44,100 Hz. Not 44,000. Not 48,000. Not even 40,000 or 50,000, which would at least have the virtue of roundness. The number that defines CD-quality audio is specific in a way that invites a question most people never think to ask: why that number?
The Puzzle
When a physical constant turns out to be $1.6 \times 10^{-19}$ coulombs, that is just nature being nature — no further explanation is needed or available. But when an engineering standard settles on 44,100 Hz rather than, say, 44,000 Hz or 45,000 Hz, there is a story hiding in the specificity.
The standard answer — the one you find on Wikipedia and in most popular accounts — is that 44.1 kHz satisfies the Nyquist criterion for 20 kHz audio, and so it was chosen to preserve the full range of human hearing. This is true. It is also almost completely uninformative. The Nyquist criterion for 20 kHz audio requires only that the sampling rate exceed 40 kHz. That constraint is satisfied by 40,001 Hz as much as by 44,100 Hz. The specific value requires a different explanation entirely.
That explanation involves Sony’s video-based PCM recorders and two closely spaced rates derived from the 625-line and 525-line television systems. The number 44,100 is not an optimisation. It is an archaeological deposit. And like most archaeological deposits, it is still with us long after the civilisation that created it has disappeared.
I want to work through the physics first, because the Nyquist theorem is genuinely beautiful and is often presented in a way that obscures what it actually says. Then I want to show you the arithmetic that made rates near 44.1 kHz practical given 1970s constraints — and why colour NTSC does not, in fact, produce exactly the same number as PAL. If you enjoy “hidden mathematics in music,” you might also find it in Euclidean Rhythms, where a 2,300-year-old algorithm turns out to encode the structure of West African and Cuban percussion.
The Nyquist–Shannon Sampling Theorem
Before the archaeology, the physics.
In 1928, Harry Nyquist published a paper on telegraph transmission theory that contained, somewhat incidentally, the germ of what would become one of the most consequential theorems in applied mathematics [[4]]. Claude Shannon formalised and generalised it in 1949 [[5]]. The theorem states: a continuous bandlimited signal whose highest frequency component is $f_{\max}$ can be perfectly reconstructed from discrete samples taken at rate $f_s$ if
$$f_s > 2 f_{\max}.$$The quantity $f_s / 2$ is called the Nyquist frequency. Sampling below it causes aliasing: high-frequency components fold back into the spectrum and appear as spurious low-frequency artefacts that are indistinguishable from genuine signal. Once you have aliased a signal, the damage is permanent. Sampling above the Nyquist rate, under the theorem’s assumptions, causes no information loss — the original continuous waveform can be recovered exactly, in principle, from the discrete sample sequence.
Human hearing extends from roughly 20 Hz to 20 kHz (and, for most adults over thirty, substantially less at the top end, but 20 kHz is the canonical engineering requirement). Setting $f_{\max} = 20$ kHz, the Nyquist criterion requires $f_s > 40$ kHz.
But here is the subtlety that the Wikipedia summary tends to skip. The theorem assumes that the signal is perfectly bandlimited before sampling — meaning that all energy above $f_{\max}$ has been removed. This requires an anti-aliasing filter: a low-pass filter applied to the analogue signal before the analogue-to-digital converter samples it. If your anti-aliasing filter passes everything up to 20 kHz and blocks everything above it with perfect sharpness, then 40,001 Hz would suffice. The problem is that such a filter is physically unrealisable.
Real filters do not have vertical cutoffs. They have a transition band: a frequency range over which attenuation increases gradually from passband to stopband. The narrower the transition, the more demanding the filter. At 44.1 kHz, a nominal 20 kHz audio passband leaves 2.05 kHz before Nyquist.
So the actual engineering requirement is not just $f_s > 40$ kHz. It is $f_s > 40$ kHz plus enough headroom for a realisable anti-aliasing filter. With $f_s = 44.1$ kHz, the Nyquist limit sits at $f_s/2 = 22.05$ kHz. The gap between the top of the audio band and the Nyquist limit is
$$22{,}050 - 20{,}000 = 2{,}050 \text{ Hz},$$That headroom is not proof that one particular 1979 filter was sufficient; the required order depends on its passband ripple, stopband attenuation, and topology. It does explain why the practical proposals sat above 40 kHz while still trying to minimise the data rate. A 50 kHz stream would use 13.4% more samples than 44.1 kHz.
