The Ar Tonelico Wiki

Wave Theory

1,395pages on
this wiki
Add New Page
Comments0 Share

Wave Theory, also known as Wave Science, Sound Science, Wave Physics and Phonetics; is the ficticious science that serves as the main basis for Song Magic, and everything that happens in the world of Ar tonelico.[1] [2]

Basic Section

Wave Introduction

Composition of Matter and Static D-Waves

The frequencies of the waves can go from 1 Hz to the infinite, and the multiple ways in which the various waves can entwine, with differing grades of complexity, are what form the different kinds of matter. If these waves are called [Static Detail Waves], then they will be characterized for continuing to remain in repose. The strength and direction of the energy of the various frequencies of waves that compose the matter, acting upon its minimal point, is what allows matter to change to its different states through the Spectrum (the frequencies of the waves that compose it): from solid to liquid, and then, to gas.


Detail Waves and how they compose matter.

Magic and the Dynamic D-Waves

All the kinds of paranormal powers are caused due to [Dynamic Detail Waves]. The vanishing and birthing Dynamic D-Waves are the [Undulations] that produce measurement errors on the Static D-Waves. They are the components of the Spectrum that produce the measurement errors on the coordinates of space where the Static D-Waves have their power field, and if they are placed over a time axis, they seem to be undulating, spreading and converging between them. These measurement errors end turning into residual energy, and that unstable power field turns into the source of magic.

The Power of the Voice and the H-Waves

The ordinary sounds have frequencies ranging from 50 Hz to 20000 Hz, but whenever any living creature emits its voice, it also emits multiple waves with extremely low and high frequencies. These are D-Waves and also, a special different kind of waves called H-Waves, which are commonly called the [Waves of Feelings]. The H-Waves are also divided in [Dynamic Hymmno Waves] and [Static Hymmno Waves], the former being the ones that form the feelings carried in the voice and the songs, and the latter are called the origin of life (life energy). Because the H-Waves exist in a different dimension from the D-Waves, they are not able to manifest themselves in the physical world, but they also exist equally from extremely low to extremely high frequency bands, and through an item called the [Songstones], these wave frequencies can be emitted, converted into D-Waves.

Wave Comparison Chart



Dynamic D-Wave


Static D-Wave


Dynamic H-Wave


Static H-Wave


Forms Dynamic energy Matter Song, feelings Life energy
Essence Distortion of


Matter itself Songs,

brain waves

Motive Energy High Low High Low
Wave Nature Ether wave Ether wave Astral wave Astral wave
Wave Nature Radiation,

continous motion




continous motion.



The Role of the Songstones

The Songstones are composed of two components called [Grathnode] and [Parameno]. The Parameno part reacts to the Dynamic H-Waves, and absorbs and sends over their energy to the Grathnode part. When these external waves reach the Grathnode part, it creates D-Waves inside of it in response to the Dynamic H-Waves that it had absorbed, and releases them into the surrounding environment when it reaches its limit. This Dynamic D-Wave release process does not have a limit in how much power it can create. The Grathnode part will release the power and it will overflow whenever the distortions stockpiled inside of the crystal are too numerous and surpass its limits to contain them. Therefore, if the crystal is smashed in the presence of sounds, it will always release sonic waves upon the areas around of it.

H-Wave Band

The Soulspaces of Humans and Reyvateils are made up from Static H-Waves, and if we were to analyze them, we would be able to decode even their innermost feelings and emotions. What allowed to systematize this were the Dive Machines. The Diver (human) emits Dynamic H-Waves, which cause a vibration in the Static H-Waves of the Reyvateil, and that interference ends turning up into new Dynamic H-Waves: this is the basic structure of the process of crafting a song. The Static H-Waves of a Reyvateil are divided into the following frequency layers:

Individual Consciousness Fields

This zone extends up to 116000000 Hz, and is in this region where the consciousness of an individual can reside. It is commonly called the [Cosmosphere], and it is possible to Dive within this area.

