Artojh's Renderings

The Resonant Crowns of Khemet

Looking at the White Crown of Upper Egypt (Hedjet, hdt) indicates a technological reasoning behind it design, yes I do not think they just randomly invented it without simple reasoning and logical inclusion. As with the other crowns they all served a similar function, one of communication through logical utility and natural means. “Per Neter”, “House of Nature”, the nature of sound, light and vibrations of communion to each other and other living beings. This is understood as the longitudinal vibrations of sound and of light, each only being a multiple octave distant from each other, one medium is the Ether the other is Matter (Air, Water, Earth).

The messenger of our time who understood this “Neter” was Nikola Tesla, in the past Christiaan Huygens was a proponent of it in his time and Roger Boscovich in his time as well. Fortunately you cannot fudge the longitudinal “neter” of sound, it is all around us and our ears and voices are organs we are closely connected to. On the other hand the fake Scientism movement which began in the early part of the 20th Century, which hijacked the symbols and contorted the mathematics to be some surreal multidimensional occult scheme. We are lucky that we have had some great minds and logical thinkers who knew the false paradigm was being perpetrated onto our scientific community.

As a Musician, I could recognise the acoustic volumetric of the crown almost immediately, that being in a vocal range. After taking great care to find the measure of what constituted the Resonator, I quickly found the design concepts that was used by the Khemtians. The next step was to look if there were schematics in any wall art, as possible translations of vibrations of sound to electricity and back to sound was taking place.

The fundamental wave length came from a careful measure using Google Earth was to reveal the base wave frequency that I should look at. After reading many volumes of Geological data regarding the Density, Bulk Modulus and Sonic Velocity of rocks of different genre, local to Egypt and other ancient sites, I can estimate the bedrock sonic velocity is usually around 5979.85 m/s, the Density about 3000 kg/vol and the Modulus is 10.7 Gpa, when translated to the Ancient measures, we have a Velocity of 80000 P per sec, a Density of about 2 Q/vol and the Modulus of about 1500. The distance from Senusret II Pyramid to The Great Pyramid is exactly 160000 Royal Cubits, simple calculations reveal that 14 seconds will transpire before your signal will be received and 28 seconds for the return signal, this could be considered a Time standard.

The Resonant frequency of the source to and from the destination = 0.0714285714 Hz

The Vocal Chord Range

= 65.714 – 4600 hz Wide Band
= 131.43 – 2044.44 hz Medium Band
= 262.857 – 920 hz Narrow Band

Male Speaking Vocal Range        = 85 – 155 hz
Female Speaking Vocal Range     = 165 – 255 hz
Children’s Speaking Vocal Range = 180 – 360 hz

The Crowns and head gear Range = 36 – 440 hz

The Wave Lengths
WB = 343.841/65.714 = 5.232365 mtrs = 10 RC = 280 F
= 343.841/4600 = 0.074748 mtrs = 1 P = 4 F

MB = 343.841/131.43 = 2.616194 mtrs = 5 RC = 140 F
= 343.841/2044.44 = 0.168183 mtrs = 1 SH = 9 F

NB = 343.841/262.857 = 1.308091 mtrs = 5 LS = 70 F
= 343.841/920 = 0.373740 mtrs = 1 D = 16 F

The design of the Hedjet Crown was a well drawn out study, I referred to many icons that show clear pictures, the first being the Narma Palette and many beautiful sculptures and large statues. It seems to have a slightly different size depending on the region and the Dynasty that had created the artwork. So instead of slavishly copying something that we had no sample of, with only diagrams or sculptured versions, I went with the most direct method, think like an Ancient and design like an artist of the time and build like an engineer of Khemet. As the Royal Cubit was the fundamental rule that all these ancient wonders that were created, I used my perfected measure of 1 RC (523.2365mm) as the foundation of design and engineering, also being 28 fingers (18.687mm), where I could use the finger as the smallest measure.

The large curvature of the circle D3 of the Hedjet is 4 RC, I could have chose 3 RC but the cavity would have been too small and the curve too tight, also if it was 5 RC the crown would have been to tall, 4 RC was the best fit that also matched the edge of D4, which is 12 F or 1 Small Span. The A1 dimension of 2 F was not a hard choice, it lined up to most crowns and was easy to pick, whereas the body had to be dissected to cylinders to get an approximate volume, using a basic form of calculus and the Egyptian measure I achieved a simple design tool that could be used on many semi-organic designs. The inside of the Hedjet could be two chambers or more, in line with the design of the cochlea, when unwound has two basic chambers, this could indicate a slightly modified version of my interpretation, which I will express in another design.

My intuition told me that I would arrive at a tonal resonance around the vocal region, being 95 Hz it was just about right for the low end of a set of large male vocal chords. The measure was the key, whole numbers of Fingers is the how we can design natural machines, like a resonator. The DNA understands these forms, your ears and your vocal chords are the result of this understanding, how can we imagine these were randomly adapted, they were designed by a master architect of the universe, we can only imitate its great design.

Here is is short list of Gems used by the Ancient Egyptians (PZ is the preferred piezo ):

Tourmaline Blue PZ
Amethyst Purple PZ
Sapphire PZ
Emerald PZ
Ruby PZ
Diamond PZ
Garnet Red
Lapis Lazuli Blue
Obsidian grey
Carnelian Orange
Jasper Orange
Turquoise Blue
Carnelian

All the crowns have the basic form of an acoustic device of some sort, this was their unique mastery of this most ancient technology and science, Tourmaline was the first choice for the Piezo crystal, this was one of the regular stones used in Egyptian jewellery and art.

