Your phone plays a song and the singer sounds close enough to touch. Nobody was ever that close. The voice was caught by a microphone a hand's width away, turned into 48,000 numbers a second, shaped by an equaliser, squeezed by a compressor, placed in a fake room and then made louder by a mastering engineer so that it would not sound quiet next to the song before it. Not one of those steps is "natural", and every one of them is a choice.
Music technology and production teaches those choices at the level of the signal: what is a sample, what does a filter do to a sound, what is a compressor really doing, and how loud is too loud for the music and for your ears. This piece builds a small version of each tool so you can hear it. It plays real synthesised sound in your browser; keep your volume low, start with Play and end with Stop. Everything also shows its numbers, so it works with sound off. The hearing section describes risks and is not medical advice.
A microphone makes a voltage that wobbles like the air pressure. A converter measures that voltage at evenly spaced instants, the sample rate, and writes each measurement as a number with a fixed number of steps, the bit depth. That is all digital audio is: a long list of measurements. The theorem that makes it work, usually credited to Nyquist and Shannon (Shannon stated it in 1948 and 1949, and Kotelnikov proved it independently in 1933), says that sampling faster than twice the highest frequency in the signal captures it completely.
Hearing tops out around 20,000 Hz in young listeners, so 2 × 20,000 = 40,000 plus room for a filter gives the CD's 44,100 samples a second; 48,000 is common in video and many studios. Sample too slowly and the frequencies above half the rate do not vanish: they come back as false lower tones, aliasing.
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Dots are the samples. The red curve is the sine that passes through them, which is the tone a converter without a filter in front would record. Tones above 8 kHz aren't played (some are painful); the alias is. At 24 kHz and 8 kHz sampling the samples land on a whole number of cycles and the "alias" is 0 Hz: silence.
Set 8 kHz and 5,000 Hz: the dots sit on a 5,000 Hz wave, but the red curve says 3,000 Hz (8,000 − 5,000). Real converters put a steep filter in front so that nothing above half the rate gets in, and the problem moves to the mathematics inside plug-ins and synths, which can create overtones past the limit and must be built to avoid them.
Bit depth sets the other limit: the quietest detail you can store before it is lost in the steps. Each added bit halves the step size, which lowers the "quantisation noise" floor by about 6 dB. A full-scale sine in N bits has a theoretical signal-to-noise ratio of roughly 6.02·N + 1.76 dB: 98 dB at 16 bits, 146 dB at 24.
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The loop is a two-second drum-and-chord pattern generated in code (illustrative, no recording). Each sample is rounded to the nearest of 2N levels with no dither, which is what makes the low-bit result harsh.
The decibel is a ratio on a log scale: 20·log₁₀ of an amplitude ratio. Double an amplitude and you add 6.02 dB; multiply it by ten and you add 20 dB. Sound spreading from a small source in open air falls with the inverse of the distance, so each doubling of distance loses about 6 dB, and a microphone three times farther away than another hears the source about 9.5 dB quieter.
That is the reason for the engineers' 3:1 rule for two microphones on one source: put the second at least three times as far from the source as the first, and its sound is about 10 dB lower and does little harm. Why does it matter? Sound reaches the farther microphone a little later, and when the two signals are added, some frequencies cancel. The delay is the extra distance divided by 343 m/s.
The result is a comb filter: a row of equally spaced notches, the sound hollow and phasey. At d = 0.5 m, τ = 1.46 ms and the first notch falls at 343 Hz, then again at 1,029, 1,715 Hz and so on.
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Noise (soft, filtered toward pink) is delayed and mixed with itself exactly as the formula says. Real rooms add reflections, so real combs are messier. Level 1 means the same level in both mics; 0 means mic 2 is off.
Play it with level 1 and slide the distance: the "phasing" sweep is the notches moving. Pull the level down to 0.3 and the comb shallows to a ripple: the response only swings between −3.1 dB and +2.3 dB (20·log₁₀ of 0.7 and of 1.3), which is why the 3:1 rule works. Comb filtering is also what you hear when a speaker and its reflection from a table top arrive together.
