Learn · Tides and beats
Spring–neap as a binaural beat
The short version
The ocean already has a binaural beat. You just cannot hear it. The principal lunar semidiurnal tide (M2) repeats about every 12.420601 hours. The principal solar one (S2) repeats every 12 hours exactly, because that is a solar day cut in half. Two close frequencies produce a slow envelope: spring tide when they pile up, neap when they cancel. That envelope takes 14.7653 days. Hear the Date multiplies the whole pair until the difference is 7.83 Hz, then splits the two carriers left-ish and right-ish — except the pan is later overridden by the local sky if you have set a place.
Listen to a date
The lab is the proof. Turn the month wheel from new moon to full and the pulse gets harder; quadrature lets it slacken. Free accounts: 5 minutes per UTC day. Members: no cap. Guests: orrery only.
This is older than headphones
William Thomson (Kelvin) and George Darwin spent the 1860s–80s turning harbor records into sums of sines. Darwin’s 1883 report to the British Association is the one people still footnote. A.T. Doodson later gave each partial a six-integer argument so you could look up M2, S2, N2, K1, O1 without arguing about names. None of that work was about audio. It was about predicting when a dock floods.
A “partial” is just a cosine with a known astronomical speed. M2 is the Moon’s mean motion, doubled, because the bulge has two highs per rotation. S2 is the same trick with the Sun and a 24-hour day. N2 is the lunar elliptic (the Moon is not on a circle; perigee tides are a real nuisance in some estuaries). K1 and O1 are diurnal. Hear the Date does not sonify N2 or the declinational terms. If you are a harmonic analyst that will bother you. It bothered me for about an afternoon and then I left them off, because the headphone image was already crowded and the point of the lab is the spring–neap beat, not a 37-constituent reconstruction of Immingham.
The numbers that actually go into the machine
Period of M2, commonly quoted: 12 h 25 min 14 s, or 12.4206012 h if you are keeping the mean lunar day honest. Frequency fM2 = 1 / 12.4206012 h ≈ 22.420146 °/h in the Darwin speed convention, or 2.236×10−5 Hz if you insist on SI. S2 is 2 / 86400 s = 2.3148148×10−5 Hz. The difference is 7.88×10−7 Hz. Invert that and you get 1.269×106 seconds, which is 14.7653 days. That is the synodic fortnight — new to full is half of a 29.53-day month, and the tide envelope hits twice per month, at both syzygies.
Scale factor in the lab: 9.9889×106. Multiply the SI difference and you land on 7.83 Hz within a rounding error. I did not pick 7.83 because the math demanded it. I picked it because the rest of this site already treats 7.83 as a near-theta design target and because the Schumann merch industrial complex has made that number searchable. The honest page for the cavity physics is 7.83 Hz and the Schumann resonance. Electromagnetic cavity ≠ headphone difference tone. If someone tells you otherwise they are selling a sticker.
| Quantity | Ocean / sky | In Hear the Date |
|---|---|---|
| M2 period | 12.420601 h | Moon carrier 223.40 Hz |
| S2 period | 12.000000 h | Sun carrier 231.23 Hz |
| |fM2 − fS2| | 7.88×10−7 Hz | 7.83 Hz beat |
| Envelope | 14.7653 d spring–neap | LFO depth and filter open with syzygy |
| Equilibrium tide | a ≈ 2GMR / d³ | Amplitude of each carrier |
Spring is alignment, not the season
English is unhelpful here. “Spring tide” is the one that springs up, from an old verb, and it happens at new moon and full moon when lunar and solar bulges add. “Neap” is the weak one at first and third quarter. You can see this in the lab without believing anything mystical: jump to next full, then next quarter, and watch the CRT tension and the audible pulse. Distance still matters. A perigean spring (new or full near lunar perigee) is louder than an apogean one. An annular solar eclipse is a spectacular syzygy and a slightly disappointing tide because the Moon is far. The instrument will tell you that if you drag to the right date. It will not announce “supermoon.” You have to notice the Moon’s distance in the orrery.
Local geography — amphidromes, shelf resonance, the Bay of Fundy’s 13 m range — is not in the code. We use the equilibrium form, then a local factor (3 sin² altitude − 1) / 2 so a body on the horizon pulls differently than one overhead. That is the P2 Legendre piece of the tide potential, not a hydrodynamic model. If you live in a place with weird tides, the headphones will not reproduce your harbor. They will reproduce the forcing.
Why split them across the ears
A binaural beat is |fR − fL| generated in the brainstem, not in the air. Classic demo: 200 Hz left, 210 Hz right, you perceive 10 Hz. Same idea here, except the two carriers are the scaled M2 and S2 analogues rather than arbitrary sliders. Default pan without a sky would be Moon hard-left, Sun hard-right, which is a diagram, not a place. Once you set a lat/lon, azimuth takes over: the same two oscillators walk around the stereo field as they rise and set. The beat still exists as long as both are audible. If the Sun is buried and the Moon is up, you mostly hear the lunar carrier and the beat gets thin, which is physically decent — you cannot have a two-tone difference with one tone.
Monaural mixing (both tones in both ears) would give you an acoustic beat in the waveform. That is a different percept, and we do not do it in this lab. For the A/B, use binaural vs monaural.
Planets, briefly
Venus and Jupiter raise tides. The textbooks mention them in a footnote and then go back to the Moon. In amplitude they are negligible; in a headphone mix they are useful as coloration if you compress the dynamic range (the lab uses weight ∝ (a/amoon)0.18 times a syzygy term). They do not get their own beat against the Moon. That would be a mess of µHz on µHz. They sit as quiet carriers near the Sun’s pitch and take the same east-facing pan as everything else. If you came here from astrology Discord, this will feel like a downgrade. It is.
Limits I am not going to paper over
The lunar longitude in the instrument is a truncated series, not DE440. Fine for phase to a couple of degrees, not for occultation work. The 18.6-year nodal scale on the wheel exists because the Moon’s orbital plane regresses and that does change tidal range in the real ocean (the 18.6-year nodal modulation of M2 is a measured thing, order 4% in some places). We expose the date range. We do not claim we modeled every nodal partial.
Scaling a fortnight into a 7.83 Hz pulse means you hear the state of the envelope, not the envelope as a 14-day whoosh. To hear the whoosh you would have to time-lapse the date, which the wheel will do if you spin it, and it sounds like a filter opening, because that is what we wired. It is closer to scrubbing a tide gauge than to standing on a beach for two weeks.
Read next
Established: M2, S2, and the spring–neap beat exist in tidal analysis. Hypothesis in this product: that mapping those frequencies into the audible range is a useful way to listen to a date. Not established: any health effect from doing so. Not a tide table. Headphones required.