**Pendulum for celestial rhythms**

**For a given length from the suspension to the center of gravity, a pendulum swings back and forth at a given frequency (frequency per unit time).**

Regardless of whether the pendulum swing is wide or small, the frequency of the back-and-forth swing is always the same for a given length.

The longer a pendulum is, the lower the frequency with which it swings back and forth.

The formula for calculating the so-called mathematical pendulum (string pendulum) was discovered by the Italian scientist Galileo Galilei after he observed the movements of the lamps hung there in different lengths in a church.

He recognized the connection of gravitational acceleration (which is 981 centimeters per second squared on the earth's surface), pendulum length and oscillation time.

**A quarter of a pendulum length oscillates with twice the frequency !**

The pendulum formula

(from the book "Die Kosmische Oktave" by Hans Cousto):

It is

g = 981 cm ^{. }sec ^{-2} = Acceleration due to gravity*L*
= the length of the pendulum (suspension to the center of mass)

π = 3.14159 Pi

T = Duration of a complete oscillation period (back and forth).

It goes:

T = 2 ^{.} π^{ .} √ (l:g) = 2 ^{.} π ^{.} L ^{-0,5 .} g^{0,5}

In our case, T and g are known, and the length L is the quantity we are looking for, so the equation must be solved for L. To do this, the equation is first squared:

T^{2} = 4 ^{.} π^{2 .} *L*^{ .} g^{-1}

This equation is now solved for L:

*L* = T^{2 .} g^{ . }π^{-2 . }0.25 = T^{2 . }g : (4^{ . }π^{2})

Any value for T can now be inserted into this equation, whereby the equation can still be transformed expediently beforehand:

*L*= T^{2 .} g^{ . }π^{-2 . }0.25 = T^{2 . }24.85 cm^{ . }sec^{-2}

Only the time has to be squared and multiplied by 24.85 cm . sec-2 and the result, the pendulum length, is known. However, one can also divide the number 24.85 cm . sec-2 by the square of the frequency f and likewise obtain the desired pendulum length.

The 16th octave of the synodic solar day corresponds to the time:

T = 86400 sec ^{. }2^{-16} = 1.31836 sec

and the frequency

f = 86400^{-1 . }2^{16} = 0.7585 Hz

and so the corresponding pendulum length is:

*L* = 1.31836^{2} sec^{2 .} 24.85 cm^{ . }sec^{-2} = 43.2 cm

*L* = 24.85 cm^{ . }sec^{-2 . }0.7585^{-2}sec^{2} = 43.2 cm

In the table "Planets - Sounds - Colors — Meters" the pendulum lengths of the different cycles of the earth, the moon, the planets and the sun are listed.

With a quarter of the pendulum length a pendulum swings back and forth with double frequency, with four times the length with half frequency !

Cosmic Pendulum Mass Tape

to print, cut out and glue (on a cardboard or wooden strip):

Download here as PDF