Hymn Code

This area is located approximately 100 Hz near the 116000000 Hz band zone, and no matter which feelings the individual has, this zone is absolutely impossible to modify through them. The people of the First Era, during the creation of the first Pureblooded Beta-types, noticed how stable this band zone was, and decided to use it as the region that allowed Ar tonelico to attach a prerecorded tag to their [FFT Spectrum]. Declaring a Hymn Code is actually ordering the Tower to compare the FFT Spectrum of the Reyvateil to ensure that it matches the declared Hymn Code. Though this band is mostly composed of genetic information that cannot be inherited, even though some of the Third Generation Reyvateils ended carrying a Hymn Code, even if they did not register their FFT Spectrum in the Tower (in other words: they are registered under a Hymn Code that they do not actually have). This is what happened to Aurica, and they are very rare cases, but even if they inherited the Hymn Code of another Reyvateil, it happened because the Tower mistook them for another person, and for no other reasons.

Shared Consciousness Fields

This region is located in the highest wave frequencies, and furthemore, an individual is unable to control anything in them, given that doing so would involve pulling the feelings of other people. However, the feelings of an individual can influence the feelings of others. This zone can be used with purposes of control as well, and that is because the Shared Consciousness Fields of the Reyvateils were developed too shallowly. During the events that caused the end of the Second Era, what caused the Reyvateils to become so aggressive against the people to which they did not have any sort of ill will before was that other Reyvateils used this zone for amplifying the feelings of distrust towards humans, and what was initially an unconscious desire to attack humans rose up until they began actually attacking them.


Comparison between the spectrum and frequencies of the different wave kinds.


Dives as Proven Under Wave Science

The area in which Diving is possible starts at the Level 1 of the Soulspace, which is located in the lowest wave frequencies (approx. in the 20000Hz range), while the max level, Level 9, is located in the highest frequencies (approx. in the 110000000Hz range). If anyone tried to Dive beyond that point, it would be extremely dangerous, not only because the interferences caused by the waves of the high frequency bands are able to completely destroy the mind of the Reyvateil, but also because the Diver and its consciousness, given where they are located (in the Shared Consciousness Fields) could end affecting the minds of the other Reyvateils. Because the consciousness at low frequencies are greatly influenced by the consciousness at high frequencies, and there is not a limit about how close the interfered wave frequencies of the Diver and the Reyvateil can become, if the feelings of the Reyvateil in its purest form (High-Frequency Dynamic H-Waves) are not interfered, the H-Waves of the Diver will end up being absorbed by the H-Waves of the Reyvateil (in other words, the Diver will be unable to return to the real world). To avoid these dangers, the Cosmosphere was developed with a series of layers called "Levels", and a security mechanism called the "Mind Guardians" was created, both with the purpose of protecting the lives of both the Reyvateil herself and the Diver.

Paradigm Shifts and Limits to Diving

When the Dynamic H-Waves of the Diver raise considerably the frequency of the Static H-Waves of the Reyvateil, the waves of the Reyvateil vibrate greatly, and that materializes a Paradigm Shift. If the changed waves end being much more fine (= of higher frequencies) than how they were before, they cannot do anything but raise their coordinates in the FFT Spectrum by one stratum. In short, a Paradigm Shift is the ascension of the waves of the Reyvateil into waves of a higher frequency. The consciousness of the Diver is also ascended together with the consciousness of the Reyvateil, so this could also be called a process in which both of them grow spiritually. The Dive ends at Lv. 9. In Lv. 9 there is only a small band of low-frequency waves, the Hymn Code, and generally, waves of a higher frequency than it are unable to interfere it. Depending on how much the Diver cares for the Reyvateil, it will vary the level in which their interacting Dynamic H-Waves will be able to advance to higher frequencies.


Comparison between the spectrums for different situations during a Dive.

