Planetary frequencies chart: every tuning fork and its period

Eighteen objects and sixteen frequencies; fifteen of them are calculated from a period, while the Sun has no orbit. Most of the numbers were published by Hans Cousto; we recalculated them from astronomical periods, and nowhere do they differ by more than a hundredth of a hertz.

Frequencies of the Cosmic Octave tuning forks: hertz, note, cycle period, computed color, the paint on the metal and the school's name for it
Object	Frequency	Note	Cycle it is computed from	Computed color	Acutonics fork paint
Om	136.10 Hz	C#	Earth's orbit around the Sun365.2422 days (tropical year)	blue-green501 nm	gold“Gold” — school page · Acutonics Canada
Earth Day	194.18 Hz	G	Earth's rotation on its axis24 hours (solar day)	orange-red700 nm	dark green“Green” — school page · Acutonics Canada
Zodiac	172.06 Hz	F	precession of Earth's axis, the “Platonic Year”25 920 years	violet396 nm	blue-violet“Purple” — school page · Acutonics Canada
Sun	126.22 Hz	B	a special case: there is no orbitnot an orbit	yellow-green540 nm	orange“Sunflower Yellow” — school page · Acutonics Canada
New Moon	210.42 Hz	G#	synodic lunar month, from new moon to new moon29.53 days	orange648 nm	blue“Metallic Blue” — school page · Acutonics Canada
Full Moon	227.43 Hz	A#	sidereal lunar month, the Moon's orbit relative to the stars27.32 days	yellow-orange599 nm	white“White” — school page · Acutonics Canada
Mercury	141.27 Hz	C#	orbit around the Sun87.97 days	blue-green483 nm	silver“Silver” — school page · Acutonics Canada
Venus	221.23 Hz	A	orbit around the Sun224.7 days	yellow-orange616 nm	pink“Rose Pink” — school page · Acutonics Canada
Mars	144.72 Hz	D	orbit around the Sun686.98 days	blue471 nm	red“Red” — school page · Acutonics Canada
Jupiter	183.58 Hz	F#	orbit around the Sun11.86 years	red743 nm	dark blue“Ultra Marine Blue” — school page“Cobalt Blue” — Acutonics Canada
Saturn	147.85 Hz	D	orbit around the Sun29.46 years	blue461 nm	brick red“Copper Brown” — school page · Acutonics Canada
Uranus	207.36 Hz	G#	orbit around the Sun84.01 years	orange657 nm	blue“Sky Blue” — school page · Acutonics Canada
Neptune	211.44 Hz	G#	orbit around the Sun164.8 years	orange645 nm	turquoise“Sea Green” — school page · Acutonics Canada
Pluto	140.25 Hz	C#	orbit around the Sun248.4 years (the value Cousto used)	blue-green486 nm	black“Black” — school page · Acutonics Canada
Chiron	172.86 Hz	F	orbit around the Sun: perihelion inside Saturn's orbit, aphelion near Uranus's orbit50.39 years	violet394 nm	none: the green Chiron of the Acutonics school is a different fork with a different tone
Sirius	173.76 Hz	F	mutual orbit of the binary star Sirius A and Sirius B50.13 years	violet392 nm	none: Acutonics has no such fork
Nibiru	not published≈ 161 Hz from a recording	≈ E	not publishednot published	not computed	burgundy“Burgundy Wine” — Acutonics Canada
Sedna	not published≈ 128 Hz from a recording	≈ C	not publishednot published	not computed	black“Copper on Black” — school page“Black with Brown Speckles” — Acutonics Canada

What the columns mean

Frequency is the so-called middle octave: the one that falls within the 120–240 Hz band. This is usually what people mean when they say “the frequency of Venus”. An octave lower or an octave higher, it is still the same planet: dividing or multiplying by two changes the pitch, not the meaning.

Note is calculated against standard tuning, A = 440 Hz, and it almost always lands between notes: planetary frequencies are under no obligation to fall on the keys of a piano. That is why the nearest note depends on the chosen tuning, and sources sometimes give two different notes for the same object — Mercury, for example.

Color is not the paint on the metal but the result of the same technique taken all the way: the frequency keeps being doubled, up into the range of visible light, and you look at the wavelength that comes out. A check that surprised even us: for all fourteen objects, the computed wavelength matched the color printed in Cousto's brochure.

How the Earth year becomes 136.10 Hz

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

The Earth year lasts 31 556 926 seconds, so the frequency of this cycle is one thirty-one-and-a-half-millionth of a hertz, that is 0.000 000 031 7 Hz. Nobody can hear that: human hearing begins at about 20 Hz. But a frequency can be doubled as many times as you like, and every doubling is an octave up — the same note, only higher. After the thirty-second doubling you get 136.10 Hz, a tone that is easy to hear and comfortable to hold near the body.

