Are you ready to dive into the heart of the matter? Where the magic of the universe and the harmony of structure all began?
Seek balance between your left and right brain, synchronicity between your ears and your eyes to uncover the code behind Arkhante ancients’ knowledge!
This puzzle opens the way toward discovering Arkhante culture and knowledge, where everything all began: «The Origins».
This puzzle goes even further in terms of teachings: it tackles many fields (Numerology, Geometry, Sound, Music theory, Arkhomes…) that work their ways in total harmony with the Arkhante culture and magic. But first, let us focus on solving the puzzle and on what was expected from you to solve it: «filling the points».
Like every other civilization, Arkhante ancient people have invented their own ways of communication, crafting, trading…etc, but before all, they had to count!
Numbers and calculations are the core of all civilizations and all knowledge, even prior to any scriptures of language, people from all cultures always had to agree on how they count first!
So it’s all started with NUMBERS!
At the end of the7^{th} video of CTA Game Review (link above), you can spot the picture above along with a 7-notes melody sound afterwards:
As you probably noticed, out of the 3 shapes in this picture, one of them do not have any points in it, and is located at the center of the image: the «Polygons» shape.
This means that there’s nothing to fill in this shape, it’s rather there as an indication of what to look for: it is your first lead to start your solving journey!
The shape represents regular polygons (by definition, polygons where all angles and sides are equal) building-up from the smallest one (the triangle) to the largest (the circle). Note that the total of polygons represented here is 7 (Triangle, Square, Pentagon, Hexagon, Heptagon, Octagon, Circle).
These polygons have been hidden in background shapes in the video for you to find and start your quest toward unveiling Arkhante numerology. And since our team made a great job hiding them ^^…clues have been given to point where to look at:
(Clues #0 and #1)
NB: The most obvious of them was the circle (on the DJ’s headset); it was supposed to be the first to catch your observant eye and lead you to investigate more! It’s a bit like the «Spot the 7 differences» game, but in video format!
So here are the 7 hidden polygons you had to find:
Hidden Polygons | |||
Triangle | Time stamp: 0:45 | ||
Square | Time stamp: 0:45 | ||
Pentagon | Time stamp: 13:59 | ||
Hexagon | Time stamp: 6:13 | ||
Heptagon | Time stamp: 8:57 | ||
Octagon | Time stamp: 14:00 | ||
Circle | Time stamp: 2:51 |
Now that these hidden polygons were found, you still have to find a meaning to the encryptions inside each one of them: what could that be?…
You can easily guess that they are related to each polygon, but what are they? Polygon names? Is that a new language? That can’t be…they all have 3 symbols only (even worse, the circle has only one)…
Soon enough, you’ll find yourself on the most plausible lead you can think of : «Geometry and Maths».
Because after all, these are geometrical shapes that raise memories of your math lessons right!?
Furthermore, numbers and maths are the code/language of all things in the universe, hence the background picture!
Therefore, further in your investigation, the next step you should think of is numbers since it is the only way to have 3 symbols for each polygon: matching angles properties (The sum of interior angles of regular polygons triangle: 180°, Square: 360°, Pentagon: 540°, Hexagon: 720°,Heptagon: 900°, Octagon: 1080°…circle: ∞°).
NB: The sum of interior angles of a circle is not 360° here. It is considered as the ultimate polygon as we increase the sides number to infinity, so it is the sum of an infinite number of ≈ 180° angles. This is why the polygons shape has been given as «multiple polygons building-up one after another». (See polygons table below for more details).
But wait…there’s something wrong with the Octagon, there’s 3 symbols inside of it instead of 4.
Well, it would have been too simple if the symbols were just exactly matching the base 10 digits you know of, right!? The puzzle would have ended here!…So there must be a twist somewhere!
To help you with that matter, a hint was pointing since the beginning toward the base system used here, which is «THE BASE 12» counting system: The Dodecahedron shape
It is placed at the central base of both the left and right pattern because it’s the core symbol for many things in Arkhante culture (as we will see later on), and among them: the numeral base-12 system!
