The Cosmic Octave: how a period becomes sound

In 1978 the Swiss mathematician and musicologist Hans Cousto noticed something simple: every cycle has a frequency, and a frequency can be doubled until it becomes audible. Doubling a frequency gives an octave, which is why the technique was called “the law of the octave”.

Let us start with what surprises people most: there is nothing mystical about the conversion. If an event repeats once a second, that is 1 Hz. If it repeats once a year, that is one thirty-millionth of a hertz. The number is tiny, but it is real, and you can work with it like any other number.

Then music comes in. Multiplying a frequency by two raises a sound by exactly one octave: the note stays the same, only its pitch changes. The A above middle C at 440 Hz and the A an octave higher at 880 Hz are the same note. Nobody disputes that they are “different sounds”, and nobody disputes that they are the same A.

Cousto took the next step: if doubling keeps the note, you can just as well double thirty times in a row. Take the Earth year, double it thirty-two times, and you get 136.10 Hz. It is still “the note of the Earth year”, only moved to where the ear can hear it.

Thirty-two doublings in one picture

The axis is logarithmic: each doubling raises the sound by exactly one octave. The pitch goes up, the note stays the same.

The whole formula

Below is the entire calculation. It fits into six lines, and it is exactly how every number in this section was computed.

f₀ = 1 / P — the frequency of the cycle itself, with P in seconds

n = round(log₂(170 / f₀)) — how many times to double

f = f₀ · 2ⁿ — the audible tone

s = 12 · log₂(f / 440) — how many semitones it lies from A

cents = 100 · (s − round(s)) — how far it misses the note

λ = c / (f · 2ᵐ) — the wavelength of the same tone as light

The only arbitrary number here is 170. It is the middle of the 120–240 Hz band by pitch, where every octave is an equal step: √(120 · 240) ≈ 170; on an ordinary linear scale the middle would be 180. The band's numbers are ours: for every tone we compute from a period that also appears in Cousto's Tuning Data, rounding around 170 gives the same octave as it has there. It is the lower part of the hearing range, and a fork at that pitch is convenient to hold near the body. Had Cousto picked other octaves, every tuning fork would sound higher or lower while remaining the same note. In other words, the choice of octave is a convention, not a property of the planet, and that is worth knowing.

Reproducible

You can check the formula on any object that has a period: on our site it recalculates all fifteen such frequencies on every build, and nine reference values from Cousto's brochure match to the hundredth.

Where “432 Hz” comes from

Planetary frequencies almost never land exactly on the notes of standard tuning, where A = 440 Hz. The Om tone lies 31 cents below C# — roughly a third of a semitone. But you can look at it from the other side: in which tuning would 136.10 Hz be an exact C#? The answer is A = 432.10 Hz.

That is the whole connection between the “Earth tone” and the famous 432 tuning. Not secret knowledge of the ancients, but a consequence of the Earth year not dividing evenly into twelve semitones. Every object has a tuning like this of its own: for Mercury it is A = 448.5 Hz, for Venus 442.5, for the Full Moon 429.3. None of them is “more correct” than the rest.

Where all these tones sit on the scale of hearing

All the forks on this scale lie in the 120–240 Hz band: that is the lower part of the hearing range, and forks at that pitch are convenient for working with the body. The same tone an octave lower or higher is still the same planet.

Where one quantity has two “official” values

Dualities of planetary frequencies and their sources
Object	What differs	First value	Second value
Om	which year to use	tropical, 365.2422 days → 136.10 HzCousto, The Cosmic Octave booklet	Julian, 365.25 days → 136.0993 Hzastronomical convention
Earth Day	which day	solar, 24 hours → 194.18 HzCousto	sidereal, 23 h 56 min → 194.71 HzCousto, on a separate row
New Moon	fork color	orange (by wavelength, 648 nm)Cousto	metallic bluethe Acutonics school itself: the color name on the page for its hand chimethe school's New Moon hand chime
Full Moon	why it is the “full moon”	227.43 Hz is the sidereal monthastronomy	named the “full moon”Acutonics
Mercury	note	C#Cousto's table	DCousto's text in the same booklet
Venus	chakra	the third eye, and only the third eyeCousto: one planet, one chakra	five chakras in different sets; the product pages single out the throatAcutonics: a chakra is matched not with a planet but with a set of planets and intervalsthe school's article on chakras · Venus Middle fork · Venus gong
Pluto	frequency	140.25 Hzclassic Cousto: the 1984 book and the list of forks in his booklet	140.64 HzCousto's revised booklet: the tables and the Pluto page
Chiron	which fork is called Chiron	172.86 Hz, note F, from a period of 50.39 yearsPlanetware and Meinl forks; this page is about that one	about 151 Hz, note D sharp, a major second with Om, green paintthe Acutonics school's fork: the school publishes the note, interval and color but not the frequency; about 151 Hz is our measurement from Acutonics Canada recordingsthe school's Chiron Middle fork · Acutonics Canada: color and note · recording of the low fork · recording of the high fork
Chiron	frequency	172.86 Hz, from a period of 50.39 yearsNASA fact sheet for the 1996 epoch; Planetware has tuned its forks to it since May 2014	171.80 Hz, from a period of 50.7 yearsthe earlier value in the same fact sheet; Planetware tuned its forks to it until 2014
Sirius	published value	173.76 Hz, the exact calculationperiod of 50.1284 years (Bond, 2017, Hubble observations)	173.8 Hz, roundedmanufacturers' practice
Nibiru	name of the paint color	burgundythe forks in the school's catalog photos; Acutonics Canada gives the color the same nameAcutonics Canada	“Violet”the Acutonics school: the Color field on the hand chime pagethe school's Nibiru Middle hand chime

Why this period and not another?

For the planets, the sidereal orbit around the Sun is used — the orbit measured against the stars. For the day it is the rotation about the axis, and here there are two versions at once: the solar day of 24 hours and the sidereal day, shorter by almost four minutes. For the Moon it is the synodic month (from new moon to new moon) or the sidereal month (against the stars). The choice of version changes the frequency, which is why the table lists both rather than one “correct” value.

Why is the Sun calculated differently?

The Sun has no orbit from which a period could be taken. Cousto derived its tone in another way and transposed it down by octaves rather than up. The formula itself does not appear in the available sources — there is only the result, 126.22 Hz. We mark this line as unverified: not because we doubt the number, but because we cannot reproduce it.

Is a planet's color a calculation too?

Yes, and by the same technique. If you keep doubling the frequency beyond the audible, after about forty octaves it reaches the range of visible light, and a wavelength corresponds to it. Hence “the color of a tone”. This is a model, not the measured color of a planet — Mars does not turn blue because of it. But the arithmetic holds: for all fourteen objects, the computed wavelength matched the color printed in the brochure.

So do the planets really make a sound?

No. Sound is a vibration of air, and there is no air in space. The correct way to put it is this: we took the period of a planet's motion and built a sound from it. It is the conversion of a quantity, not a recording. Anyone who says “listen to what Jupiter sounds like” is either simplifying or has not looked into it.

Next: the chart of all frequencies · why there are two tuning forks · what has been proven

Comments

Comments are temporarily closed — the site is in development.