What can be checked here, and what cannot

Reproducible

Arithmetic you can repeat yourself: the same period and the same formula give the same hertz. It is a statement about a number, not about a person.

Tradition

A system of correspondences with its own inner logic and many years of practice, but no clinical confirmation. Not worse and not better, just a different kind of statement.

Unverified

The number or claim appears in sources, but the original source could not be found.

Every frequency in the table except the Sun has the level “Reproducible”: plain arithmetic derives it from the period, the section's pages recalculate each one on every build of the site, and our guard test compares the result with the published number. The “What tradition ascribes” block on the object pages has the level “Tradition”: it is a system of correspondences, not a measurement. The Sun is marked separately: its frequency was not derived from an orbit, and no formula for it appears in the available sources.

Every frequency calculated, step by step

Open any object and you will see the whole path from period to hertz: the division, the doublings one after another, the note, the tuning and the color. The numbers are real and are filled in right here; nothing is rounded “to look nice”.

Om — 136.10 Hz

Earth's orbit around the Sun

Given: the period of the Earth year (Om)

365.2422 days (tropical year) = 31 556 926 seconds

1The frequency of the cycle itself: how many times it repeats per second

1 ÷ 31 556 926 = 0.000 000 031 689the same in short form: 3.17 × 10⁻⁸ Hz

A tiny number that cannot be heard: human hearing starts at about 20 Hz. But it is a real frequency, and we can keep working with it.

2Raising it into the audible range: each doubling is one octave up

0.000 000 031 689 × 2 = 0.000 000 063 3781st doubling

0.000 000 063 378 × 2 = 0.000 000 126 762nd doubling

0.000 000 126 76 × 2 = 0.000 000 253 513rd doubling

⋮28 more doublings just like these

68.05 × 2 = 136.1032nd doubling: now it is in the middle fork band

Or, in a single line:

0.000 000 031 689 × 2³² = 136.10 Hz

where 2³² = 4 294 967 296, the number of times the frequency has grown

The value Cousto published is 136.10 Hz. It matches.

3Which note it is

12 × log₂(136.10 ÷ 440) = −20.31semitones from A

nearest whole number: −20 = C#and that is the note

remainder: −0.31 of a semitone = −31 centshow far the tone is from the note

One hundred cents make one semitone. Planetary frequencies almost never land exactly on a note: orbits know nothing about musical tuning.

4In which tuning it would be an exact note

136.10 ÷ 2^(−20 ÷ 12) = 432.10 Hz

An ordinary piano is tuned to A = 440 Hz. Here the tone gets a tuning of its own, and for the Om tone it is exactly the much-discussed 432 Hz.

5Color: the same frequency raised all the way to light

136.10 × 2⁴² = 598 583 840 182 535 Hzthat is 5.99 × 10¹⁴ Hz, already visible light

299 792 458 ÷ 598 583 840 182 535 = 501 nmwavelength → blue-green

Divide the speed of light by the frequency and you get the wavelength. This is a model, not the measured color of a planet, but the arithmetic is exactly the same as for sound.

Earth Day — 194.18 Hz

Earth's rotation on its axis

Given: the period of one Earth day

24 hours (solar day) = 86 400 seconds

1The frequency of the cycle itself: how many times it repeats per second

1 ÷ 86 400 = 0.000 011 574the same in short form: 1.16 × 10⁻⁵ Hz

A tiny number that cannot be heard: human hearing starts at about 20 Hz. But it is a real frequency, and we can keep working with it.

2Raising it into the audible range: each doubling is one octave up

0.000 011 574 × 2 = 0.000 023 1481st doubling

0.000 023 148 × 2 = 0.000 046 2962nd doubling

0.000 046 296 × 2 = 0.000 092 5933rd doubling

⋮20 more doublings just like these

97.09 × 2 = 194.1824th doubling: now it is in the middle fork band

Or, in a single line:

0.000 011 574 × 2²⁴ = 194.18 Hz

where 2²⁴ = 16 777 216, the number of times the frequency has grown

The value Cousto published is 194.18 Hz. It matches.

3Which note it is

12 × log₂(194.18 ÷ 440) = −14.16semitones from A

nearest whole number: −14 = Gand that is the note

remainder: −0.16 of a semitone = −16 centshow far the tone is from the note

One hundred cents make one semitone. Planetary frequencies almost never land exactly on a note: orbits know nothing about musical tuning.

4In which tuning it would be an exact note

194.18 ÷ 2^(−14 ÷ 12) = 435.92 Hz

An ordinary piano is tuned to A = 440 Hz. Here the tone gets a tuning of its own, and for the Om tone it is exactly the much-discussed 432 Hz.