The Obligations of the Dive Shops

If a considerable variation arises between the consciousnesses of the Reyvateil and the Diver, then it is necessary to conduct a emergency suspension. Because of that, the Dive Shop operator has the obligation of watching over the [FFT Spectrums] of the people that are Diving. In case something like, the waves of the Reyvateil becoming so similar to the consciousness of the Diver that it turns almost impossible to tell them apart, happens. For example, if Aurica told Lyner [Come on, live inside of my Soulspace], and Lyner even only thought [That'd be okay], Aurica's high-frequency waves would change Lyner's low-frequency waves and erode them, creating an extremely dangerous situation. To avoid such a danger, the Dive operator is constantly monitoring their waves, however, they have forbidden themselves of watching the actual events that unfold inside of the Cosmosphere.

Why It is Impossible to Dive into Humans

The mental structure of the Reyvateils, the [FFT Spectrum], was designed by the Humans based on the existence of wave circuits, and for making safe the examination of it, they also designed an artifact used to analyze the FFT Spectrum gently (the Dive System) at the same time. A Dive System can be used for examining humans, but usually, nothing will happen (though there is 1/1000000 probability of causing a mental collapse to the one being examined). To be able to Dive into a Human, it is necessary to analyze their minds with a detailed method that allows to make up a Mind Map (a display of how their Static H-Waves are structured), which was in-progress during the First Era, but was left incomplete, because back then it was impossible to completely understand how the human mind was structured. Now, in the current generation (the people of the Third Era), Humans are able to Dive with people of mixed blood, but the reason for that is because these mixed blood people (the Third Generation Reyvateils) have replicated naturally the mind structures of the Pureblooded Beta-type Reyvateils, which is something that humans would need to have {C}in order to be able to Dive into them, since the Static H-Wave part from which their minds are made is impossible to modify with a Dive Machine.

Reyvateil Anatomy

Spectrum Gene

The existence that has the most part in the formation of the physical body of a Reyvateil is called the [Spectrum Gene]. This is an aggregate of Dynamic H-Waves that are carried within an spectrum of special wave frequencies, and said aggregate is aligned in a 60-grade angle, forming a regular tetrahedron called the [Nuclear Triangular Loop]. The Nuclear Triangular Loop is like an unique clock inside of each Reyvateil that carries the [Standard Spiritual Frequency], and its timing is what ends turning into the basis of the structure {C}for the Static H-Wave FFT Spectrum of the Reyvateil. {C}The Spectrum Gene has an extremely low capacity for storing information, so when a clone of a Reyvateil is made, because of the concatenation of Grathnode, Parameno and the Nuclear Triangular Loop being influenced by the [flickering] of an infinitesimal number of various interference errors, they will not end having a similar body to the Reyvateil from which they were cloned, though they are still called clones.


The Nuclear Triangular Loop.

The Bodies of the Reyvateils

The bodies of the Reyvateils basically also have as their base the same proteins that the bodies of the humans have, but it also has Parameno and Grathnode compounds to keep tied together their D-Wave (Body) and H-Wave (Mind) components, and to protect the Nuclear Triangular Loop. These compounds are similar to the Hymn Crystals in the fact that they are compounds with a perfect wave balance, which prevents them from changing into any other kind of compounds. {C}The [Spiritual Standard Frequency] acts as the root for the Reyvateil's body, since it continually releases Dynamic H-Waves. The Parameno and Grathnode compounds in the body of the Reyvateil then react to them, absorbing these waves and converting them into D-Waves, which will have the role of creating and maintaining the body. In other words, to say that the creation itself of a Reyvateil's body is out from a [Song Magic] would not be an exaggeration. In fact, it is possible to say that [the root of the Reyvateils is made from sounds].