Early electronic instruments took the same idea as the vocal tract, a rich source through a filter, and made it a machine. An oscillator makes a harmonically rich wave (sawtooth, square, triangle); a low-pass filter removes the high partials above a cutoff; an amplifier shapes the loudness over time with an envelope. The standard envelope has four stages, ADSR: Attack (time to rise), Decay (time to fall to the sustain level), Sustain (the level held while the key is down) and Release (time to fade after the key is lifted). The Moog modular synthesisers of the 1960s worked this way, and the Minimoog (1970) put it into one portable box with three oscillators and a 24 dB-per-octave low-pass filter; that is the sound behind much of the electronic music that followed.
Hold a key (touch or click) to sustain; let go for the release.
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The curve is the low-pass magnitude from the formula; bars are the first 16 partials of a C3 note (130.8 Hz) before the envelope opens the filter, weighted 1/n for saw, odd 1/n for square, odd 1/n² for triangle, then multiplied by the filter. Cutoff is 100 Hz to 8 kHz on a log scale. Web Audio's low-pass takes resonance in decibels; the chart uses the same.
Four moves make most of the classic sounds. Turn the cutoff down: the sound goes dark and soft. Add resonance: the filter rings at its cutoff and the sound goes "wow". Give the envelope a few octaves of filter opening and a fast attack: each note starts bright and then closes, a pluck or a bass "bwow". Raise the attack to 800 ms and you have a pad, a sound that swells in.
Frequency modulation (FM) sounds odd until you try it: let one oscillator, the modulator, wobble the frequency of another, the carrier, hundreds of times a second. The result is not vibrato; it is a new spectrum with sidebands at the carrier frequency plus and minus whole multiples of the modulator frequency, whose strengths are Bessel functions of the modulation index I.
John Chowning developed the idea at Stanford from 1967; he published it in 1973, and Yamaha licensed it that year. The Yamaha DX7 (1983) made digital FM the sound of the decade's electric pianos and bells. Its great trick: two oscillators and one number (the index) give a bright-to-dark sound that follows a note's decay, which is hard to do in subtractive synthesis. A whole-number ratio of modulator to carrier gives sidebands on a harmonic series (a pitched, tonal result); a ratio like 1.41 gives sidebands that are not harmonic (a bell or a clang), the same inharmonic spectrum you met in bars.
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Sidebands are plotted from Bessel functions of the first kind computed in code (negative-frequency sidebands fold back, shown as positive). Their squares always add to 1, which the readout checks. Carson's rule of thumb for the width: 2·fm·(I + 1).
Sampling synthesis is the plainer idea: record a real sound and play it back from the keyboard. Play a recording faster and everything speeds up together: pitch, speed of the notes, and the spectral envelope. A voice sung at one pitch and played back a fifth higher sounds like a chipmunk, because its formants moved too. That is why sample libraries record instruments every few notes and switch between them, and why pitch-shifting software works to keep formants still.
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The "sample" is a synthetic "ah" at 150 Hz generated in code (formants 730 and 1,090 Hz), played through a playback-rate control. Everything scales by r = 2semitones/12: pitch, formants and speed up by r, length down by r.
MIDI carries no audio at all. It sends messages: which key, how hard, when. Dave Smith of Sequential Circuits and Ikutaro Kakehashi of Roland pushed the idea; the MIDI 1.0 specification was published in August 1983, and the two men received technical Grammy Awards for it in 2013. A "note on" message is three bytes: a status byte (the high nibble 9 means note on, the low nibble is the channel, 0 to 15), then the note number (60 is middle C in most software; some makers number the octaves differently) and a velocity from 0 to 127. The cable ran at 31,250 bits per second, and each byte costs 10 bits on the wire (start, 8 data, stop), so a note takes 0.96 ms. The longer standard, MIDI 2.0, was announced in 2019 and shown at NAMM in January 2020.