5Color: the same frequency raised all the way to light

194.18 × 2⁴¹ = 427 007 964 669 203 Hzthat is 4.27 × 10¹⁴ Hz, already visible light

299 792 458 ÷ 427 007 964 669 203 = 702 nmwavelength → orange-red

Divide the speed of light by the frequency and you get the wavelength. This is a model, not the measured color of a planet, but the arithmetic is exactly the same as for sound.

Zodiac — 172.06 Hz

precession of Earth's axis, the “Platonic Year”

Given: the period of the Platonic Year (Zodiac)

25 920 years = 817 972 992 000 seconds

1The frequency of the cycle itself: how many times it repeats per second

1 ÷ 817 972 992 000 = 0.000 000 000 001 222 5the same in short form: 1.22 × 10⁻¹² Hz

A tiny number that cannot be heard: human hearing starts at about 20 Hz. But it is a real frequency, and we can keep working with it.

2Raising it into the audible range: each doubling is one octave up

0.000 000 000 001 222 5 × 2 = 0.000 000 000 002 445 11st doubling

0.000 000 000 002 445 1 × 2 = 0.000 000 000 004 890 12nd doubling

0.000 000 000 004 890 1 × 2 = 0.000 000 000 009 780 33rd doubling

⋮43 more doublings just like these

86.03 × 2 = 172.0647th doubling: now it is in the middle fork band

Or, in a single line:

0.000 000 000 001 222 5 × 2⁴⁷ = 172.06 Hz

where 2⁴⁷ = 140 737 488 355 328, the number of times the frequency has grown

The value Cousto published is 172.06 Hz. It matches.

3Which note it is

12 × log₂(172.06 ÷ 440) = −16.26semitones from A

nearest whole number: −16 = Fand that is the note

remainder: −0.26 of a semitone = −26 centshow far the tone is from the note

One hundred cents make one semitone. Planetary frequencies almost never land exactly on a note: orbits know nothing about musical tuning.

4In which tuning it would be an exact note

172.06 ÷ 2^(−16 ÷ 12) = 433.55 Hz

An ordinary piano is tuned to A = 440 Hz. Here the tone gets a tuning of its own, and for the Om tone it is exactly the much-discussed 432 Hz.

5Color: the same frequency raised all the way to light

172.06 × 2⁴² = 756 712 050 026 574 Hzthat is 7.57 × 10¹⁴ Hz, already visible light

299 792 458 ÷ 756 712 050 026 574 = 396 nmwavelength → violet

Divide the speed of light by the frequency and you get the wavelength. This is a model, not the measured color of a planet, but the arithmetic is exactly the same as for sound.

New Moon — 210.42 Hz

synodic lunar month, from new moon to new moon

Given: the period of the synodic month (New Moon)

29.53 days = 2 551 443 seconds

1The frequency of the cycle itself: how many times it repeats per second

1 ÷ 2 551 443 = 0.000 000 391 94the same in short form: 3.92 × 10⁻⁷ Hz

A tiny number that cannot be heard: human hearing starts at about 20 Hz. But it is a real frequency, and we can keep working with it.

2Raising it into the audible range: each doubling is one octave up

0.000 000 391 94 × 2 = 0.000 000 783 871st doubling

0.000 000 783 87 × 2 = 0.000 001 567 72nd doubling

0.000 001 567 7 × 2 = 0.000 003 135 53rd doubling

⋮25 more doublings just like these

105.21 × 2 = 210.4229th doubling: now it is in the middle fork band

Or, in a single line:

0.000 000 391 94 × 2²⁹ = 210.42 Hz

where 2²⁹ = 536 870 912, the number of times the frequency has grown

The value Cousto published is 210.42 Hz. It matches.

3Which note it is

12 × log₂(210.42 ÷ 440) = −12.77semitones from A

nearest whole number: −13 = G#and that is the note

remainder: 0.23 of a semitone = 23 centshow far the tone is from the note

One hundred cents make one semitone. Planetary frequencies almost never land exactly on a note: orbits know nothing about musical tuning.

4In which tuning it would be an exact note

210.42 ÷ 2^(−13 ÷ 12) = 445.86 Hz

An ordinary piano is tuned to A = 440 Hz. Here the tone gets a tuning of its own, and for the Om tone it is exactly the much-discussed 432 Hz.

5Color: the same frequency raised all the way to light

210.42 × 2⁴¹ = 462 715 268 113 996 Hzthat is 4.63 × 10¹⁴ Hz, already visible light

299 792 458 ÷ 462 715 268 113 996 = 648 nmwavelength → orange

Divide the speed of light by the frequency and you get the wavelength. This is a model, not the measured color of a planet, but the arithmetic is exactly the same as for sound.

