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New Moon tuning fork — 210.42 Hz

210.42 Hz is the tone of the synodic lunar month: the 29.53 days from one new moon to the next. It is the very cycle a lunar calendar follows, which is why the fork is called “New Moon”.

A young Moon as a thin crescent, the start of the synodic month that gives 210.42 Hz
A young Moon as a thin crescent, the start of the synodic month that gives 210.42 Hz · NASA/GSFC, public domain
Frequency (middle octave)210.42 Hz
NoteG# · +23 cents from standard tuning A = 440 Hz
Tuning in which this is an exact noteA = 445.86 Hz
Cyclesynodic lunar month, from new moon to new moon29.53 days
Doublings from the cycle's frequency29
Color (the same frequency as light)orange · 648 nm
Paint on the Acutonics tuning forkblueshade measured from photos in the school's catalog — this is NOT the computed colorcolor name “Metallic Blue” — school page · Acutonics Canada
What can be checkedReproducible

Paired with Om, this tone gives the “New Moon 5” interval, which in Acutonics is considered the main “opening” interval and is often placed at the start of a session. It is called a fifth because of its notes: C sharp and G sharp really are a fifth apart. But the Om tone sits below its note and the New Moon tone above its own, so in actual sound the frequency ratio comes out at 1.546 instead of a clean 1.5, almost halfway between a fifth and a minor sixth.

The fork has two “official” colors, and for anyone putting a set together by color that is no small detail: by wavelength its color is orange, while the school paints its own fork metallic blue, which is the color name on its product page. The first is computed from the frequency; the second was chosen by a person.

How this number is obtained

middle fork band, 120–240 Hzstart8 doublings16 doublings24 doublings210.42 Hz0.000 000 392 Hz: the frequency of the cycle itself29 doublings → note G#
The axis is logarithmic: each doubling raises the sound by exactly one octave. The pitch goes up, the note stays the same.
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.

Octave ladder

OctaveFrequencyHow it is used
2^2626.30 Hzbelow or at the edge of hearing
2^2752.60 Hzbelow or at the edge of hearing
2^28105.21 Hzlow: stronger vibration on the body
2^29210.42 Hzthe main tuning fork
2^30420.84 Hzhigh: work in the field above the body
2^31841.67 Hzhigh: work in the field above the body

Two values, and both are “official”

fork color: orange (by wavelength, 648 nm) (Cousto) and metallic blue (the Acutonics school itself: the color name on the page for its hand chime).

The first color is computed from the frequency; the second is the paint the school chose for its fork. They are different things, and they get mixed up all the time.

the school's New Moon hand chime

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What tradition ascribes

Tradition

Beginnings, intention, yin. The sacral chakra.

This is a system of correspondences, not the result of a measurement: controlled studies of planetary frequencies do not exist. We present the tradition because it exists and the practice is built on it — but we call it tradition.

Intervals with this tone

IntervalPairRatioDifference
New Moon 5Om + New Moon1.54674.32 Hz
Sun + MoonSun + New Moon1.66784.20 Hz

All frequencies in one chart · how the calculation works · what has been proven