What frequency is relaxing? What studies found, and the 432 Hz and 174 Hz pair

Is there one frequency that relaxes everyone?

No. No study has found a pitch that relaxes people on its own. What research has tested is music, and there the effect is real but modest. A review of 104 randomised trials with 9,617 people found that music lowered measures of stress by a small to moderate amount on average (de Witte and colleagues, 2020). The trials used music of every kind, not a chosen frequency.

Music and stress: average effects

What was measured	Average effect
How stressed people said they felt	0.55
Heart rate	0.46
All the body's measures together	0.38

Inside music, tempo mattered more than anything else in one study that took it apart. There, 24 adults heard six styles of music and a two minute pause, in random order, while their breathing and heart rate were recorded. Faster music raised both, and the pause brought heart rate below where it started (Bernardi and colleagues, 2006). The authors put it in one line: "Slow or meditative music can induce a relaxing effect; relaxation is particularly evident during a pause."

Even music chosen for being relaxing does not act the same way on every measure. In another study, 60 women heard Allegri's Miserere, the sound of rippling water, or nothing, before a standard stress test (Thoma and colleagues, 2013). The rise in cortisol, a stress marker measured in saliva, was highest after the music and lowest after the water, while another saliva marker settled back faster after the music. Heart rate, and how stressed the women said they felt, did not differ between the three groups.

Which pitches sound calm?

Lower ones, in the one test that asked. Researchers at the Australian National University played twelve pure tones to 37 adults, 20 seconds each, and asked them to rate each tone from 1 to 10 for how happy, sad, calm and angry it sounded (Kumar, Abhayapala and Samarasinghe, 2022). Calm fell steadily as the pitch rose: 110 Hz scored 8.3, 174 Hz 8.1, 440 Hz 4.4 and 963 Hz 1.9.

Mean calm rating of each tone, 1 to 10

Tone	Calm rating
110 Hz	8.3
174 Hz	8.1
220 Hz	7.6
285 Hz	6.7
396 Hz	5.0
417 Hz	4.7
440 Hz	4.4
528 Hz	3.3
639 Hz	2.5
741 Hz	2.2
852 Hz	2.2
963 Hz	1.9

Download the calm ratings (CSV)

The paper prints its ratings only as a graph. Harmonance read each value from the graph's own pixels, against the graph's own axes, and gives them here to one decimal place, so a reader can check them against the original.

What the test does not show matters as much. It asked how calm a tone sounded, not how calm anyone became. The tones came in rising order and each was rated against the ones either side of it, so part of the slope may simply follow the order. People listened at home, on their own headphones, at a volume of their choosing, and most were young, with a median age of 27. It is one study.

Is 432 Hz a relaxing frequency?

It is the number most often offered online, and the evidence for it is one small pilot. 432 Hz is a tuning rather than a single tone: the note A set at 432 Hz instead of the standard 440 Hz, which lowers every note by about a third of a semitone. The 432 Hz guide tells where that idea comes from.

In Italy, 33 volunteers heard the same film music tuned to 440 Hz on one day and to 432 Hz on another, 20 minutes each. Their heart rate averaged 4.79 beats a minute lower with 432 Hz, right on the usual line for chance at p = 0.05 (Calamassi and Pomponi, 2019). The authors start from the point that "there are no scientific studies that support this hypothesis", and close by asking for larger randomised trials.

In the rating test, 432 Hz itself was not one of the twelve tones. Its nearest neighbour, 440 Hz, landed in the middle at 4.4, and the authors read the stretch from 432 to 440 Hz as "neutral from human emotion perspective": neither calm nor tense. So the tone the 432 Hz page plays has no measured calm of its own. For how it compares with 528 Hz, see the guide to 528 Hz and 432 Hz.

Why pair 432 Hz with 174 Hz?

Because 174 Hz sits at the low end of the numbers people reach for. It is the lowest of the nine Solfeggio frequencies, a number added to the set after the book that began it, as the 174 Hz guide traces. In the rating test it came out the calmest-sounding of the nine Solfeggio tones, at 8.1, with only the 110 Hz test tone rated higher.

Harmonance's relaxation pairing plays the two together: 432 Hz on top, and 174 Hz an octave and a little more below it. That pairing is a listening idea, not a finding. No study has played 432 Hz and 174 Hz together, so nothing is known about the pair beyond how it sounds, which the next two sections measure.

How do 432 Hz and 174 Hz sound together?

Smooth. 432 divided by 174 is 2.483, an octave and a little less than a major third. In cents, the hundredths of a semitone that musicians use to measure intervals, that is 1,574.3 cents, 12 cents short of the pure major tenth, 5 to 2, which would put the upper tone at 435 Hz. Both numbers divide by 6, so the two waves start together again every sixth of a second, after 29 waves of 174 Hz and 72 of 432 Hz.

Whether two tones rub against each other depends on the ear's hearing bands. The inner ear sorts sound into overlapping bands, and two plain tones that fall inside one band beat and sound rough. In a classic study, Plomp and Levelt found that listeners judged two plain tones most dissonant about a quarter of a critical band apart, and consonant once they were more than a critical band apart. Their critical bands, Zwicker's, are wider than the bands drawn below: 258 Hz apart, 174 Hz and 432 Hz are more than two of them apart.

The width of a band grows with pitch. By Glasberg and Moore's formula, 24.7 × (0.00437 f + 1), which hearing scientists use today, one band is 43.5 Hz wide at 174 Hz and 71.3 Hz wide at 432 Hz. Counted in bands, the two tones sit 4.6 apart, far into the smooth range. That is a fact about the sound, not about the listener: no study shows that a smooth pair relaxes anyone. It does mean this pair will not beat or flutter.