Full Moon — 227.43 Hz

sidereal lunar month, the Moon's orbit relative to the stars

Given: the period of the sidereal month (Full Moon)

27.32 days = 2 360 591 seconds

1The frequency of the cycle itself: how many times it repeats per second

1 ÷ 2 360 591 = 0.000 000 423 62the same in short form: 4.24 × 10⁻⁷ Hz

A tiny number that cannot be heard: human hearing starts at about 20 Hz. But it is a real frequency, and we can keep working with it.

2Raising it into the audible range: each doubling is one octave up

0.000 000 423 62 × 2 = 0.000 000 847 251st doubling

0.000 000 847 25 × 2 = 0.000 001 694 52nd doubling

0.000 001 694 5 × 2 = 0.000 003 389 03rd doubling

⋮25 more doublings just like these

113.72 × 2 = 227.4329th doubling: now it is in the middle fork band

Or, in a single line:

0.000 000 423 62 × 2²⁹ = 227.43 Hz

where 2²⁹ = 536 870 912, the number of times the frequency has grown

The value Cousto published is 227.43 Hz. It matches.

3Which note it is

12 × log₂(227.43 ÷ 440) = −11.42semitones from A

nearest whole number: −11 = A#and that is the note

remainder: −0.42 of a semitone = −42 centshow far the tone is from the note

One hundred cents make one semitone. Planetary frequencies almost never land exactly on a note: orbits know nothing about musical tuning.

4In which tuning it would be an exact note

227.43 ÷ 2^(−11 ÷ 12) = 429.33 Hz

An ordinary piano is tuned to A = 440 Hz. Here the tone gets a tuning of its own, and for the Om tone it is exactly the much-discussed 432 Hz.

5Color: the same frequency raised all the way to light

227.43 × 2⁴¹ = 500 125 353 635 705 Hzthat is 5.00 × 10¹⁴ Hz, already visible light

299 792 458 ÷ 500 125 353 635 705 = 599 nmwavelength → yellow-orange

Divide the speed of light by the frequency and you get the wavelength. This is a model, not the measured color of a planet, but the arithmetic is exactly the same as for sound.

Mercury — 141.27 Hz

orbit around the Sun

Given: the period of Mercury

87.97 days = 7 600 522 seconds

1The frequency of the cycle itself: how many times it repeats per second

1 ÷ 7 600 522 = 0.000 000 131 57the same in short form: 1.32 × 10⁻⁷ Hz

A tiny number that cannot be heard: human hearing starts at about 20 Hz. But it is a real frequency, and we can keep working with it.

2Raising it into the audible range: each doubling is one octave up

0.000 000 131 57 × 2 = 0.000 000 263 141st doubling

0.000 000 263 14 × 2 = 0.000 000 526 282nd doubling

0.000 000 526 28 × 2 = 0.000 001 052 63rd doubling

⋮26 more doublings just like these

70.64 × 2 = 141.2730th doubling: now it is in the middle fork band

Or, in a single line:

0.000 000 131 57 × 2³⁰ = 141.27 Hz

where 2³⁰ = 1 073 741 824, the number of times the frequency has grown

The value Cousto published is 141.27 Hz. It matches.

3Which note it is

12 × log₂(141.27 ÷ 440) = −19.67semitones from A

nearest whole number: −20 = C#and that is the note

remainder: 0.33 of a semitone = 33 centshow far the tone is from the note

One hundred cents make one semitone. Planetary frequencies almost never land exactly on a note: orbits know nothing about musical tuning.

4In which tuning it would be an exact note

141.27 ÷ 2^(−20 ÷ 12) = 448.51 Hz

An ordinary piano is tuned to A = 440 Hz. Here the tone gets a tuning of its own, and for the Om tone it is exactly the much-discussed 432 Hz.

5Color: the same frequency raised all the way to light

141.27 × 2⁴² = 621 321 368 637 337 Hzthat is 6.21 × 10¹⁴ Hz, already visible light

299 792 458 ÷ 621 321 368 637 337 = 483 nmwavelength → blue-green

Divide the speed of light by the frequency and you get the wavelength. This is a model, not the measured color of a planet, but the arithmetic is exactly the same as for sound.

Venus — 221.23 Hz

orbit around the Sun

Given: the period of Venus

224.7 days = 19 414 166 seconds

1The frequency of the cycle itself: how many times it repeats per second

1 ÷ 19 414 166 = 0.000 000 051 509the same in short form: 5.15 × 10⁻⁸ Hz

A tiny number that cannot be heard: human hearing starts at about 20 Hz. But it is a real frequency, and we can keep working with it.