Special Characteristics for the Life Span and Growth

As mentioned above, the body of a Reyvateil is made with magic, and if the Nuclear Triangular Loop continues crafting its song eternally, then she will never grow old. During the approximately 150 years that the Nuclear Triangular Loop of a Pureblooded Beta-type is said to have as functional limit, the appearance of the Reyvateil does not change almost in anything, and her abilities will not diminish either, given they were programmed by the humans to keep living in good conditions for such a time. {C}However, when they are young, they are the same as humans, having a body that is still on the process of growing. That is, since their birth, the Nuclear Triangular Loop slowly releases Dynamic H-Waves upon the body of the Reyvateil so her physical body begins growing (and her mind also begins developing), and it will continue to do so while these waves continue to be released on her body. The Dynamic H-Waves that have as their purpose being the energy that allows the Reyvateil to grow are contained in a part of the Nuclear Triangular Loop called the [Hexagonal Hinges], and their energy slowly diminishes with the passing of time. When that energy is completely depleted, the body of the Reyvateil stops growing. In a normal [Nuclear Triangular Loop], this happens approximately when the Reyvateil reaches the age of 18 years.

What Happens on the Body of a Third Generation

The reason behind the need of life extending medicines for the Third Generation Reyvateil is the [Nuclear Triangular Loop]. That is because they have similar bodies to the ones that humans have, but are able to use magic because their bodies also are structured similarly to the bodies of the other kinds of Reyvateils, and that allowed them to inherit some of their characteristics. {C}However, given that they do not have a [Nuclear Triangular Loop] that regenerates the Dynamic H-Waves of their bodies, an special mechanism inside of the LEM (the Life Extending Mechanism of the Reyvateils), called the [HD Ring], causes the Static H-Waves of the Reyvateil to vibrate (makes them undulate), and turns them into Dynamic H-Waves to preserve the body, but the actual effect of this is the gradual self-destruction of the body. The body of the Reyvateil needs increasing amounts of Dynamic H-Waves, and when she reaches the age of 18 years and matures, the demands for Dynamic H-Waves will be so great that they will end surpassing the body's natural capacity to revert them, and it will end leading to the death of the Reyvateil. The Diquility is no more than an aggregate of [Static H-Waves] that do not possess any special properties, but also are of a very high purity, and that allows to regenerate the Dynamic H-Waves of the Reyvateil. When a Diquility crystal is installed, the HD Conversion Ring will give priority to the waves that form the Diquility crystal, and convert them into Dynamic H-Waves and energy. After three months, the HD Ring will have completely converted the Diquility into Dynamic H-Waves, and its effects will end wearing out, so because of that, it is said that [It is necessary to Install a Diquility once each three months to increase the life span of a Reyvateil].

Graphs 5

Comparison between the bodies of a Pureblooded Beta and a Third Generation.

Installs and Grathnode Crystals

For the feelings of a Reyvateil to leave her Cosmosphere, be stabilized and reach the Tower, they have to pass through a checksum verification to guarantee that these feelings are conveyed entirely to the Tower, and in case that these feelings don't have enough power, then the Tower sends back a correction feedback to stabilize the power carried in these feelings. {C}What the Install does is deceive this feedback. For example, if a Reyvateil has a feeling of [I want to save you with 10 times my power!], and we Install a Grathnode Crystal called [Power Up+3], the checksum interprets the feeling as [I want to save you with 13 times my power!]. Because the Cosmosphere is unable to send more than 10 times the power, the correction feedback would send a warning of [Missing 3!], but still, the sending of the 13 times the power would be forced on. This, essentially, allows the Reyvateils to use more power than what they normally could handle, but also puts a heavier burden upon them. Because it separates so much the Cosmosphere feelings and the checksum, it increases frighteningly the mental fatigue rate for the Reyvateils.

Graph 6

Differences between singing with and without an Install.

Install Ports

The Install Port is not only a point of contact with the Tower, but it also is like an I/O Port that is able to cause interferences in the Static H-Waves at the time of a Dive (incidentally, because this was designed to be a point of scanning during the Dives, it should not hurt if the scanning is performed during a Dive). And since this also is the point where the Grathnode Compound is exposed to the exterior, also exposing the Reyvateil's [feelings] in its purest form, the natural reaction is that the Reyvateils do not allow other people to see it.

