Pure Frequencies One sine, no harmonics

A pure tone is one sine wave. One frequency, one amplitude, nothing else in the signal. Play 440 Hz as a pure tone and the air pressure at your eardrum rises and falls 440 times a second along a perfectly smooth curve, and that is the whole of it.

Every other sound is a stack of these. That is not a metaphor. Any repeating waveform can be broken down into a sum of sine waves at different frequencies, which is the result Fourier arrived at in the early 1800s while working on heat conduction. A violin playing A4 puts out 440 Hz plus energy at 880, 1320, 1760 and upward, in proportions particular to a violin. Shift the balance of those harmonics and you get a clarinet, or a voice, or a struck bowl. Most of what makes an instrument recognisable is in that recipe, along with how the note starts. A sine wave has neither, which is why it has no character.

It is also the least natural sound you will ever hear. Practically nothing in the physical world produces a single frequency. A tuning fork gets close, and only once the clang of the strike has died away. Bowed strings, vocal folds, drum skins, wind through a gap, water on stone — all of them generate harmonics, because that is what happens when an object with mass and stiffness is driven into vibration. A held sine is a mathematical idea pushed through a speaker, and it sounds like one: hollow, electronic, faintly like a test signal, because that is mostly what it has ever been used for.

Pure tones are oddly hard to place in a room, too. You locate sounds partly by comparing arrival time and level between your two ears, and partly from the way your head and outer ear filter different frequencies before they reach the eardrum. A single frequency gives that second mechanism nothing to work with. You can still tell which side a sine tone is on, since timing and level differences survive, but front, back and height stay ambiguous in a way they never are with a broadband sound.

The textbook figure for human hearing is 20 Hz to 20 kHz. The bottom of that is roughly right for life. The top is a number from childhood.

High-frequency hearing goes first and goes early. The ceiling starts dropping in the late teens, slides slowly through the twenties and thirties, then falls faster from around forty. That is presbycusis, age-related hearing loss, and it is gradual, symmetrical between ears and permanent. By middle age the top of the range typically sits somewhere between 12 and 16 kHz rather than 20. Little of the sound that matters lives up there, so the loss is easy to miss.

You can find your own ceiling in about a minute with a full-range tone generator — not the one on this site, which is built for the band the presets use and stops at 1 kHz. Two cautions. Small speakers lie in both directions, so use decent headphones and a real sine wave rather than a compressed video. And come down from above rather than sweeping up from below: sweep upward and you will hear the amplifier straining, the file artefacting, or your own expectation, and count it as a tone.

Pitch perception gives up somewhere near 20 Hz. Below that the ear stops fusing the pressure cycles into a note and you are left with separate events: flutter, throb, or nothing. So a file that calls itself a 2 Hz pure tone cannot be doing what the name says. Either it is an audible tone whose volume is being pushed up and down twice a second, or it is genuinely a 2 Hz sine, in which case there is no pitch in it to hear and your playback chain is not delivering it at useful level either.

That is why the delta and theta bands are never addressed with pure tones. You cannot hear 4 Hz, so the rate has to be carried by something you can. A binaural beat puts an audible tone in each ear a few Hz apart and lets your auditory system build the difference. A monaural beat sums them first, so the pulse is physically in the air. An isochronic tone gates an audible tone on and off. Each of those has its own page here; what they share is that the rhythm is the payload and the audible tone is only the vehicle.

Pure tones are for the other case: when the frequency you actually want is itself audible. 174 Hz. 432 Hz. 528 Hz.

Two different things get called 40 Hz, and the confusion sells a lot of audio. A 40 Hz audible tone is a very low bass note. Forty-hertz gamma is a rate of brain activity. They are not the same object, and playing the first does not deliver the second: the cortical responses at 40 Hz in the research literature come from sound modulated at 40 Hz, not from a 40 Hz sine held steady.

Arkhitec ships a 40 Hz tone in its pure category. It is a bass note. It is not a gamma rate, and nothing about it is. A 40 Hz sine barely exists on a phone speaker either, so if you have played one and concluded nothing happened, there is a decent chance nothing arrived.

Two pure tones at identical level, one at 20 Hz and one at 1 kHz, are nowhere near equally loud. Sensitivity varies enormously with frequency, and the shape of that variation is standardised as ISO 226, the equal-loudness contours, still widely called the Fletcher–Munson curves after the 1933 Bell Labs experiments that first mapped them.

On the 40-phon contour, the set of tones that all sound as loud as a 1 kHz tone at 40 dB SPL, the 1 kHz point sits at about 40 dB and the 20 Hz point at about 100 dB. Sixty decibels apart, for the same sensation. In power terms that is a factor of a million. Sensitivity peaks in the 2–5 kHz region, which is where the consonants of speech sit, and that peak is mostly a consequence of the ear canal's own resonance.

Set the level per tone, not per session: a 40 Hz preset and a 528 Hz preset at the same slider position are two different things, and the low one can be moving far more air than it feels like. It is also why hearing tests report in dB HL rather than dB SPL. That scale is pre-corrected against a reference curve, so a flat line on an audiogram means normal hearing rather than equal pressure.