So 44.1 kHz is in the right neighbourhood given real-world filter constraints. But it is still a specific number. The question of why 44,100 rather than 44,000 or 43,500 or 44,800 is still open. That is where the VCRs come in.
The VCR Problem
In the late 1970s, Sony was developing digital audio systems that would feed into the Compact Disc project. One of the fundamental engineering problems was storage: where do you put the data? A 74-minute stereo recording at 16 bits and 44.1 kHz contains about 783 million bytes of raw samples. Contemporary disk storage at that scale was not a practical mastering medium. Video tape, however, already offered a reliable high-bandwidth recording path [[1]].
The practical route was a video tape recorder. Consumer PCM adaptors existed, but Sony’s professional PCM-1600 mastering chain used U-matic VTRs. The video signal bandwidth was sufficient to carry digital audio if the bits were formatted as a video waveform.
Sony’s solution was elegant to the point of audacity. Rather than inventing a new tape transport, the PCM adaptor encoded audio words into a pseudo-video signal that a VTR could record. Sony introduced the professional two-channel PCM-1600 in 1978; it supported 16-bit recording at either 44.056 or 44.1 kHz when paired with U-matic equipment [[7]].
The sampling rate of the audio was now determined not by any audio engineering consideration but by the geometry of the video signal. And the geometry of the video signal was fixed by the television broadcast standard — which brought entirely different historical contingencies into the calculation.
The NTSC Arithmetic
The 525-line system provides 245 usable lines per field for this PCM format, with three samples per usable line. If we use the old monochrome field rate of 60 fields per second, the familiar arithmetic is
$$f_s = 60 \times 245 \times 3 = 44{,}100 \text{ Hz}.$$Colour NTSC does not run at exactly 60 fields per second. Its rate is $60{,}000/1001 \approx 59.94$ fields per second, so the corresponding rate is
$$f_s = \frac{60{,}000}{1001} \times 245 \times 3 \approx 44{,}055.94 \text{ Hz}.$$That is why contemporary engineering records distinguish 44.056 kHz for the 525-line colour system from 44.1 kHz for the 625-line system [[6]]. The two are close. They are not equal.
The PAL Arithmetic
For the 625-line, 50-field system, the format uses 294 usable lines per field and again three samples per line:
$$f_s = 50 \times 294 \times 3 = 44{,}100 \text{ Hz}.$$The two video families therefore produced 44.05594 and 44.1 kHz. The difference is about 0.1%, small enough for parallel recorder variants but large enough that the rates cannot be treated as one clock. What converged was the engineering region and the integer structure, not the last two digits.
I find the corrected arithmetic more interesting than the myth. A clean story in which two continents independently print the same number is satisfying. The real story contains a fractional colour-video rate, two mastering clocks, and then a standards decision that selects one of them. That is how engineering usually looks when the covers come off.
From Tape to Disc
When Philips and Sony negotiated the Red Book format in 1980, they brought existing converter and mastering systems to the table [[3]]. Video-based PCM infrastructure had made both 44.05594 and 44.1 kHz familiar. The task force still had to choose a single disc rate.
Immink’s participant history records the choice plainly: the candidates were 44.1 and 44.056 kHz, and the task force chose 44.1 because it was easier to remember [[3]]. Existing mastering compatibility constrained the choice; it did not make one rate mathematically inevitable. The rate was already in the room, and the committee selected it.
This is a pattern worth recognising. Major technical standards are rarely chosen by optimisation from first principles. They consolidate theory, available components, installed equipment, and institutional negotiation. The 44.1 kHz CD rate carries all four.
The Other Rates
Not all digital audio runs at 44.1 kHz, and the coexistence of different rates in the modern audio industry is the direct legacy of 44.1 kHz’s awkward origins.
48 kHz is a preferred professional interchange rate under AES5 and is common in video, broadcast, and studio systems [[9]]. It was standardised alongside 44.1 and 32 kHz rather than derived from one universal broadcast clock. Its history is separate from the Red Book choice.
The exact ratio is $48/44.1 = 160/147$. A rational sample-rate converter can conceptually upsample by 160, filter, and downsample by 147. That does not mean it literally emits 160 intermediate samples for every 147 in a modern implementation, nor that conversion must introduce an audible error. Finite filters and arithmetic create engineering trade-offs, but a competent converter can make them negligible. The awkward fraction is a compatibility fact, not a permanent wound in every converted recording.