Hymmnos Language

The Hymmnos Language and the Causality of the Natural Laws

The Hymmnos language was developed by Shamans on the ancient times. These Hymmnos incantations weren't able only to manifest effects out from the [Words] {C}that were pronounced in them, but also, thanks to the knowledge and experience {C}of the ancient ones, the waves contained in these words, which are waves of super-ultra high frequencies (Dynamic H-Waves beyond the 200000 Hz range), could be sensed by a lot of people. Furthermore, from these experiences, they were able to study more deeply the effects of the incantations, until they were able to cast their effects at will, such as for example, calling the rain. To be more precise, these words included a high concentration of dynamic waves, whose trend of effect was the condensation of the moisture present in the atmosphere, but even if they were able to understand such a simple concept, they could not go as far as converting these dynamic waves into static waves. {C}The energy emitted by a person in this fashion is very weak, and as such is unable to bring about great effects. However, when these words are sung in unison by many people, then the extent of the effects of their words gets much higher. Furthermore, when the consciousness of all the singers was synchronized with other, and their pronunciation spectrums resembled and called to each other, they were able to perform songs with great effects. {C}In the times of the Third Era, the multiple Hymmnos choruses are used for a great variety of things, and all of them stem from the experiences from these ancient times.

The [Tower of Origins] Interpreter

The predecessor of Ar tonelico, the [Tower of Origins], did not support the Hymmnos language. Between the capabilities it had, there was the capacity of regenerating simple structures that had a fixed wavelength, but creating anything from the nothingness was still beyond the wildest dreams of the researchers, since at most it could only produce sonic waves and water, but it was incapable of doing something on the level of producing unsubstantial energy. To allow it to become the main tool for the realization of the more complicated magic we see today, it was necessary to add a system that allowed the expansion of an instantaneous emotion spectrum (Song) in the time axis.

The Songs and the ω Spectrum (Deployment in the Time Axis)

When someone sings a song, the singer is expressing the emotions that he/she is feeling at each instant from the beginning to the end of the song. A high dimensional world where the waves have free movement in the time axis is built inside of the brain during the singing, and furthermore, if the song was sung in a determined instant, then the variations of its component waves in the time axis, and the spectre of the feelings and voice contained in them can be drawn out from the brain of the singer. That is possible only in frequencies beyond the 20000 Hz range that limits the [Individual Consciousness Fields], and since the frequency zone where the Individual Consciousness Fields and the audible sounds are located is the same (50~20000 Hz), that entangles both of them, allowing the expansion of the waves in the time axis. The audible sounds (the Songs) are [Carrier Waves], and as such, they are able to capture the Spectre from the Individual Consciousness Fields from the beginning of the song, and convey the [Feelings] that the song contains. {C}There is a wave spectrum that shows the [Time Axis], [Individual Consciousness Fields and [Energy], and is even able to display its changes and interactions in a tridimensional fashion, and because of that, it can be used as a tool for expanding complicated emotions and magic. That wave spectrum is known as the [FFT Spectrum]. Furthermore, in the current times there is even another wave spectrum that can show the fluctuations in the mind per δ units (microscopic time units),and the waves they contain at each instant, and is generally used for the physical manifestation of magic. {C}This spectrum that is able to gather all that information in fluctuations per microscopic time units and develop them in the time axis (however, it displays the information in a quadradimensional fashion, given that the number of data makes it impossible to display in three dimensions) is called the ω Spectrum.

Hymmnos Vocabulary

The Hymmnos Vocabulary was collected based from the experiences of the Shamans, with new words added to it. Staying true to its name as the [Language of Emotions], Hymmnos was polished in a way that each of its pronunciations expressed emotions at its fullest, and so the waves of [Feelings] (all the waves beyond the 20000 Hz range) could turn into carrier waves (sound waves) that could carry these emotions with the maximum efficiency possible, they attached the meanings of these [Emotions] to the pronunciations, and these words became the Hymmnos vocabulary. With the great intuition of the shamans, and the application of scientific research, the sound waves (carrier waves) of these words and the emotions they carried were tied into a vocabulary in the best form possible. After that, all the other words were developed with the intent of allowing an easier transmission of feelings.