Moreover, another clue (Clue#2) has been given along the quest to help you identify the counting system and find the corresponding number/digits in Base-12:
As you may know it, the origins of our current Base-10 counting system is nothing more than the fact we have 10 fingers on our hands and that it was the most intuitive way to count. But is it reaaly the best system we could come up with?
People of Arkhante, on the other «hand», found it easier to count on their phalanges to make the most numbers out of their hands:
– 1 x finger (or phalange) = 12
– 2 x fingers (or phalanges) = 24
– 3 x fingers (or phalanges) = 36
and so on…
NB: The order you choose for fingers and phalanges is not important since you stick to an order the suits you: going from the pinky to the index, from the pinky’s first phalange down or to the next first phalange, or the complete other way around starting from the index again…it doesn’t matter!
This is why there’s no numbers associated to the bottom picture in Clue#2, you can understand the order you want it won’t change anything; only the Dodecahedron shape as a reminder of the base-12 counting system is important!
To get a better understanding of the Base-12 system (also called the «Dozenal» or «Duodecimal» system), you can try and picture the old mileage-meter we had on our old cars (The Mechanical Odometer):
...10^{3}+10^{2}+10^{1}+10^{0}
...10^{3}+10^{2}+10^{1}+10^{0}
In Base-10: Each mechanical wheel goes from 0 to 9 (10 digits) starting from the 1^{st} wheel at the right, and increments the next wheel by 1 when it starts over.
In Base-12: Each mechanical wheel goes from 0 to 11 (12 digits) starting from the 1^{st} wheel at the right, and increments the next wheel by 1 when it starts over.
Your right hand being the 1^{st} wheel, your left hand being the second one…you count from 1 to 12 on your left hand (since you cannot materialize 0 on your fingers, but the principle remains the same: 12 digits) and you increment your left hand by 1 finger (or phalange) each time your left hand starts over.
Now that you see clearly through the Base-12 numeral system, let’s get back to business.
For the sake of a clearer «1-digit numeration» for our 12 digits, let’s agree on the following notation:
«0, 1, 2, 4, 5, 6, 7, 8, 9, A(10), B(11)».
To get back to our polygons, in the clue#2 you also had and additional hint regarding the sum of interior angles of a regular polygon : (N-2) x 180°
This is the general mathematical formula for any regular polygon (starting from the smallest, N=3: the triangle) where N is the number of edges/sides or vertexes of the polygon. Of course this formula has been given in base-12, in Arkhante symbols. Otherwise where’s the fun in it right 🙂 ?
NB: Giving this formula also provides direct deciphering of 0, 1 and 2 symbols – Even if you don’t read it in base-12:
Base-10 : (N-2) x 180
Base-12 : (N-2) x 130
Now that you have all the information needed, here’s a summary of the findings you should get from these hidden polygons:
If you look at how consecutive symbols evolve from 0 to 3, you will easily notice that each step adds a new point, and these points start progressively forming polygons again:
So far, you understand that a digit (X) is represented by (X+1) points and a «/» sign.
So you can assume the this last sign means (-1), Which would be a good guess!!! Congratulations…But, do not jump to the conclusion that the opposite sign «\» means (+1) yet! Because that would be wrong!
Actually, you have one simple case that will help you discard this assumption once and for all: «The symmetry between the 3 and 9 symbols». Once you notice that, you will know for sure that the «\» sign cannot mean (-1).
Moreover, if there’s a symmetry between 3 and 9 symbols…in a 12 digits panel…that means they are both symmetrical with respect to number 6, which, in that case, must have no other symmetrical relative than itself. Then you take a look at its symbol again, and…there it is: it has a perfect symmetrical shape and its only symmetrical relative IS itself: Bingo…that’s it!
All the digits symbols are symmetrical with respect to number 6 symbol (or the 0-6 vertical line if we think of symbols arranged as a clock).