Sound Refraction

The focal length of a spherical lens (measured from the surface of the lens to the focal point) is given by focal length sphere where r is the radius of the sphere, m1 is index of refraction of the surrounding medium and m2 is the index of refraction of the lens material.

r = Radius of Sphere
m1 = Index of refraction of surrounding medium
m2 = Index of refraction of the lens material
v1 = Velocity of Sound of surrounding medium
v2 = Velocity of sound of the lens material
f = Focal length from the surface of sphere to the Focal point

f = r*(2-m2/m1)/2*(m2/m2-1)
f = r*(2-v1/v2)/2*(v1/v2-1)

If the lens material has a greater velocity then it becomes a convergent lens and if it is less that it is a divergent lens.

Zp = Acoustic Impedance Piezo Electric Material
Zl = Acoustic Impedance of Loading Material
Wm = Matching Material Layer Wavelength

Best impedance match:

Wm/4 = Zm

Impedance of matching layer material is:

Zm = (Zp x Zl)^(1/2)

Wide band acoustic impedance:

Zm = (Zp x Zl^2)^(1/3)

Improving acoustic matching:

Zm1 = (Zp^4 x Zl^3)^(1/3)
Zm2 = (Zp x Zl^6)*(1/7)

Mixing powdered piezo materials with hard resins and creating a polymer is one way of fabricating matching layers.

Hedjet Crown

This was the first I had seen that would work acoustically, using the Helmholtz resonator as the basic design to follow. The volumes are best approximated as the chambers are narrow band devices and not just singular tone, The narrow band fits the voice well, my criteria was to use it like a musical instrument, where pure tones resonate distinctly, a vibration from an external source being simple not highly modulated, one from the vibrations of a staff or device that has a limited tonal range. The connections to the circuit and ears are not included, these would be more decorative and need to be adjusted for the head of the user. The main chamber could be split in two, as per the uncoiled cochlea. I chose the size in accordance to the Royal Cubit as the standard, by it having direction relationship to the Longitudinal velocity of light. The original crown was worn by Narmer and he was a giant, so I figured this was the most suitable size, as I noticed the Hedjet sometimes seemed over size when the king was not as big in many wall carving. Later Hedjets could have been smaller, making the frequencies much higher than 95Hz.

Deshret Crown

This one was simple once I found the first crowns acoustic design logic. The spiral piece could be a hollow chamber as well, making it look like the cochlea, where adjustments to the tone and frequency could be made or even a direct contact to another acoustic vessel. The Green outlined section is the simplified version of the crown volumes that makes the mathematics much simpler. Tr1 is a golden triangle that was found after I had almost drawn the whole unit, it points to the heart, the size is 471/18 x 818/18 fingers = 488,977mm x 849.221mm. The Uraeus I put on the crown is mainly to show its location and design elements, the scale is not correct, it would be at least 1/2 to 3/4 of the size I have drawn.

Hathors Head Gear

This was a simple progression, now using the symbolic shapes of the sun disk and horns to create the necessary configurations. The C2 chamber in green is an approximation of the neck of the horn resonators. The P5, P6 and P7 are other positions the Piezo crystal could be placed and change how the horn chambers worked harmonically. The P6 is also connected to the main chamber, so a feedback will occur. The P7 connection is used when you use both horns, what you will get is one horn in compression while the other horn is in expansion, as opposite phases. P5 will drive the side horn but will also have a short wave of 1/7nth the of the wave length of the horn, thus giving you a complex sound wave. Tr2 is another golden triangle that I discovered after drawing most of the head gear, it points to the mouth, the size is 18.2 x 28 Fingers(1 RC).

Other Crowns and Head Gear

After intuitive generating these designs, I could see every crown and head gear designs were connected to the cochlea and other sound chambers. The feathered version of the Hedjet called the Atef Crown makes me consider that the internals as two chambers and the feathers as ticklers for a variety of harmonics. Amun crown has two distinct chambers, and it’s appearance is significantly like a straightened out cochlea. The Shuti Crown has spiral chambers(rams horns) which would be a shorter version than long straight chambers. The blue Khepresh Crown is much shorter and has a chamber as well, while the Cap crown has even a smaller chamber,

Each crown or head gear or combinations seems to indicate a narrow band of frequencies and could possibly be that each has a function of communication at those frequencies, where the deployment of signals were directed to those who wore a specific crowns or hats in a region. What I could gather by the wonderful hieroglyphs is that stock holdings were relayed among the Khemtian empire using false doors as exchanges with a schedule using specific times by officials with certain hats, which were regulated in a religious fashion to keep the communication channels linked up. The pyramids served to create, amplify and relay the complete network of acoustic signals around the empire.

The transmission of signals via a sonic device inside the sarcophagus like I have previously described would be linked to the regular acoustic carrier pyramid frequencies, with the use of a Sistrum as the calling ring when pressed against the walls in certain locations, like the false doors, when done at regular intervals to indicate a transmission signal.

The Uraeus is a 1 1/2 or 3/2 wave system, the locations of the Piezo crystal help with feedback tuning and aerial reception of Sonic frequencies, these would be coupled to the main acoustic chamber and also act like the diode mixer in radio when separating frequencies to be decoded. By the design it looks like a single balanced mixer, where the RF (Radio frequencies) is the Sonic wave and the LO (Low frequencies) is the voice and the IF (intermediate frequencies) are the carrier frequencies.

As this is still a working document, excuse any errors or omissions, but if you found this work of value please donate to keep this and other projects alive. regards Arto