The Purpose of Ar tonelico (the Tower)

Ar tonelico manifests in the physical world the feelings of the Reyvateils. The Dynamic H-Waves, containing their feelings, are always producing magical effects on higher or lesser extents if they are released in presence of Songstones, but this only produces weak effects, and also, since the receiving capabilities of the Songstone are weaker the more pure the stone is, the singer wouldn't be able to send enough feelings to cast magic without getting tired. So the function of the Tower is to refine the all of the waves of feelings that were absorbed into the Parameno Discs, and manifesting these feelings in the physical world after passing them through a Feedback Booster to amplify their effects. Thus, is said that the Tower is the Super Computer whose resources are used by the Reyvateils, enabling them to produce and use enormous amounts of power that no normal person could use by themselves.

Wave Transmission Methods

The Waves of the Reyvateils are sent through an special power line that is located inside of their Cosmospheres, called the [Tower of Life]. Because it is a direct connection to the Tower, they are able to transmit their feelings in their most pure state without problems. This is the reason behindthe Reyvateils being able to send through their requests for magic without the Parameno Discs, and it also was the first reason behind the development of the Reyvateils. If a human sang, the waves would be sent through the atmosphere, and because of that, they would become extremely fragmented, and the [Parameno Discs] wouldn't be able to receive them.

Why Humans Cannot Use Song Magic

This is because the humans also have feelings and songs, but since they are filled with great [Fluctuations], no matter the kind of song that is being sung, they won't be able to craft precise waves from it. Still, when a human sings, they at the same time are thinking and feeling about a lot of things. This is putting these thoughts and feelings into the [Sounds], but actually, the [Mind] can't integrate these feelings to the song consistently, and because of these great number of inconsistencies, the humans are unable to produce Dynamic Waves to send off in a song. For a song to exist without fluctuations it has to be composed of earnest [Feelings], and this was the second reason for the development of the Reyvateils. When a Reyvateil sings, she is also demonstrating an astounding power of concentration, and no matter if she gets attacked or hurt, she won't stop singing, but still, she needs protection because she can't defend by herself while singing. The songs of the Pureblood Beta-types are almost completely free of fluctuations, but the Third Generations do have a great number of fluctuations, though lesser than the number of fluctuations that humans have. That has become the difference between their abilities. {C}
Graph 7

Structure of the Hymmnos Words

Song Magic

Reasons Behind the Physical Manifestation of the Song Magic

As it's explained in Wave Science: [When the Dynamic D-Waves are used upon a target point, they will change into Static D-Waves, bringing something into existence upon that point]. The Static D-Waves are the components of matter, with the low frequency ones being gases and the high frequency ones being solid structures. Therefore, if the Dynamic D-Waves of high frequencies end producing Static D-Waves of high frequencies, then they will create [something] from the air, which is a very advanced class of magic.

High-Capacity Ring for Wave Frequency Disparity

Because of the wave frequency disparities that exist when using high-level magic, it's necessary to have strong feelings when singing the song that manifests it. For example, for things such as creating or destroying matter, even if the Tower does the amplification work for the feelings, the feelings must be equally strong to the level of energy that the song needs to perform its effects successfully. {C}The simplest method for raising the energy level of the Reyvateil is crafting magic inside a high-leveled Cosmosphere. That is because the magic crafted inside a high-leveled Cosmosphere allows to approach and receive power from the Tower with the same level as the power that was used to craft the song. Since the higher levels are closer to the Tower, the feelings are much easier to convey through the Tower of Life, and allows to receive back very high amounts of energy very easily.

Graph 8

Process of Execution for a Song.

Bonus Explanation: The Relationship Between Aurica and Mir

Aurica's Static H-Waves are unexpectedly similar to Mir's Spectrum Gene, even up to her High Frequency Waves. Because in the Hymn Code zone both had very similar wavelengths, Mir was able to easily open up Aurica's [Boundary Gate], and in that way, she materialized viruses using Aurica' mind as a intermediary during her visit to the Musical Corridor, and also, projected the model data of Goddess Tylia inside of her Cosmosphere. When Shurelia said that [Probably Aurica has a hole in her mind], she was referring to their similar wavelengths. This also means that Mir and Aurica don't share any kind of relationship.