And there you have it…combining logic and symmetry will make you decipher all the 12 Arkhante symbols:
Now that the basics of Arkhante numerology has been set, we can proceed to filling the expected points in the picture!
Going from 2D dimensional shapes to 3D-perspective shapes, we discover in this image the Arkhomes’ geometrical shapes organized in «Crucible» shape. As this sacred place relates the Arkhante Arkhomes’ Origins and History.
As you certainly noticed, next to each Arkhome there’s a certain amount of points to fill. Some have 3 points (Fire and Air) and others have 4 points (Earth, Water, Nature, Light, Darkness and…Yes, Prana! As Prana is the central source of energy on the Artellium continent, it is also the central shape in this image: from it derives all energy that fuels the Arkhomes Magic!)
So the goal here is to find the link between each Arkhome’s geometrical shape and numbers to fill in the points.
And for this to happen, you have two ways to go:
To kill the suspense, here’s the final solution expected for this image first, the we will go through the detailed explanations:
Explanations:
To make things less redundant, let’s start with the sound melody:
The melody you hear at the end of the video consists of 7 sounds/beeps (or to be more precise: 7 sounds + 1 silence). The goal here is to find frequencies (hence the graphical oscillations) and not music notes (hence the beep sounds and not any music instrument sound).
NB: There is no music-theory knowledge required to solve this puzzle, even though there’s a link with music that we will discover and explain later on!
So, for solving this first image, you were expected to identify the frequencies of each Arkhome (identifiying them by their colors), and multiply them by their respective associated factor (of the same color) to get the «Arkhome’s resonance frequency».
(NB: Due to the moving pixels of the oscillations, it can sometimes be hard to identify the color, it is why colors have been duplicated on the multiplying factors).
And to do so, you can use many online tools or mobile apps that can measure the frequency of any audio sound. An easy task for the CTA community right!
Once you get the frequencies, the next step is to simply convert them in Base-12 then write them in Arkhante numerology symbols!
Results:
Arkhome | Frekency to find | Multiplying factor | Original Frequency in Base-10 | Original Frequency in Base-12 | Original Frequency in Base-12 |
Fire | 720 Hz | nothing (or x1) | 720 Hz | 500 Hz | |
Water | 900 Hz | x4 | 3600 Hz | 2100 Hz | |
Earth | 1080 Hz | x2 | 2160 Hz | 1300 Hz | |
Darkness | 0 Hz (or ∞) | – | 0 Hz (or ∞) | 0 Hz (or ∞) | |
Prana | 810 Hz | x8 | 6480 Hz | 3900 Hz | |
Light | 1080 Hz | x4 | 4320 Hz | 2600 Hz | |
Nature | 900 Hz | x4 | 3600 Hz | 2100 Hz | |
Air | 720 Hz | x2 | 1440 Hz | A00 Hz |
NB: Regarding the «Darkness» element, both symbols ( Or ) are right since our human ears can perceive sounds in an average range of 20-20k Hz, silence can be considered as:
Or
Musical interlude:
But let’s take a few moments here to talk to music lovers. Of course we cannot go passed that, can we? Many of you have maybe even tried to solve the puzzle through music, right!?
Actually there’s a a big link with music here, but to see it, you should not think according to the usual tuning system you know of! (And that actually was planned for a third Clue#3, to give an additional way for finding the frequencies through exact music notes… if the puzzle hadn’t been solved by that time, which it did!)
For those of you who have tried to find a way through music notes, you probably tried to reproduce the melody on a music instrument (let’s say a piano for instance) to find the notes you’re hearing, and then look for the corresponding frequency of each note, right?!
But it won’t work…yet! And here’s why:
In our universal tuning system (A4 = 440 Hz), you will find 2 close melodies (one in F4 key and the other in F#4 key), but never the perfect exact pitch you hear on the video beeps…and therefore, the exact frequency number!
For that you would have needed a fret-less instrument (like a violin for example, with no notes sectioning), and even then you’d have to play and find the exact pitch, then use a tool to find its frequency, because you won’t find it by referring to the notes you universally know.