What is in Harmonance's 432 Hz and 174 Hz tones?

The 432 Hz and 174 Hz pages each play a 20 second loop. Harmonance measured the two files mixed sample for sample, as if both played at once. The two strongest lines sit at 174.000 and 432.000 Hz, at exactly the same level. Each tone carries two faint overtones, its second harmonic 23.1 dB down and its third 34 dB down. The 174 Hz file also carries faint low lines that are not its harmonics: the strongest three, at 52, 64 and 102 Hz, sit 43.4 to 44.6 dB down, and 34 fainter ones run from 32 to 300 Hz, each at least 45.9 dB down. The 432 Hz file holds one such line, at 436 Hz, 59.8 dB down.

The numbers behind the chart

Line	What it is	Below the tones
174 Hz	the 174 Hz tone	0 dB
432 Hz	the 432 Hz tone	0 dB
348 Hz	second harmonic of 174 Hz	23.1 dB
864 Hz	second harmonic of 432 Hz	23.1 dB
522 Hz	third harmonic of 174 Hz	34.0 dB
1,296 Hz	third harmonic of 432 Hz	34.0 dB
102 Hz	faint line in the 174 Hz file	44.2 dB
64 Hz	faint line in the 174 Hz file	43.4 dB
52 Hz	faint line in the 174 Hz file	44.6 dB
258 Hz	not in the files: the difference tone's place	64.4 dB

Download the measurements (CSV)

Even the overtones keep their distance. The closest two lines in the mix are 432 Hz and the third harmonic of 174 Hz, at 522 Hz: 90 Hz apart, 1.18 bands. No two lines share a band. Apart from those six lines, the strongest thing in the files is faint coding noise low in the 174 Hz file, 43.2 dB below the tones. Equal level in a file is not equal loudness in the ear, though: the 174 Hz guide explains why a low tone sounds quieter than a higher one at the same level.

What about binaural beats for relaxation?

Search for a relaxing frequency and binaural beats come up next: two tones a few hertz apart, one in each ear, with the claim that the brain follows the slow beat between them. A 2019 meta-analysis of 22 studies found a medium average effect across the outcomes it pooled (Garcia-Argibay and colleagues). A 2023 review of 14 studies that recorded brain activity found five that fitted the idea that the brain follows the beat, eight that did not, and one mixed (Ingendoh and colleagues). The binaural beats guide sets out how they work.

How do you listen for relaxation?

Choose sound you like, keep it slow and quiet, and leave room for silence. Those are the things the studies above point to, more than any number. Keep the volume low: the World Health Organization's guide to safe listening says "you can safely listen to a sound level of 80dB for up to 40 hours a week", and suggests a device volume of no more than 60 per cent of maximum.

Research on music and health as a whole is still at an early stage. The US National Center for Complementary and Integrative Health sums it up:

However, because much of the research on music-based interventions is preliminary, few definite conclusions about their effects have been reached.

The NCCIH adds that loud listening is a risk of its own: "listening to music at too high a volume can contribute to noise-induced hearing loss".

How do you play 432 Hz and 174 Hz on Harmonance?

Press play at the top of this guide to hear 432 Hz, or open the 432 Hz page and the 174 Hz page. Each plays its tone alone, or with Strings switched on. Nothing plays until you press play, and no account is needed.

To hear the two together, open Harmonance Studio, the free Harmonance instrument, which plays several tones at once after you sign in with a free account: add 432 Hz and 174 Hz, then set 174 Hz a little lower and balance them by ear. The relaxing sounds theme gathers gentle tones for quiet evenings, and the Need to unwind page the tones people reach for at the end of a day.

For sound at night, the guide to music and sleep sets out that research, and what the science of sound healing shows covers the wider field.

Sources and limits

No frequency has been shown to relax people by itself. The rating of calm pitches comes from one online test, read from its graph. The 432 Hz evidence is one pilot of 33 people. No study has played 432 Hz and 174 Hz together. The arithmetic, the hearing bands and the measurements of the two tone files are checkable, and the measurements are Harmonance's own, made from the files the pages play.

1. Kumar, Abhayapala and Samarasinghe (2022), frequency-dependent cues for human emotions, in Acoustics: 37 listeners rate twelve pure tones.
2. de Witte and colleagues (2020), music interventions and stress, two meta-analyses, in Health Psychology Review: 104 randomised trials.
3. Bernardi, Porta and Sleight (2006), the importance of silence, in Heart: tempo, and the pause.
4. Thoma and colleagues (2013), the effect of music on the human stress response, in PLOS ONE: music, water and silence before a stress test.
5. Calamassi and Pomponi (2019), music tuned to 440 and 432 Hz, in Explore: 33 volunteers.
6. Garcia-Argibay and colleagues (2019), a meta-analysis of binaural beats, in Psychological Research: 22 studies.
7. Ingendoh, Posny and Heine (2023), binaural beats and brain activity, a systematic review, in PLOS ONE: 14 studies.
8. Plomp and Levelt (1965), tonal consonance and critical bandwidth, in The Journal of the Acoustical Society of America: when two tones sound smooth or rough.
9. Moore (2014), the Cambridge loudness models, in Trends in Hearing: the width of the ear's bands.
10. National Center for Complementary and Integrative Health, music and health: the state of the research, and loud listening.
11. World Health Organization, safe listening: how loud, and for how long.