Sumerian Cyclical Tuning System & 432

After studying the cuneiform tablets it was clear the system they were using was of simple, symmetric beauty. Switching to a different key was as easy as turning one of the pegs.

This made sense to me from the standpoint of being a guitar player - If I want to switch to a different key {on an instrument already laid out in equal temperament} i just change one note in the mode i am playing.

The changing of one note/peg is the exact same concept.

One thing I did think was of great interest when studying the tablets on the cyclical lyre tuning system was that the central note had to be the 2nd mode of the 'scale' you were devising, in order for the symmetry of the system to work properly. I didn't know why it was or what it meant... Only that in our modern system this means that the central note would have to be the DORIAN mode, in order to generate the standard 'western-scale' IONIAN mode. I figured I'd just keep an eye out for that to pop up again somewhere else...

I decided to make the image below to graphically outline the process ->

so simple. so symmetric. so beautiful.

The next question i asked myself was, "How does this apply to the 'equal temperament' we use today?" I figured I could probably just use the same system used for the lyre, and just apply it to an unknown octave of 12.

The kicker was using the frequency of 432 as the starting point. I had no idea what I was going to find, but i had a gut feeling telling me to keep going and incorporate 432.

Part 1 - So starting with the Sumerian cyclical tuning system I learned through the lyre, I determined that p5 (perfect fifth) & p4 (perfect fourth) are reciprocals & will result in the same number if you alternate between dividing with the one, and multiplying with the other, respectively.

I could easily see the numbers 144, 72, 36, 18, 9 popping up for the key of 'D'. I recognized 162 from Plato's Lambda sitting in the key of "E". The first thing that came to mind was a random scene from the bible about nets, catching and an overflow:

Luke 5:5 & 5:6 -

"Master, we’ve worked hard all night and haven’t caught anything. But because you say so, I will let down the nets. When they had done so, they caught such a large number of fish that their nets began to break."

My net was breaking. I continued the process to step 6. Once I got to the middle, I wondered to myself - What's the next step ?

I need to, at least, verify that these numbers are right, that I didn't fudge a number somewhere. I was kinda amazed to see every one of the numbers from Plato's Lambda clearly encoded in the system.

It made me go back and re-read Plato again -

... from Timaeus, by Plato, 360 BC ...

""First of all, he took away one part of the whole [1], and then he separated a second part which was double the first [2], and then he took away a third part which was half as much again as the second and three times as much as the first [3], and then he took a fourth part which was twice as much as the second [4], and a fifth part which was three times the third [9], and a sixth part which was eight times the first [8], and a seventh part which was twenty-seven times the first [27].

After this he filled up the double intervals [i.e. between 1, 2, 4, 8] and the triple [i.e. between 1, 3, 9, 27] cutting off yet other portions from the mixture and placing them in the intervals, so that in each interval there were two kinds of means, the one exceeding and exceeded by equal parts of its extremes [as for example 1, 4/3, 2, in which the mean 4/3 is one-third of 1 more than 1, and one-third of 2 less than 2], the other being that kind of mean which exceeds and is exceeded by an equal number.

Where there were intervals of 3/2 and of 4/3 and of 9/8, made by the connecting terms in the former intervals, he filled up all the intervals of 4/3 with the interval of 9/8, leaving a fraction over; and the interval which this fraction expressed was in the ratio of 256 to 243.""

The exact ratio mentioned by Plato of 256:243 (C:B) was encoded here in this cyclical 432 tuning system.

The next step was to tackle the TRITONE location in the middle of the system. I knew from Pythagoras that we were probably looking for whole number simplicity. I knew from Plato's Lambda that you can approach averages in 3 separate ways, so i figured on the basic numeric average of A+B/2=C. The first location that will yield a whole number in this way = 144+162 = 306/2 = 153.

wow. 153. I'm pretty sure the 1st quote that came to my head after figuring this out was the OTHER scene of Jesus doing some fishing:

JOHN 21:11 -

"So Simon Peter climbed back into the boat and dragged the net ashore. It was full of large fish, 153, but even with so many the net was not torn."

