Mixing & Signal Processing: Making Room for Every Sound

Take any song you love and listen for the voice. It sits in front of the guitars, though the guitars are louder when you measure them. The kick and the bass share the bottom of the sound without turning to mud. The snare has a short echo of a room that never existed. Somebody made those decisions, a track at a time, and the decisions are called a mix.

Nothing in a mix is magic. The recorded tracks are lists of numbers (Digital Audio & the DAW, 36/62), and mixing is a handful of operations on them: multiply by a gain, add copies, delay a copy, filter some frequencies, turn the loud parts down. A mixing engineer is a person who has heard each operation so often that they can predict the result before they reach for the knob. This piece builds the five operations, with real arithmetic, so you can hear and see what they do.

EQ: every filter is a shape on a frequency plot

An equaliser changes how loud each frequency is. Draw the result as a curve, with frequency across (spaced evenly in octaves, so each doubling is the same width) and gain up and down in decibels. Every EQ move is one of a few shapes. A peak (or bell) lifts or cuts a band around a centre frequency. A shelf lifts or cuts everything above (high shelf) or below (low shelf) a corner. A high-pass filter removes everything below a corner, which clears rumble and handling noise from a vocal. The Q of a peak sets how narrow it is: high Q is a scalpel, low Q a broad brush.

These shapes have a precise recipe. The standard one for digital EQ is the "Audio EQ Cookbook" by Robert Bristow-Johnson, which gives five numbers for each filter from three choices: centre frequency, gain and Q. For a peak, with A set by the gain, the sample rate and the frequency fix an angle, and the five numbers follow. A filter built this way is a biquad, the building block of nearly every EQ plug-in and of the filters in your browser, and the same maths appears in Signals & Systems (34/37).

Here is the number that surprises beginners. A +6 dB peak at 1 kHz with Q = 1 is +6 dB only at its centre. One octave away, at 500 Hz and 2 kHz, it is only +1.9 dB, and two octaves away just +0.4 dB. Narrow it to Q = 4 and the same boost is +0.2 dB at 500 Hz. Build your own below and hear it on a hiss that has equal energy in each octave.

Without JavaScript: a +6 dB, Q = 1 bell at 1 kHz gives +6.0 dB at 1 kHz, +1.9 dB at 500 Hz and 2 kHz, and +0.4 dB at 250 Hz and 4 kHz. A high-pass at 80 Hz is 3 dB down at 80 Hz, 12 dB down at 40 Hz and 0.3 dB down at 160 Hz.

Why would you cut at all? Because of masking. When two sounds have energy in the same range, the louder one hides the quieter. The ear sorts sound into overlapping bands, each about one "equivalent rectangular bandwidth" wide, from a formula by Glasberg and Moore (1990): about 36 Hz at 100 Hz, 133 Hz at 1 kHz and 1,100 Hz at 10 kHz. A kick drum at 60 Hz and a bass note at 80 Hz sit inside one such band at the bottom, so they fight for it. The usual fix is not to boost one but to carve the other: a dip in the bass where the kick lives, a dip in the guitars where the voice lives. Cuts also cost nothing in level, while a boost of 6 dB leaves the track 6 dB closer to clipping.

Range	What engineers often listen for
50–100 Hz	weight, thump of kick and bass
200–400 Hz	"mud" or boxiness when too much
1–4 kHz	presence and clarity; harshness when too much (the ear is most sensitive here)
5–8 kHz	sibilance on voices; cymbal bite
10 kHz and up	"air" and sparkle

These are habits, not laws: every voice and room is different, and engineers disagree on the names. Every analogue-style EQ also shifts the timing of frequencies a little, called phase shift; "linear-phase" EQs avoid that at the price of delay and a faint pre-ring.

Compression: a hand on the fader that never gets tired

A singer whispers one line and belts the next. If you set the fader for the whisper, the belt jumps out; set it for the belt and the whisper vanishes. A compressor is an automatic hand on that fader: when the level goes above a threshold, it turns the signal down by an amount set by the ratio. At 4:1, every 4 dB over the threshold comes out as 1 dB over. The knee softens the corner at the threshold. Make-up gain then turns the whole thing back up, because a compressor only ever turns things down.

The other half is time. Attack says how fast the gain falls once the signal passes the threshold, release how fast it climbs back. The tutorial by Giannoulis, Massberg and Reiss (2012) lays out the standard digital design: first the static curve above, then a smoother that moves the gain reduction toward its target with one time constant for attack and one for release. The earlier piece (35/73) shows the curve and the sound. This one looks at what the compressor is doing to the gain over time, which is how an engineer thinks about it.