But those of you who have a great ear should notice right away that the perfect note is in between F4 and F#4…so there must be something different with the tuning!
Anyways, here are the two closest attempts (on a piano keyboard) you can try on universal notes basis (A4 = 440 Hz):
Attempt 1: Key of F4
(Embedded F440 video)
F4/A4/C5/-/G4/C5/A4/F4
Attempt 2: Key of F#
(Embedded F440 video)
F#4/A#4/C#5/-/G#4/C#5/A#4/F#4
Original melody
(Embedded original audio)
Quite different from the original right!?
So, the teachings from this is that Arkhante people have chosen a different tuning than the usual universal tuning system. To be perfectly in line with the Arkhomes «resonance and vibrations», and create perfect harmony with the elements’ magic, they had to follow the frequencies that have been imposed by the Arkhomes geometrical shapes (see geometrical method below), which happen to be the EXACT INTEGER frequencies in a A4 = 432 Hz tuning system!!!
To get a better grasp of the exact melody, here it is on a 432 Hz tuned version on the same piano keyboard (which happens to be in F#4 key, in A4 = 432Hz tuning) :
Exact melody in A4 = 432 Hz
(Embedded F#432 video)
F#4(720 Hz)/A#4(900 Hz)/C#5(1080 Hz)/-/G#4(810 Hz)/C#5(1080 Hz)/A#4 (900 Hz)/F#4 (720 Hz)
NB: Now you can see why the original bigger frequencies (that are the same notes on higher octaves) have been downgraded to the same octave (between octave 4 and 5)… using those frequencies would have hurt your ears first, and it would’ve been utter shambles, a cacophony and not a melody anymore. Being on the same octave helps making it a harmonious melody: «The Arkhomes sacred polyphony».
More on that topic in musical teachings of Arkhante (To be continued)
II. Geometrical shapes
As said before, the other way to solve this first image is using geometry and maths. As in previous polygons part, if you focus on counting angles you can easily find the way.
As you can see, this time is about 3-Dimensional shapes, each one of them having different polygon shapes as faces forming their outer surface.
5 of them are regular polyhedron (same face shape all over the surface), also called platonic solids (Fire, Earth, Air, Water, Prana), and 3 of them are sacred geometry 3D shapes (fundamental structures and templates of life in the universe).
If we use the same logic of summing all the angles of all the faces of the outer surface, we get the exact same numbers as the frequencies in our previous melody.
For example:
– Fire (tetrahedron), has 4 triangle-faces on its outer surface: 4 x 180° = 720°
– Earth (Hexahedron or Cube), has 6 square-faces: 6 x 360 = 2160°
…and so on!
NB: For the light element (Start-tetrahedron) you should not count 2 x tetrahedron, but rather 8 x smaller tetrahedrons with 3-triangle faces each, and not 4! Because the 4^{th} face is on the inner volume of the shape, and here it’s all about faces on the outer surface. Which make it 3 x 8 x 180° = 4320 Hz! So…. the light is vibrating at a A4 harmonic (A4 x 10).
Are you beginning to see the magic and harmony of Arkhante yet!? Where magic, music, geometry, frequencies and vibrations work all hand in hand!?… Stay tuned for more teachings from the Arkhante culture!