2Raising it into the audible range: each doubling is one octave up

0.000 000 051 509 × 2 = 0.000 000 103 021st doubling

0.000 000 103 02 × 2 = 0.000 000 206 042nd doubling

0.000 000 206 04 × 2 = 0.000 000 412 073rd doubling

⋮28 more doublings just like these

110.61 × 2 = 221.2332nd doubling: now it is in the middle fork band

Or, in a single line:

0.000 000 051 509 × 2³² = 221.23 Hz

where 2³² = 4 294 967 296, the number of times the frequency has grown

The value Cousto published is 221.23 Hz. It matches.

3Which note it is

12 × log₂(221.23 ÷ 440) = −11.90semitones from A

nearest whole number: −12 = Aand that is the note

remainder: 0.10 of a semitone = 10 centshow far the tone is from the note

One hundred cents make one semitone. Planetary frequencies almost never land exactly on a note: orbits know nothing about musical tuning.

4In which tuning it would be an exact note

221.23 ÷ 2^(−12 ÷ 12) = 442.46 Hz

An ordinary piano is tuned to A = 440 Hz. Here the tone gets a tuning of its own, and for the Om tone it is exactly the much-discussed 432 Hz.

5Color: the same frequency raised all the way to light

221.23 × 2⁴¹ = 486 486 659 851 607 Hzthat is 4.86 × 10¹⁴ Hz, already visible light

299 792 458 ÷ 486 486 659 851 607 = 616 nmwavelength → yellow-orange

Divide the speed of light by the frequency and you get the wavelength. This is a model, not the measured color of a planet, but the arithmetic is exactly the same as for sound.

Mars — 144.72 Hz

orbit around the Sun

Given: the period of Mars

686.98 days = 59 355 072 seconds

1The frequency of the cycle itself: how many times it repeats per second

1 ÷ 59 355 072 = 0.000 000 016 848the same in short form: 1.68 × 10⁻⁸ Hz

A tiny number that cannot be heard: human hearing starts at about 20 Hz. But it is a real frequency, and we can keep working with it.

2Raising it into the audible range: each doubling is one octave up

0.000 000 016 848 × 2 = 0.000 000 033 6961st doubling

0.000 000 033 696 × 2 = 0.000 000 067 3912nd doubling

0.000 000 067 391 × 2 = 0.000 000 134 783rd doubling

⋮29 more doublings just like these

72.36 × 2 = 144.7233rd doubling: now it is in the middle fork band

Or, in a single line:

0.000 000 016 848 × 2³³ = 144.72 Hz

where 2³³ = 8 589 934 592, the number of times the frequency has grown

The value Cousto published is 144.72 Hz. It matches.

3Which note it is

12 × log₂(144.72 ÷ 440) = −19.25semitones from A

nearest whole number: −19 = Dand that is the note

remainder: −0.25 of a semitone = −25 centshow far the tone is from the note

One hundred cents make one semitone. Planetary frequencies almost never land exactly on a note: orbits know nothing about musical tuning.

4In which tuning it would be an exact note

144.72 ÷ 2^(−19 ÷ 12) = 433.67 Hz

An ordinary piano is tuned to A = 440 Hz. Here the tone gets a tuning of its own, and for the Om tone it is exactly the much-discussed 432 Hz.

5Color: the same frequency raised all the way to light

144.72 × 2⁴² = 636 490 372 094 185 Hzthat is 6.36 × 10¹⁴ Hz, already visible light

299 792 458 ÷ 636 490 372 094 185 = 471 nmwavelength → blue

Divide the speed of light by the frequency and you get the wavelength. This is a model, not the measured color of a planet, but the arithmetic is exactly the same as for sound.

Jupiter — 183.58 Hz

orbit around the Sun

Given: the period of Jupiter

11.86 years = 374 336 251 seconds

1The frequency of the cycle itself: how many times it repeats per second

1 ÷ 374 336 251 = 0.000 000 002 671 4the same in short form: 2.67 × 10⁻⁹ Hz

A tiny number that cannot be heard: human hearing starts at about 20 Hz. But it is a real frequency, and we can keep working with it.

2Raising it into the audible range: each doubling is one octave up

0.000 000 002 671 4 × 2 = 0.000 000 005 342 81st doubling

0.000 000 005 342 8 × 2 = 0.000 000 010 6862nd doubling

0.000 000 010 686 × 2 = 0.000 000 021 3713rd doubling

⋮32 more doublings just like these

91.79 × 2 = 183.5836th doubling: now it is in the middle fork band

Or, in a single line:

0.000 000 002 671 4 × 2³⁶ = 183.58 Hz

where 2³⁶ = 68 719 476 736, the number of times the frequency has grown

The value Cousto published is 183.58 Hz. It matches.