Try one thing below: set the attack to 1 ms, then 100 ms. A fast attack catches the start of each note and the loudest and softest notes end up almost level; a slow attack lets each note's first moment through, so the notes keep their punch and their differences. Neither is wrong. It is the choice between squeezing a performance and shaping it.

Without JavaScript: on the vocal phrases at threshold −24 dB, ratio 4, knee 6, attack 10 ms and release 200 ms, the gain falls by up to 12.4 dB and the gap between the loudest and softest note shrinks from 11.9 to 9.1 dB. With a 1 ms attack the gap shrinks to 3.5 dB; with 100 ms it is 11.1 dB.

Two relatives are worth knowing. A gate or expander does the reverse below a threshold: it turns quiet sounds down further, which removes bleed from a drum microphone between hits. A compressor whose detector listens to a different signal (a "side-chain") lets the kick duck the bass for a moment, or lets a radio presenter's voice duck the music. And the "wet share" slider is parallel compression: keep the original and blend in a heavily squashed copy, so the quiet details come up while the peaks stay alive. Watch the gain trace: at 50% the gain swings far less than at 100%, though the loud-to-soft range only narrows a little.

Delay and reverb: time makes space

A sound with no echo of any room sounds like it is inside your head. Space is made of copies that arrive late. Two tools make them. A delay returns the sound once or several times, after a time you choose. A reverb returns thousands of copies, so dense they blur into a tail. The tail's key number is RT60, the time it takes to fall by 60 dB; in practice it is read off a shorter fall of 20 or 30 dB and extended. Another is pre-delay, the gap between the dry sound and the start of the reverb: a gap of a few tens of milliseconds keeps the words clear before the room arrives.

Delay times that follow the song's tempo feel in time; ones that don't, smear. At a tempo of B beats per minute a quarter note lasts 60,000 ÷ B ms; an eighth is half of that, and a dotted eighth is three quarters of a quarter note. At 120 BPM those are 500, 250 and 375 ms. Reverb has a tempo problem too: a tail that has not faded when the next beat arrives piles up on it. Try it.

Without JavaScript: at 100 BPM a beat is 600 ms; with 20 ms of pre-delay and an RT60 of 1.8 s the tail has fallen only 19 dB when the next beat lands.

Now the other end of the time scale. Take a sound and add a copy of it after a very short delay. For delays under about 1 to 2 ms the ear hears one sound that sits between the two places. Past that, in what Wallach and colleagues called the precedence effect, the ear fuses the pair and puts the image where the first arrival came from. Helmut Haas described the same thing in his doctoral work (1949, published 1951): for delays up to roughly 40 ms on complex sounds, the later copy adds fullness and width but does not pull the image away. The limits depend on the sound: clicks separate sooner than sustained notes, and the echo threshold is often put near 50 ms for speech and near 100 ms for music. Engineers use it to widen a mono guitar by putting a 15 to 25 ms copy in the other speaker.

Panning: the middle should not be louder

To place a sound between the speakers you play it from both at different levels. The obvious rule is a straight swap: hard left means all in the left, centre means half in each. That rule has a flaw. Sound power goes with the square of amplitude, so half in each channel is only half the power in total: a track moving from the edge to the middle gets 3 dB quieter. The fix is the constant-power law: the two gains are the cosine and sine of an angle, so the squares always add to one. The cost is at the other end: if the two channels are later summed to mono, the centre is now 3 dB too loud.

So there is no free law. Mixing software lets you choose how much the centre drops: −3 dB if the result stays in stereo, −6 dB if it may be summed to mono (a phone speaker, a club's mono bass, a radio), and −4.5 dB as a compromise between the two. The meters below show the trade.

Without JavaScript: at the centre the −6 dB law has each side at −6.0 dB, total power −3.0 dB and mono sum 0 dB; the −3 dB law has each side at −3.0, power 0 dB and mono sum +3.0 dB; the −4.5 dB law has −4.5, −1.5 and +1.5 dB.

Summing: forty faders do not add like forty numbers

At the end of the mix, every track is added into one stereo bus. Turn up ten identical tracks by 10 dB each and the sum is not 100 dB; decibels are logarithms. What matters is whether the tracks are correlated, that is, whether they rise and fall together. Two different instruments are nearly uncorrelated: their peaks rarely coincide, so their powers add, and the sum of N equal tracks is 10·log₁₀ N dB above one of them. Two identical tracks (a doubled copy, or the same source on two microphones) add their amplitudes, and the sum is 20·log₁₀ N dB higher.