Intermediate Section

The Laws of the World

The Definition of this World

World > Universe > Galaxies > Planetary Systems > Planets> Regions > Individuals

The extremely enormous "border" that shapes this universe is the world. {C}And for clarifying the terminology used in this book, [Planet] is how we {C}call the [Planet of Ar Ciel], and [Region] is how we call [Metafalss] and {C}[Sol Ciel].

The Laws of the Universe

This Universe is made from waves, as well. The event that created [this {C}world], called the Big Bang, was caused by just an small atomic nucleus. {C}That atomic nucleus is called [Exa Pico], and by means of its enormous {C}will, it crafted the [Universe].

The other kind of existences, such as the stars and galaxies, were all born {C}from Exa Pico, as well. The expansion from Exa Pico and indicating the creation {C}of every thing has been said metaphorically in Metafalss as [Whenever Exa {C}Pico crafts a song, it also creates something].

It can be said that the atomic nucleus of Exa Pico also composed an unlimited {C}number of waves (Static Waves). And thus, each one of these waves (for example: {C}the D-Waves) can be said in a unlimited number of ways that it also carries {C}an unlimited number of wave frequencies as its components.

Exa Pico also emits the astronomical kind of waves at such a rapid and violent {C}rate that our general concept of time isn't even able of measuring it. And when the expanding waves come from different directions and bump into each other, they cause interference to each other, and originate waves that have lost the equilibrium in their undulation. These new waves are the [Dynamic Waves] (Pic. 1).

The newly created Dynamic Waves will propagate through the space of this world, and create the [Universe] of Exa Pico. In short, we can say that the Universe, under the general concept of [World], is [an area where Exa Pico exerts its influence).

Thus, the expanded Dynamic Waves will create a new kind of waves, called Static Waves. This phenomenon is said to be the result of the Dynamic Waves created by Exa Pico expanding through the Sea of Num (the space where the amplitude and frequency of all the waves are zero). The theories established under Wave Science
stipulate that the Dynamic D-Waves gave their frequencies and amplitudes to the Sea of Num, and that created the Static Waves, turning the [Universe] into [Something that Continues to Exist]... or at least, that's what these theories say. (Pic. 2)

This wave interference doesn't happen because of special Static Waves. Except for the Dynamic D-Waves, all of the waves are the result of a simultaneous interference, which also produced the assembly of new atomic nucleuses. We actually could say that the Exa Pico continues creating an unlimited number of new assembled atomic nucleuses. Among these assemblies we have the stars, the black holes, and the waves of energy that are invisible to the naked eye. These countless creations are born from the [Song] of Exa Pico. The creations also include H-Waves, which, even if they are called in various ways, they aren't anything more than [Will]. Namely, they are {C}the [Feelings] of Exa Pico.

At2 p142 derivation of dynamic waves

Derivation of Dynamic Waves

When two waves of the same kind (i. e. two identical D Waves) collide with {C}other, the wave interference causes the creation of a new wave.

At2 p142 formation of the static waves

Formation of the Static Waves

Is only in this stationary point where the Dynamic Waves meet, and because {C}of the resonance phenomenon, they are amplified, creating an static power {C}exactly where they meet. That power ends turning into a new Static Wave.