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Pick up to 6 notes. Velocity here sets loudness as (velocity/127)2 in power terms; how velocity maps to loudness is up to each instrument. 31,250 baud, 10 bits per byte. "Running status" is a real MIDI shortcut that skips repeated status bytes.
A ten-note chord is thirty bytes, 9.6 ms from first note to last, which is why early MIDI chords could sound very slightly spread. The deeper limit in modern studios is not the cable but the buffer in the digital audio workstation (DAW), the software that records, edits and mixes: audio is processed in blocks, and a block must fill before it can be handled. Tape editing meant cutting; digital editing is non-destructive. Digidesign's Pro Tools system, launched in 1991 (after its 1989 Sound Tools ancestor), helped make the computer the studio.
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Real interfaces add converter and driver delay on top. The echo plays a click and a second click one round trip later (two buffers). Where delay becomes noticeable depends on the player and the instrument; the 10 ms line is a common rule of thumb, not a law.
Mixing is balance, panning and shaping in frequency (equalisation) so that each part can be heard. The tool that most changes a mix's feel is the compressor: an automatic volume control. When the signal goes above a threshold, the compressor turns it down by a ratio: at 4:1, every 4 dB over the threshold comes out as 1 dB over. Attack sets how fast it reacts and release how fast it lets go. A soft knee eases into the bend. The usual static rule, with input level L, threshold T and ratio R above the knee, is:
Attack and release are where the character lives. A slow attack lets a drum's first instant through and pulls down what follows, which keeps the punch; a fast attack flattens the peak itself. A quick release lets the gain recover between hits, and a quiet pad under a loud kick is pulled down and swells back: the "pumping" that producers sometimes want and sometimes fight.
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The processor runs in your browser on a generated two-second loop (kick, hats and a chord pad, illustrative, not a recording): a peak detector, the static curve above and attack and release smoothing of the gain. "Match loudness" scales the result to the dry RMS (never past 0.95 peak) so that louder doesn't fool you into thinking it's better.
Press Dry and Compressed with Match loudness on, then try to hear what changed. With the defaults the kick is trimmed by 9.4 dB at most, and the crest factor, the gap between peak and average level, goes up from 13.3 dB to 18.7 dB: the 10 ms attack lets each kick's first moment through while the body of the sound is turned down. Drag the attack to 1 ms and the gain reduction deepens to 12.2 dB and the crest factor falls back to 15.9 dB. Turn Match off and the compressed version is simply quieter, which is the trap: a louder version nearly always sounds "better" at first, so a fair comparison must match the loudness. Mastering pushes the same idea to its limit, and the next section is what went wrong.
Mastering is the last pair of ears. The mastering engineer makes small corrections to balance and tone, makes the songs of an album sit together, sets the gaps between them and prepares the files for each format. It also includes setting the final level, and that is where the loudness war happened. Compact discs allowed a maximum level (0 dBFS), so the way to sound louder than the neighbouring song was to compress and clip so that the average level rose toward the ceiling. Chroniclers often point to Oasis's (What's the Story) Morning Glory? (1995), many of whose tracks averaged about −8 dBFS RMS, and to Metallica's Death Magnetic (2008), whose CD clipped so noticeably that fans compared it with a less-squashed version made for the game Guitar Hero. Not everyone reads the data the same way: a 2011 study by Deruty and Tardieu found that the crest factor fell between 1985 and 2010 but the loudness range stayed fairly constant, and argued that this does not prove a loss of musical dynamics, while Shepherd and Katz countered with peak-to-loudness measurements that show reduced dynamic range through the 1990s.
The fix came from measuring loudness the way ears hear it. LUFS (loudness units relative to full scale, from the ITU-R BS.1770 standard) filters the signal to mimic hearing, averages it over the whole track and ignores silence. A streaming service can then play every track at a common target: Spotify's default is −14 LUFS and Apple Music's is −16, with other services in between (these change; check each platform). European broadcasters work to the EBU R 128 recommendation, which uses −23 LUFS for programmes.