96 kHz and 192 kHz are marketed as “high-resolution audio.” Here the physics and the listening evidence need to be kept separate. The conventional upper bound for airborne human hearing is about 20 kHz, with substantial variation by listener and age. Higher sampling rates also move converter transition bands farther from the audible band and can simplify some production processing. Those are engineering properties; they do not by themselves prove an audible benefit in a released recording.
A 2016 meta-analysis of 18 experiments found a small but statistically significant ability to discriminate high-resolution from standard audio, with training affecting the result [[8]]. That is not the same as a large or universal preference, and the included studies varied in signal chain and test design. What is straightforward is the data rate: at fixed bit depth and channel count, 96 kHz uses about 2.18 times as many samples as 44.1 kHz, while 192 kHz uses about 4.35 times as many.
The Irony
Here is the situation we are actually in. The canonical CD format — 16-bit, 44.1 kHz PCM — inherited its sampling-rate candidates from systems that encoded digital audio into video waveforms. Television timing constrained the mastering equipment; Sony and Philips then selected the 44.1 kHz member of the pair for the disc.
When someone tells you that 44.1 kHz is the “natural” or “perfect” sampling rate for audio, they are mistaking a workable standard for a constant of nature. The number carries video timing, converter economics, and a committee choice. It is the right number in the practical sense that it works.
I find this genuinely satisfying rather than disappointing. The history of physics and engineering is full of contingent numbers that turned out to be good enough, and whose goodness was only rationalised after the fact. The metre was originally defined as one ten-millionth of the distance from the equator to the North Pole along the Paris meridian — an arbitrary geodetic choice that turned out to produce a unit of length that is remarkably convenient for human-scale physics. The kilogram was a cylinder of platinum-iridium alloy in a vault outside Paris for over a century. 44,100 Hz is in good company.
The Archaeology of a Number
The numbers we inherit from engineering history are rarely arbitrary at every level simultaneously. 44,100 Hz is not arbitrary at the level of sampling theory: it sits above twice the nominal 20 kHz audio band and leaves a finite transition band. That is a genuine constraint, and the number sits in the right region of parameter space for it.
But it is contingent at a deeper level. Television timing produced nearby 44.056 and 44.1 kHz recorder rates; video tape made those systems practical; Sony and Philips selected 44.1 kHz for the Red Book in 1980. The precise CD number is the output of that chain, not of PAL and colour NTSC independently landing on an identical clock.
Science and engineering produce exact numbers from messy contingencies. The number 44,100 satisfies a well-defined engineering constraint, descends from specific video hardware, and survived because institutions standardised it. All three things are true at the same time.
The VCRs are gone. The sampling rate remains.
References
Literature checked through 2026-07-11.
[1] Pohlmann, K. C. (2010). Principles of Digital Audio (6th ed.). McGraw-Hill.
[2] Watkinson, J. (2001). The Art of Digital Audio (3rd ed.). Focal Press.
[3] Immink, K. A. S. (1998). The compact disc story. Journal of the AES, 46(5), 458–465. AES record
[4] Nyquist, H. (1928). Certain topics in telegraph transmission theory. Transactions of the AIEE, 47(2), 617–644. DOI: 10.1109/T-AIEE.1928.5055024
[5] Shannon, C. E. (1949). Communication in the presence of noise. Proceedings of the IRE, 37(1), 10–21. DOI: 10.1109/JRPROC.1949.232969
[6] Tanaka, K., & Ishida, Y. (1978). Digital audio standards. Journal of the Audio Engineering Society, 26(4), 242–253. AES standards history
[7] Sony Corporation. (n.d.). Sony’s professional audio: Chapter 2. Company history
[8] Reiss, J. D. (2016). A meta-analysis of high resolution audio perceptual evaluation. Journal of the Audio Engineering Society, 64(6), 364–379. DOI: 10.17743/jaes.2016.0015
[9] Audio Engineering Society. (2023). AES5-2018 (r2023): AES recommended practice for professional digital audio — Preferred sampling frequencies for applications employing pulse-code modulation. Current AES standards-project status
Changelog
- 2026-07-11: Corrected the colour-NTSC rate from 44.1 to 44.05594 kHz and replaced the claim that NTSC and PAL converge exactly with the documented two-rate history; corrected the PCM-1600 date and U-matic context; bounded filter and sample-rate-conversion claims; and updated the high-resolution-audio evidence.