3Which note it is

12 × log₂(183.58 ÷ 440) = −15.13semitones from A

nearest whole number: −15 = F#and that is the note

remainder: −0.13 of a semitone = −13 centshow far the tone is from the note

One hundred cents make one semitone. Planetary frequencies almost never land exactly on a note: orbits know nothing about musical tuning.

4In which tuning it would be an exact note

183.58 ÷ 2^(−15 ÷ 12) = 436.62 Hz

An ordinary piano is tuned to A = 440 Hz. Here the tone gets a tuning of its own, and for the Om tone it is exactly the much-discussed 432 Hz.

5Color: the same frequency raised all the way to light

183.58 × 2⁴¹ = 403 689 802 864 139 Hzthat is 4.04 × 10¹⁴ Hz, already visible light

299 792 458 ÷ 403 689 802 864 139 = 743 nmwavelength → red

Divide the speed of light by the frequency and you get the wavelength. This is a model, not the measured color of a planet, but the arithmetic is exactly the same as for sound.

Saturn — 147.85 Hz

orbit around the Sun

Given: the period of Saturn

29.46 years = 929 592 223 seconds

1The frequency of the cycle itself: how many times it repeats per second

1 ÷ 929 592 223 = 0.000 000 001 075 7the same in short form: 1.08 × 10⁻⁹ Hz

A tiny number that cannot be heard: human hearing starts at about 20 Hz. But it is a real frequency, and we can keep working with it.

2Raising it into the audible range: each doubling is one octave up

0.000 000 001 075 7 × 2 = 0.000 000 002 151 51st doubling

0.000 000 002 151 5 × 2 = 0.000 000 004 303 02nd doubling

0.000 000 004 303 0 × 2 = 0.000 000 008 605 93rd doubling

⋮33 more doublings just like these

73.92 × 2 = 147.8537th doubling: now it is in the middle fork band

Or, in a single line:

0.000 000 001 075 7 × 2³⁷ = 147.85 Hz

where 2³⁷ = 137 438 953 472, the number of times the frequency has grown

The value Cousto published is 147.85 Hz. It matches.

3Which note it is

12 × log₂(147.85 ÷ 440) = −18.88semitones from A

nearest whole number: −19 = Dand that is the note

remainder: 0.12 of a semitone = 12 centshow far the tone is from the note

One hundred cents make one semitone. Planetary frequencies almost never land exactly on a note: orbits know nothing about musical tuning.

4In which tuning it would be an exact note

147.85 ÷ 2^(−19 ÷ 12) = 443.05 Hz

An ordinary piano is tuned to A = 440 Hz. Here the tone gets a tuning of its own, and for the Om tone it is exactly the much-discussed 432 Hz.

5Color: the same frequency raised all the way to light

147.85 × 2⁴² = 650 245 230 889 013 Hzthat is 6.50 × 10¹⁴ Hz, already visible light

299 792 458 ÷ 650 245 230 889 013 = 461 nmwavelength → blue

Divide the speed of light by the frequency and you get the wavelength. This is a model, not the measured color of a planet, but the arithmetic is exactly the same as for sound.

Uranus — 207.36 Hz

orbit around the Sun

Given: the period of Uranus

84.01 years = 2 651 218 560 seconds

1The frequency of the cycle itself: how many times it repeats per second

1 ÷ 2 651 218 560 = 0.000 000 000 377 19the same in short form: 3.77 × 10⁻¹⁰ Hz

A tiny number that cannot be heard: human hearing starts at about 20 Hz. But it is a real frequency, and we can keep working with it.

2Raising it into the audible range: each doubling is one octave up

0.000 000 000 377 19 × 2 = 0.000 000 000 754 371st doubling

0.000 000 000 754 37 × 2 = 0.000 000 001 508 72nd doubling

0.000 000 001 508 7 × 2 = 0.000 000 003 017 53rd doubling

⋮35 more doublings just like these

103.68 × 2 = 207.3639th doubling: now it is in the middle fork band

Or, in a single line:

0.000 000 000 377 19 × 2³⁹ = 207.36 Hz

where 2³⁹ = 549 755 813 888, the number of times the frequency has grown

The value Cousto published is 207.36 Hz. It matches.

3Which note it is

12 × log₂(207.36 ÷ 440) = −13.02semitones from A

nearest whole number: −13 = G#and that is the note

remainder: −0.02 of a semitone = −2 centshow far the tone is from the note

One hundred cents make one semitone. Planetary frequencies almost never land exactly on a note: orbits know nothing about musical tuning.