Holding a sine in your ears for an hour is an unusual thing to do, so one note on level. The cochlea maps frequency to position along its length, so a sustained tone drives one narrow region continuously instead of spreading energy across the whole membrane the way music does. That is not a reason to avoid pure tones. It is a reason to run them quietly.

There is a second reason to keep them quiet, and it is the argument for putting rain over the top instead of turning the tone up. Masking by a tone is narrow and lopsided: it reaches up in pitch much further than it reaches down, and it never covers a spectrum the way noise does. Turning a single frequency up does not make it sit in a mix. It makes it loud.

Play a pure tone through speakers, then lean thirty centimetres sideways. Sometimes it nearly disappears.

Sound moves at about 343 metres per second in room-temperature air, so a 50 Hz tone has a wavelength of nearly seven metres and a 100 Hz tone about 3.4 metres. Those are room-sized. The wave reflects off the far wall, comes back, and interferes with itself, and because the tone never changes the resulting pattern of loud spots and dead spots never moves either. A room with a 3.5 metre wall resonates at roughly 49 Hz along that dimension, with a pressure null in the middle of the span. Sit in the null and the tone drops away. Move out of it and it returns.

Music hides this. Broadband, constantly shifting sound averages across hundreds of wavelengths and the peaks and nulls smear into each other. A single held frequency gives the room one thing to do, and the room does it. No amount of EQ fixes a null, because at that point in space the energy has genuinely cancelled; turning it up only makes the loud spots louder.

Headphones remove the room entirely, which is one of the few unambiguous arguments for wearing them with this category. Failing that, move yourself or move the speaker, rather than reaching for the volume.

The standard air-conduction set is 250, 500, 1000, 2000, 3000, 4000, 6000 and 8000 Hz, one ear at a time, plotted as an audiogram in dB HL. That range stops well short of the ceiling because it covers the band speech occupies; everything above 8 kHz is detail. The World Health Organization puts the boundary of normal adult hearing at 20 dB HL. Bone conduction repeats the lower part of the range through a vibrator on the skull, which separates a mechanical problem in the outer or middle ear from a sensorineural one.

Sine waves are used here for the same reason a chemist reaches for a reagent-grade solvent. A pure tone has one frequency and nothing else in it, so at a known level a response tells you about one place on the cochlea and nothing else. A chord, or noise, or recorded speech would test everything at once and localise nothing.

A good measuring stimulus is not a treatment.

If the bare tone is the point, play it bare. Otherwise put something over it: the 7-layer mixer runs a pure tone underneath rain, ocean, singing bowls, an affirmation track or a sleep story, each layer at its own level. When the timer runs out the whole stack stops, tone included.

The combined solfeggio and pure-tone category carries all nine solfeggio frequencies (174, 285, 396, 417, 528, 639, 741, 852 and 963 Hz), plus 432 Hz, 256 Hz, and a run of tones named after planets and orbits. Every one sits in the audible range, where a pitch actually exists.

Those planetary ones deserve a paragraph, because the arithmetic behind them is real and almost nobody explains it. A solar day is 86,400 seconds, so one cycle per day is 1/86,400 Hz. Double that 24 times and you land on 194.18 Hz, which is the preset labelled Earth. One orbit of 365.2564 days, doubled 32 times, gives 136.1 Hz. The 25,920-year precession of the equinoxes, doubled 47 times, gives 172.06 Hz. You can check any of them on a phone in under a minute, and they come out exact. What the arithmetic cannot do is say anything about what the tone does when you play it. An exact derivation and a physiological effect are separate claims, and only the first one is established here.

If you want to hear what a single frequency is like before any of that, the browser generator will do it anywhere between 50 and 1,000 Hz: set both ears to the same number, no account and no download.

Entrainment claims are about the brain following a rhythm. A held sine has no rhythm in it: no modulation in the signal, nothing to lock onto. Whatever the case for beats and pulsed tones turns out to be, it does not transfer to a steady tone.

Even for the methods that do carry a rhythm, the picture is unsettled. Ingendoh, Posny and Heine's 2023 PLOS ONE review (DOI 10.1371/journal.pone.0286023) went through fourteen binaural-beat studies and could not settle it either way, the balance leaning against. Every one of the fourteen involved a beat, because a held tone gives the argument nothing to work with.

One 2025 result is worth a line here because of what it tested against: a plain pure tone. Melnichuk, Cooper and Hawk, in Scientific Reports (DOI 10.1038/s41598-025-88517-z), randomised 80 participants across sixteen conditions and analysed 64, each of whom heard binaural beats in one session and a matched pure tone in the other. Gamma beats on a 340 Hz carrier beat that pure-tone control on percent hits, p = 0.002, and did not slow the decline in performance across the session. Roughly four people per cell, so hold it loosely.

Nothing here treats any medical condition, and the frequency-specific claims attached to particular numbers have no research behind them.