√153 = The number of full moon's per year. Stonehenge incorporates that proportion in conjunction with the Perfect Fifth interval. The cubes of 1, 3 & 5 = 153. The vesica pisces is approximated by 265/153. This is too much 'coincidence' to ignore...

... you could also take the octave before - use the 2 numbers above:below, in this case 72 & 81 -> average those, 153 again

... see the next octave above pull the same 306 from the offset below (144+162/2), then repeating :)

ahh, the symmetry is astounding


There's something really weird happening in the TRITONE location. See how it is mirroring the offset row of the key of 'G'. I have no idea how or why it is doing this. just an observation...

Squaring & Cubing -->

... add a few more columns ...

I'd seen the 'Most Harmonic Numbers' chart floating around for a while, and realized it didn't tell the whole story. We were missing a few keys. There was an easy way to figure it out - just continue the grid... The remaining keys continue to show up, in a clockwise fashion, from around the perimeter of the 'circle of fifths'.

A second method to prove the value of the TRITONE at 153 is to take the column containing 19,683 (D#), and lower it by 7 octaves.

Looking at it a little deeper, I realized there was a "model' to the squaring and cubing of numbers, as it relates to music and geometry...

You can also see the digit sums adding to 9 for every column, except for G (3 & 6 alternating), and the key of C (1,2,4,8,7,5 repeating torus pattern/Rodin coil).

Here's a brief snippet of the Rodin Coil/Torus -

Just notice the repeating 1,2,4,8,7,5 = the key of C {digit sums}

Definitely something going on here, i thought to myself... Numbers in flow...

A computer, or more specifically all of our digital interactions are just numbers in flow ...

All computer systems would then be seen to run in the key of C

The essence of Binary --> 1-2-4-8-16-32-64-128-256-512-1024-2048-4096

Clocks and watches that use quartz are in the key of C ....

The doctor uses 'scientific pitch' tuning forks to test your hearing in the key of C ...

This means "scientific pitch" is encoded in the ancient cyclical 432 tuning system !

The Octave {2:1} -->

double to that which is = an octave

This 432 cyclical tuning system also approximates many micro-tone intervals -->

The dissonance generated by attempting to spiral, by perfect fifths, towards a pure octave, is known as the Pythagorean Comma. This dissonance is justified - as the method is inadequate.

The Pythagorean Comma, generated by spiral tuning -> they say it's a ratio of 531,441:524,288 {1.013}. An equal temperament half-step is 1.059, so that means a Pythagorean Comma is smaller than a regular half-step.

Notice that when you reduce by 7 octaves the latter part of the proportion (524,288) you get 4096 - An actual frequency in the 432 system - The key of C.

..."The first to mention the comma's proportion of (531441:524288) was Euclid, who takes as a basis the whole tone of Pythagorean tuning with the ratio of 9:8, the octave with the ratio of 2:1, and a number A = 262,144." ...

Notice that when you reduce by 6 octaves the proportion attributed to Euclid (262,144) you get the same 4096 - An actual frequency in the 432 system - The key of C.

... "Chinese mathematicians had been aware of the Pythagorean comma as early as 122 BC (its calculation is detailed in the Huainanzi), and circa 50 BC, Ching Fang discovered that if the cycle of perfect fifths were continued beyond 12 all the way to 53, the difference between this 53rd pitch and the starting pitch would be much smaller than the Pythagorean comma. This much smaller interval was later named Mercator's Comma." ...

... "Mercator also considered that an "artificial comma" of 53√2 might be useful, because 31 octaves could be practically approximated by a cycle of 53 just fifths.' ...

Notice in the 11th position, the proportion is 86.4 -->

Trying to generate harmony in the first octave by using the Pythagorean Spiral will always fail. This is because of not properly contending with the Octave & √2.

This classical spiral system does not take the Fundamental Universal Law of the Harmonic Overtone Series into account. This is the whole reason for the generation of the Pythagorean Comma in the first place.

This is where the Sumerian Cyclical system shows it's real strength - It's basic tenant is the Octave is a Universal and must be observed.