4In which tuning it would be an exact note

207.36 ÷ 2^(−13 ÷ 12) = 439.38 Hz

An ordinary piano is tuned to A = 440 Hz. Here the tone gets a tuning of its own, and for the Om tone it is exactly the much-discussed 432 Hz.

5Color: the same frequency raised all the way to light

207.36 × 2⁴¹ = 455 988 743 385 468 Hzthat is 4.56 × 10¹⁴ Hz, already visible light

299 792 458 ÷ 455 988 743 385 468 = 657 nmwavelength → orange

Divide the speed of light by the frequency and you get the wavelength. This is a model, not the measured color of a planet, but the arithmetic is exactly the same as for sound.

Neptune — 211.44 Hz

orbit around the Sun

Given: the period of the planet Neptune

164.8 years = 5 200 212 096 seconds

1The frequency of the cycle itself: how many times it repeats per second

1 ÷ 5 200 212 096 = 0.000 000 000 192 30the same in short form: 1.92 × 10⁻¹⁰ Hz

A tiny number that cannot be heard: human hearing starts at about 20 Hz. But it is a real frequency, and we can keep working with it.

2Raising it into the audible range: each doubling is one octave up

0.000 000 000 192 30 × 2 = 0.000 000 000 384 601st doubling

0.000 000 000 384 60 × 2 = 0.000 000 000 769 202nd doubling

0.000 000 000 769 20 × 2 = 0.000 000 001 538 43rd doubling

⋮36 more doublings just like these

105.72 × 2 = 211.4440th doubling: now it is in the middle fork band

Or, in a single line:

0.000 000 000 192 30 × 2⁴⁰ = 211.44 Hz

where 2⁴⁰ = 1 099 511 627 776, the number of times the frequency has grown

The value Cousto published is 211.44 Hz. It matches.

3Which note it is

12 × log₂(211.44 ÷ 440) = −12.69semitones from A

nearest whole number: −13 = G#and that is the note

remainder: 0.31 of a semitone = 31 centshow far the tone is from the note

One hundred cents make one semitone. Planetary frequencies almost never land exactly on a note: orbits know nothing about musical tuning.

4In which tuning it would be an exact note

211.44 ÷ 2^(−13 ÷ 12) = 448.02 Hz

An ordinary piano is tuned to A = 440 Hz. Here the tone gets a tuning of its own, and for the Om tone it is exactly the much-discussed 432 Hz.

5Color: the same frequency raised all the way to light

211.44 × 2⁴¹ = 464 952 504 742 849 Hzthat is 4.65 × 10¹⁴ Hz, already visible light

299 792 458 ÷ 464 952 504 742 849 = 645 nmwavelength → orange

Divide the speed of light by the frequency and you get the wavelength. This is a model, not the measured color of a planet, but the arithmetic is exactly the same as for sound.

Pluto — 140.25 Hz

orbit around the Sun

Given: the period of Pluto

248.4 years (the value Cousto used) = 7 839 694 080 seconds

1The frequency of the cycle itself: how many times it repeats per second

1 ÷ 7 839 694 080 = 0.000 000 000 127 56the same in short form: 1.28 × 10⁻¹⁰ Hz

A tiny number that cannot be heard: human hearing starts at about 20 Hz. But it is a real frequency, and we can keep working with it.

2Raising it into the audible range: each doubling is one octave up

0.000 000 000 127 56 × 2 = 0.000 000 000 255 111st doubling

0.000 000 000 255 11 × 2 = 0.000 000 000 510 222nd doubling

0.000 000 000 510 22 × 2 = 0.000 000 001 020 43rd doubling

⋮36 more doublings just like these

70.12 × 2 = 140.2540th doubling: now it is in the middle fork band

Or, in a single line:

0.000 000 000 127 56 × 2⁴⁰ = 140.25 Hz

where 2⁴⁰ = 1 099 511 627 776, the number of times the frequency has grown

The value Cousto published is 140.25 Hz. It matches.

3Which note it is

12 × log₂(140.25 ÷ 440) = −19.79semitones from A

nearest whole number: −20 = C#and that is the note

remainder: 0.21 of a semitone = 21 centshow far the tone is from the note

One hundred cents make one semitone. Planetary frequencies almost never land exactly on a note: orbits know nothing about musical tuning.

4In which tuning it would be an exact note

140.25 ÷ 2^(−20 ÷ 12) = 445.26 Hz

An ordinary piano is tuned to A = 440 Hz. Here the tone gets a tuning of its own, and for the Om tone it is exactly the much-discussed 432 Hz.