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Drive is applied to the same two-second loop through a soft clipper with a −1 dBFS ceiling. Loudness is BS.1770 K-weighting with 400 ms gated blocks (mono), computed in code. Services differ in whether they only turn loud tracks down or also turn quiet ones up; "After the service" applies the exact gain to reach the target, capped so the peak stays at or below 0 dBFS.
Raise the drive. Loudness climbs from about −22.6 to −9.9 LUFS, the peak sits at the ceiling and the crest factor collapses from 12.7 to 5.9 dB. Now compare "Master" with "After the service" at −14: past roughly 11 dB of drive the service has to turn the track down, and the squashing that was supposed to make it louder bought only a flatter, more distorted track at the same playback level. That is the practical end of the loudness war on streaming, though loudness is still fought over in broadcast, clubs and ads.
All of this sits on top of the ear, which does not grow back its sensory cells. The World Health Organization and the International Telecommunication Union's safe-listening standard (WHO–ITU H.870, 2019) uses an adult reference of 80 dB(A) for 40 hours a week, with each 3 dB increase halving the allowed time. The WHO's fact sheet (March 2026) notes that over a billion young adults are at risk of permanent, avoidable hearing loss from unsafe listening.
Illustrative arithmetic from the WHO–ITU reference, not a measurement or a diagnosis and not medical advice. Real exposure varies by moment, and phones' volume bars don't equal dB(A) at the ear; a measuring app or a device's own listening-health readout gives a rough check. Hearing-health questions belong with an audiologist or doctor.
At 85 dB for an hour a day, five days a week, the budget is 5 hours against 12.6 allowed, a 40% dose. At 100 dB the allowance is about 24 minutes a week, so a two-hour gig averaging 100 dB(A) at your ears is five times the weekly allowance. Musicians and producers sit in the middle of this: monitoring at 90+ dB all day spends the budget in an afternoon, which is why working engineers monitor quieter than a beginner expects, take breaks and wear musician's earplugs at loud rehearsals. Ringing or muffled hearing after a loud night is a warning, not a normal result.
Recorded music is a chain of measurable steps: sampling, shaping with filters and envelopes, compressing, balancing and levelling. Each can be heard by itself, and each has a limit (half the sample rate, the buffer, the ceiling, the ear). Knowing the limits is how you use the tools on purpose and keep your hearing for the next song.
Try this: this week, play a song you love at your usual volume, then lower the volume by two notches and listen again. Notice what you still hear. If you can, open your phone's listening-health readout (many have one) to see your weekly average. And if you have any music app that shows loudness, check two tracks of different eras side by side.
Sources. Sampling theorem history (Nyquist, Shannon 1948/1949, Kotelnikov 1933): encyclopaedia summary. Bit-depth SNR 6.02N + 1.76 dB, decibel and comb-filter formulas: standard. MIDI 1.0 (August 1983), 31,250 baud, three-byte messages, 2013 Grammys, MIDI 2.0 (announced 2019, shown January 2020): encyclopaedia summary. FM (Chowning from 1967, published 1973, Yamaha licence 1973, DX7 1983): encyclopaedia summary. Minimoog (1970; three oscillators, 24 dB/oct filter), TR-808 (1980, under 12,000 sold), Pro Tools (Sound Tools 1989, Pro Tools June 1991): encyclopaedia summaries. Loudness war dates and the Deruty–Tardieu and Shepherd–Katz exchange; streaming targets (Spotify −14, Apple Music −16): the encyclopaedia's Loudness war article (targets change by service and year). BS.1770 K-weighting coefficients were implemented and checked against the standard's calibration (a full-scale 997 Hz sine reads −3.01 LUFS). EBU R 128's −23 LUFS target is stated from the recommendation and was not re-fetched. WHO–ITU H.870 (80 dB(A) for 40 h per week, 3 dB exchange rate) and the 2026 WHO fact sheet: WHO pages; worked examples of 83/86/89 dB from secondary summaries. All interactive numbers were computed in node and checked in a browser.