In this way, a framework is built, and then the whole octave is subdivided into 11 additional equal sections by using the Perfect Fifth & Perfect Fourth reciprocal intervals {1.5, 1.33}. These equal sections, when seen as reciprocals of each other, strike out from either the higher octave downwards or from the lower octave upwards to arrive at the same location.

Continuing in this way you "paint yourself into the middle", as it were, and end up being in the middle of the system at the √2 position, with 5 notes above & 5 notes below {5+1+5=11} {plus the octave/foundation/root/base=12}.

You could use this system with any frequency as your root/base/octave/foundation, but using 432 in this position opens a door to another realm !!

The 432 system then goes on to match the proportions encoded in the universal law known as the 'overtone harmonic series' ->

The clockwise movement around the perimeter of the circle of fifth's mirrors the mathematical movement {by 3 Octaves + 1 Perfect Fifth}

When you juggle the concept of 12 and then toss in 6:5 = you get the actual circumference of the Earth in miles !

The 12th Harmonic Overtone is based on the Perfect Fifth -->

Keep in mind the 11th Harmonic Overtone {√2} is where they are destroying Cancer & Disease!

Shattering the negative organisms with targeted frequencies !

Get to the heart of it @ minute 8:55 ->

Ancient South American stone flutes approximating the 432 range -->

... notice the geometric symbolism used in the native paintings & ceramics ...

... it appears the stone flute's operating between the octave range (pillars) of 432 and 864 ...

Here is video #2 in the educational series -->

2∆ The Silver Lyre Of Ur, The Sumerian Cyclical Tuning System,

The Lexical Texts, 432 Hz & The Anunnaki is a remix of the ''dumbrill-lyre" & "govier-lyre" videos ... interspersed with artwork showing the processes being described ... learn how the first stringed instruments in history were tuned ... using the ancient sumerian cyclical tuning system ... perfect fifth's & fourth's only ... my assertion is to loosen up a bit ... by 6 ... 288 Hz is a perfect fourth above 216 Hz... one octave above 144 Hz ... a perfect fourth down is 108 ... the most evenly 'weighed' of the 7 modes is Dorian ... they proved knowledge of higher mathematics by using the diagonal of the squared circle to get to √2 for their diminished fifth interval 5000 years before it was supposedly 'invented' ... showing they had concepts of harmony and dissonance before recorded 'history' ever even began!! also there are cylinder seals proving they used tuning forks 5000 years before they were 'invented'...or how about sexi maths?? the concepts of 24 & 60, as in second or minutes or hours, comes directly from here, beget by the golden proportion, phi, as the fibonacci cycle's repeating digit sum & last digit f0-f60 ... thanks to nature for her divine proportions ... sun & moon align

"Copyright Disclaimer Under Section 107 of the Copyright Act 1976, allowance is made for fair use for purposes such as criticism, comment, news reporting, teaching, scholarship, and research. Fair use is a use permitted by copyright statute that might otherwise be infringing. Non-profit, educational or personal use tips the balance in favor of fair use."

"Copyright Disclaimer Under Section 107 of the Copyright Act 1976, allowance is made for fair use for purposes such as criticism, comment, news reporting, teaching, scholarship, and research. Fair use is a use permitted by copyright statute that might otherwise be infringing. Non-profit, educational or personal use tips the balance in favor of fair use."

The Factor 9 Grid as compared to The 432 Cyclical Tuning System

... Notice how the "correct" musical parts from the "Factor 9 Grid" are a good approximation for the idea from "Pythagoras' Hammers" ...

432 / 6:5 = 360 full circle

or do the inverse and go lower octave

216 x 5:6 = 180 half circle

Just Say No --> To The "Solfeggio Tones"

147, 258 & 369 are family number groupings only -->

the 9 "rearranged" patterns of these numbers is NOT a musical scale

432 x 432 = the speed of light in miles per second

"In later Egyptian dynastic times, Ra was merged with the god Horus, as Ra-Horakhty ("Ra, who is Horus of the Two Horizons")" - Ra - Wikipedia

Stela of Djed-khonsu-ius-ankh, Singer of Amun, plays the harp before Ra-Heru-Akhety, Thebes, Third Intermediate Period, stuccoed and painted wood.