5Color: the same frequency raised all the way to light

140.25 × 2⁴² = 616 822 956 242 001 Hzthat is 6.17 × 10¹⁴ Hz, already visible light

299 792 458 ÷ 616 822 956 242 001 = 486 nmwavelength → blue-green

Divide the speed of light by the frequency and you get the wavelength. This is a model, not the measured color of a planet, but the arithmetic is exactly the same as for sound.

Chiron — 172.86 Hz

orbit around the Sun: perihelion inside Saturn's orbit, aphelion near Uranus's orbit

Given: the period of Chiron

50.39 years = 1 590 187 464 seconds

1The frequency of the cycle itself: how many times it repeats per second

1 ÷ 1 590 187 464 = 0.000 000 000 628 86the same in short form: 6.29 × 10⁻¹⁰ Hz

A tiny number that cannot be heard: human hearing starts at about 20 Hz. But it is a real frequency, and we can keep working with it.

2Raising it into the audible range: each doubling is one octave up

0.000 000 000 628 86 × 2 = 0.000 000 001 257 71st doubling

0.000 000 001 257 7 × 2 = 0.000 000 002 515 42nd doubling

0.000 000 002 515 4 × 2 = 0.000 000 005 030 93rd doubling

⋮34 more doublings just like these

86.43 × 2 = 172.8638th doubling: now it is in the middle fork band

Or, in a single line:

0.000 000 000 628 86 × 2³⁸ = 172.86 Hz

where 2³⁸ = 274 877 906 944, the number of times the frequency has grown

The value Cousto published is 172.86 Hz. It matches.

3Which note it is

12 × log₂(172.86 ÷ 440) = −16.17semitones from A

nearest whole number: −16 = Fand that is the note

remainder: −0.17 of a semitone = −17 centshow far the tone is from the note

One hundred cents make one semitone. Planetary frequencies almost never land exactly on a note: orbits know nothing about musical tuning.

4In which tuning it would be an exact note

172.86 ÷ 2^(−16 ÷ 12) = 435.58 Hz

An ordinary piano is tuned to A = 440 Hz. Here the tone gets a tuning of its own, and for the Om tone it is exactly the much-discussed 432 Hz.

5Color: the same frequency raised all the way to light

172.86 × 2⁴² = 760 241 070 303 538 Hzthat is 7.60 × 10¹⁴ Hz, already visible light

299 792 458 ÷ 760 241 070 303 538 = 394 nmwavelength → violet

Divide the speed of light by the frequency and you get the wavelength. This is a model, not the measured color of a planet, but the arithmetic is exactly the same as for sound.

Sirius — 173.76 Hz

mutual orbit of the binary star Sirius A and Sirius B

Given: the period of the binary star Sirius

50.13 years = 1 581 931 996 seconds

1The frequency of the cycle itself: how many times it repeats per second

1 ÷ 1 581 931 996 = 0.000 000 000 632 14the same in short form: 6.32 × 10⁻¹⁰ Hz

A tiny number that cannot be heard: human hearing starts at about 20 Hz. But it is a real frequency, and we can keep working with it.

2Raising it into the audible range: each doubling is one octave up

0.000 000 000 632 14 × 2 = 0.000 000 001 264 31st doubling

0.000 000 001 264 3 × 2 = 0.000 000 002 528 62nd doubling

0.000 000 002 528 6 × 2 = 0.000 000 005 057 13rd doubling

⋮34 more doublings just like these

86.88 × 2 = 173.7638th doubling: now it is in the middle fork band

Or, in a single line:

0.000 000 000 632 14 × 2³⁸ = 173.76 Hz

where 2³⁸ = 274 877 906 944, the number of times the frequency has grown

The value Cousto published is 173.76 Hz. It matches.

3Which note it is

12 × log₂(173.76 ÷ 440) = −16.08semitones from A

nearest whole number: −16 = Fand that is the note

remainder: −0.08 of a semitone = −8 centshow far the tone is from the note

One hundred cents make one semitone. Planetary frequencies almost never land exactly on a note: orbits know nothing about musical tuning.

4In which tuning it would be an exact note

173.76 ÷ 2^(−16 ÷ 12) = 437.85 Hz

An ordinary piano is tuned to A = 440 Hz. Here the tone gets a tuning of its own, and for the Om tone it is exactly the much-discussed 432 Hz.

5Color: the same frequency raised all the way to light

173.76 × 2⁴² = 764 208 463 318 105 Hzthat is 7.64 × 10¹⁴ Hz, already visible light

299 792 458 ÷ 764 208 463 318 105 = 392 nmwavelength → violet

Divide the speed of light by the frequency and you get the wavelength. This is a model, not the measured color of a planet, but the arithmetic is exactly the same as for sound.

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