Sixteen unrelated tracks at −18 dBFS each (a sensible level to record at; see Digital Audio & the DAW, 36/62) give a bus about 12 dB higher, near −6 dBFS. Make the same tracks identical and it would be 24 dB higher, which cannot fit. This is why engineers watch gain staging: every fader and plug-in is a multiplication, and the bus is the place where they all land. Modern mixing software works internally in floating point, so the bus will not clip in the middle of the mix, but the final output will.

Without JavaScript: 16 equal unrelated tracks sum to about +12.0 dB above one; 16 identical ones to +24.1 dB; with half in common, +21.3 dB.

Reference tracks and translation: checking the mix against the world

After hours with the same song your ears adapt, and a mix that sounded balanced at midnight sounds dull at noon. The answer is a reference track: a finished record you trust, in a similar style, switched in at the same loudness as your mix. Level matters because we hear louder as better; a difference of a decibel or so is enough to tip the judgement, and it is the oldest trap in the studio. Matching the level removes the trap, and the comparison shows what your mix is missing: low end, width, vocal level.

The second test is translation: does the mix hold up away from your speakers? Engineers play it on a phone, in earbuds, in a car, in mono and quietly. Some keep a small, unflattering speaker for this. The Yamaha NS-10, introduced in 1978 as a home loudspeaker, became a studio fixture because a mix that sounded right on its harsh midrange tended to sound right elsewhere. If the bass disappears on the phone, the part you hear is the harmonics, not the fundamental, and a little of it needs adding up the spectrum.

Check	What it catches
Mono	parts that cancel when the sides are summed (wide stereo effects, out-of-phase microphones)
Quiet	whether the balance still works at conversation level, where bass and treble are less audible
Phone or earbuds	vocal level and bass that only exists below what a small speaker can make
Reference at matched level	tone, width, and loudness of parts against a finished record

Notice that none of this is measuring. It is comparing, which is the thread through the whole subject. EQ, compression, delay and panning are all tools; the mix lives in the listening that decides when to stop.

What a graduate just sees

• An EQ move is a shape on a curve; a +6 dB bell loses most of its effect two octaves from its centre.
• A mix is mostly taking away: two sounds in one band hide each other, and a cut in one is better than a boost in the other.
• A compressor turns the loud parts down by a ratio, then the make-up gain hides it. A fast attack squeezes; a slow one shapes.
• Delay times belong to the tempo, and reverb tails must fade before the next beat or they muddy it.
• A copy under about 40 ms is heard as width, not as an echo, and the image stays where the first arrival was.
• Pan laws trade stereo balance against mono compatibility; the centre is either quieter, or louder when summed.
• Decibels add by power for unrelated sounds and by amplitude for identical ones: 3 dB or 6 dB per doubling.
• Louder sounds better; compare at matched level, and check the mix in mono, on a phone and quietly.

Where it shows up next

• Mastering & Loudness (36/64): the finished mix goes through the same tools, applied lightly to the whole, and then its level is measured against streaming targets.
• Live Sound Reinforcement (36/66): the same EQ finds and cuts the frequency where a microphone starts to ring, and delays line up speakers at different distances.
• Sound for Film, TV & Games (36/67): dialogue is compressed and equalised to sit over music and effects, and reverb places each voice in a room that matches the picture.
• Producing Records & the Music Business (36/70): a producer needs to say what is wrong with a mix in words an engineer can act on.
• In the world: the loudness of a podcast, the voice on a phone call, the tuning of your car's speakers and the "vocal enhance" button on a TV all use these five tools.

If you want to go deeper

• 📘 Textbook. Roey Izhaki, Mixing Audio: Concepts, Practices, and Tools (Routledge, 3rd edition, 2017), a thorough treatment of every tool in this piece; and David Miles Huber and Robert Runstein, Modern Recording Techniques (Routledge), the standard studio reference.
• 📘 Short and practical. Bobby Owsinski, The Mixing Engineer's Handbook (Cengage), a quick guide to workflow and technique; and Mike Senior, Mixing Secrets for the Small Studio (Routledge), written for people mixing at home.
• 📘 The maths. Robert Bristow-Johnson's Audio EQ Cookbook, the formulas behind the EQ curve above, free to read.
• 🌐 Free course. MIT OpenCourseWare 21M.380 Music and Technology: Recording Techniques and Audio Production (Fall 2016), with lecture notes and assignments.