To summarize it all, here’s an overview table with all the findings:
Arkhome | Polyhedron | Faces | Sum of Angles | Sound/Resonance frequency | 432 Music Note |
Fire: | Tetrahedron: | 4x | 4 x= 720° (Base12 = 500°) | 720Hz (Base12 = 500Hz) | F# (720Hz) |
Earth: | Hexahedron (Cube): | 6x | 6 x= 2160° (Base12 = 500°) | 2160Hz (Base12 = 1300Hz) | C# (1080Hz) x2 |
Air: | Octahedron: | 8x | 8 x= 1440° (Base12 = A00°) | 1440Hz (Base12 = A00Hz) | F# (720Hz) x2 |
Water: | Octahedron: | 20x | 20 x= 3600° (Base12 = 2100°) | 3600Hz (Base12 = 2100Hz) | A# (900Hz) x4 |
Prana: | Dodecahedron: | 12x | 12 x= 6480° (Base12 = 3900°) | 6480Hz (Base12 = 3900Hz) | G# (810Hz) x8 |
Nature: | Cube-octahedron: | 8x 6x Total = 14 | 12 x= 1440° (Base12 = A00°) 12 x= 2160° (Base12 = 1300°) Total = 3600° (Base12 = 2100°) | 3600 Hz (Base12 = 2100Hz) | A# (900Hz) x4 |
Light: | Star-tetrahedron: | 24x | 24 x= 4320° (Base12 = 2600°) | 4320Hz (Base12 = 2600Hz) | C# (1080Hz) x4 |
Darkness: | Torus: | 0 or ∞ | 0 or ∞ (Base12 = 0 or ∞) | 0Hz (or ∞) (Base12 = 0 or ∞ Hz) or | Silence (0Hz) / Inaudible (∞ Hz) |
And the 1^{st} image filled with all the information needed
To solve this 2^{nd} image, same numbers’ principles apply. Once you’ve found the Arkhante numbers symbols, you have to fill the points on the pattern.
This rosette represents how numbers are organized with each other and how they create some kind of magic and harmony on a base-12 dial!
For the sake of geometrical aesthetics, lets agree, from now on, on a radial notation of Arkhante symbols:
Radial convention
(symbols follow the radial orientation)
First thing you should notice the Rosette pattern is the number of points in the blanks. If you look closer, you can see that the 1^{st} inner round (or circle) of points is the only one that has a set of single points.
Those single points are a hint to indicate the we are looking for the 12 unique digits/symbols of the Arkhante base 12 system (0 to 11 or 0 to B) positioned as in a clock dial.
It is the start of all counting and calculus :
Starting from there, counting keeps increasing from the smallest inner circle to the next bigger one (hence, the increase of dots from 1 to 2 dots) as a clockwise spiral that grows bigger and bigger, jumping to the next circle each time you achieve a full round of 12 numbers:
By counting and completing the full rosette (from 0 to 60) with Arkhante symbols in a base 12 system (from 0 to 50) you would have solved this 2^{nd} image by filling all the dots.
NB: We did not stop randomly at number 60. As you may know, Base-60 is also an harmonic of Base-12 system (5×12 = 60). It is also the outer border/limit of our Rosette, It marks the end of the numbers to find, but also the beginning of Base-60 counting system (60 digits from 0 to 59 to use as a new base). Like the oldest civilization of Sumerians used to. But that’s not the topic here, more on that subject in the teachings category.
Other elements in the rosette design could also have given away some indications to help you find how numbers are arranged:
As you may have noticed, lines on this rosette (whether it is by their length or their color) were drawn differently. This was to highlight the fact that numbers (or rather digits, since we consider each singular point on each side of the line) on the same side (left or right) follow a same pattern.
The small thinnest white lines inside the rosette separate 2 kinds of patterns:
Side 1: the same digit repeats itself along the line
(Same symbol from the first to the last round of the rosette)
Side 2: Digits increment following the radial direction of the line.
(Each symbol increment by 1 from the first 2-digits round to the last round of the rosette)
Moreover, you may also have noticed that these lines end at the outer border of the rosette, but fade away through the last round and towards the faded cloud. Meaning, it is the end of a cycle (a 60 pattern base) but also the beginning of a new one (the biggest faded rosette cloud) toward expansion, and thus toward infinity!
NB: There’s a lot more to learn from this Rosette regarding mathematical and geometrical patterns. For example, if you look at the spirals, they also increment symbols by 1 each time you get a step further from the center. It also gives many teachings and links between calculus, multiplication, factors, geometry, colors, music…etc, that you’ll know more about in the «Teachings» section.
But for now, puzzle-wize, it’s all you had to know about solving this puzzle!
See you in the next section…
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