problems. Over time, trial and error will teach you a lot, but you can eliminate some of the guesswork if you learn to correlate frequencies with musical pitches. Which brings us back to our Useful Facts.

Remember, each pitch has a fundamental frequency: if you can identify the actual pitch of a problem tone, you can EQ that frequency specifically. If there's a certain bass note that sounds ugly, rather than turning down the entire low end, identify the pitch and use a narrow band of EQ to cut that specific frequency. If a guitar track sounds nasal or boxy, don't just cut the midrange; listen closely for the actual pitch(es) at fault and EQ those frequencies.

Sometimes it's not the fundamental of a tone that's causing trouble, but one of its overtones. If EQ-ing the fundamental doesn't work, try the first overtone, which is double the fundamental, or 2:1; the next two overtones are 3:1 and 4:1. (For more on overtones, see the book list below.)

If two instruments clash, give each a different combination of EQ cuts (and/or boosts... but sparingly), focusing the tonal "peaks and valleys" for each instrument in different frequency ranges.

As we learned above, interval relationships are frequency ratios, i.e. they're proportional rather than linear. In practical terms, this means that most of the notes we play (and many lower-order harmonics) are relatively low in the frequency spectrum. In fact, the highest note on a piano (or just about any instrument, for that matter) is only 4.186 kHz, well below our audible limit of 16 kHz.

So what about the higher frequencies? They contain all the higher-order harmonics, which give music its presence, clarity and brilliance. Here also are vocal sibilance (around 6.5-9.5 kHz), tape hiss, and other "sizzly" sounds. The highest frequencies, above 9-10 kHz or so, provide a sense of airiness and spaciousness. Generally speaking, too much energy in the high end makes the music harsh and brittle; too little makes it feel dull and claustrophobic.

The selective EQ process I've been describing is easiest to accomplish in studios with lots of EQ's, or in computer-based recording, where software plug-ins give you virtually unlimited bands of EQ and precise control. But even with very little equipment, if you know the frequency you're going for, EQ becomes much easier.

In order to do accurate pitch-frequency correlation, you don't need a genius IQ or a strobo-tuner, you just need a chart like the one below. Values are in Hz, rounded to the nearest .01 Hz.

A: 27.5, 55 *, 110 **, 220, 440, 1760, 3520, 7040, 14080

A#: 29.14, 58.27, 116.54, 233.08, 466.16, 932.33, 1864.7, 3729.3, 7458.6, 14907.2

B: 30.87, 61.74, 123.47, 246.94, 493.88, 987.77, 1975.5, 3951.1, 7902.2, 15804.4

C: 16.35, 32.7, 65.4, 130.8, 261.63 ***, 523.25, 1046.5, 2093, 4186, 8372, 16744

C#: 17.03, 34.05, 69.3, 138.59, 277.18, 554.37, 1108.7, 2217.5, 4435, 8870, 17740

D: 36.71, 73.42, 146.83, 293.66, 587.33, 1174.7, 2349.3, 5886.6, 11773.2

D#: 18.36, 38.89, 77.78, 155.56, 311.13, 622.25, 1244.5, 2489, 4978, 9956, 19912

E: 20.6, 41.20, 82.4, 164.81, 329.63, 659.26, 1318.5, 2637, 5274, 10548

F: 21.83, 43.65, 87.3, 174.61, 349.23, 698.46, 1396.9, 2793.8, 5587.6, 11175.2

F#: 23.13, 46.25, 92.5, 185, 369.99, 739.99, 1480, 2960, 5920, 11840

G: 24.5, 48.99, 97.99, 196, 392, 783.99, 1568, 3136, 6272, 12544

G#: 25.97, 51.93, 103.83, 207.65, 415.3, 830.61, 1661.2, 3322.4, 6644.8, 13289.6

* "A" string on bass
** "A" string on guitar
*** Middle C

Of course, there's a lot more to learn about EQ. The best teacher is experience, but books can help too, such as The Mixing Engineer's Handbook by Bobby Owsinski, and Creative Recording I: Effects & Processors by Paul White. A useful acoustics reference is The Master Handbook of Acoustics by F. Alton Everest. Enjoy!

© Copyright 2001 by Richard Middleton.
All rights reserved.

Richard Middleton is a musician, songwriter, producer, educator, and writer based in Seattle. He is the author of "Rhythm Guitar Secrets" (Countersine), and his music writing has also appeared in Smithsonian magazine, Victory Review, and SingOut! magazine.

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