The Laws of the Star Clusters and Star Systems

The assemblies of stars called Galaxies and Solar Systems are the product {C}of the many kinds of waves released by Exa Pico. And thus, these [Star Clusters] {C}are atomic assemblies which exist being essentially similar to Exa Pico. {C}As we all know, this is because the Star Clusters themselves also have their {C}own [Feelings]. However, these feelings are not actually of them, or from {C}other entities. They are nothing else but the extraordinary feelings of {C}Exa Pico. This is because the Star Clusters are existences that were contained {C}inside of Exa Pico, which causes that the [Feelings of the Star Clusters] {C}and the [Feelings of Exa Pico] to not be different at all. Thus, the Star {C}Clusters, and the feelings that were contained inside Exa Pico, were what {C}created the infinite number of stars that compose the Star Clusters. While {C}this process keeps repeating itself endlessly, it will give birth to many {C}new atomic assemblies, which take the shape we call the [Stars].

The Laws of the Planets

And when a [Planet] is created, the Will that supports its existence will even {C}transcend the astronomical kind of mathematics. And it's because, as we have stated so far, the infinite number of waves released from Exa Pico, the Universe, and from the feelings of the Star Clusters, all exert an influence over the Planets. Because they all constructed [the atomic assembly of this Planet], it's {C}that this Planet exists. And because of that, the Planet also has a Will {C}of its own, its own [Feelings]. {C}This Planet, which contains the regions of Sol Ciel and Sol Cluster is called {C}[Ar Ciel} (which in Hymmnos means [This World]). The Will of the Planet {C}Ar Ciel is what gave birth to everything that exists on its surface. From {C}all the life forms, to its own shape, including its mountains and oceans, {C}all of them consist of the waveforms that are affected by the Will of Ar {C}Ciel.

The Laws of the Life Forms

Continuing, we will now discuss the topic of the [Life Forms]. The humans {C}have a will, which is formed by their [Static H-Waves]; and also, they have {C}a body, which is formed by their [Static D-Waves]. There is also a condition {C}where they could lack D-Waves, and have only H-Waves, which is an existence {C}we are used to call [Spirits]. The humans perceive the world through their {C}[Eyes], though their eyes are no more than [Sensors capable of recognizing {C}just an small part of the existent Static D-Waves]. This is the reason why {C}they are incapable of perceiving H-Waves. {C}Now, thinking under this paradigm, you should be able to think about the {C}[Will] in a more deep way. The humans usually think that [The animals have {C}will as life forms], [The plants are life forms, but don't have a will of their own], and [The stones aren't life forms, so they don't have a will]. However, all of this is but a misunderstanding caused by just judging from what they can perceive through their eyes. The animals simply [have a body and a will that allows them to move freely]. The plants are just [life forms that don't have a will that allows them to move freely], though you can {C}see that they do have a component (their bodies) that does change over time. {C}And the stones [don't have either a body or will that allows them to move freely], but they do have a [Will] of their own. So you can be sure that everything that exists on this world has a [Will] of its own.

The Atomic Assemblies and the Bodies

The atomic assemblies are [anything] that is always being created because of wave interferences. Because of this, Exa Pico crafted an unlimited number of things through the Static D-Waves and other kinds (such as the H-Waves, which cannot be perceived by the eyes), which was what created the universe. No matter if the end result is an star cluster or a planet, they passed through the same process to be created, and at the end, many things are being created inside of the planet. For things that are visible to our eyes, such as the atmosphere and the moisture, and also, the life forms, all are created through Dynamic D-Waves. Especially in regards to the life forms, whose main components are both Dynamic H-Waves and Dynamic D-Waves, and the union of these two kinds of waves with an infinite number of other kinds of waves, which are said to be the product of a wave interference of an extremely high level, are what gives life to them.

Like this, starting with Exa Pico, and ending with the life forms, is how all the environments originated, and how new [anythings] continued to be created, but... what about the [humans]? The answer is [of course they are being born]. For example, the Static D-Waves they call their [bodies] are like that too, being constructed by cells, and as long as these cells continue exercising their metabolisms, they will continue to live, thus being called [life forms]. Besides, the exterior of the body also creates many kinds of waves, such as heat and sweat. However, that clout is so small that it cannot be perceived. For example, if we saw this from the viewpoint of the planet, it would just be as thin as a paper sheet. More or less that is how we feel the clout of our cells. But speaking In general, the meaning of everything from Exa Pico to the humans being just atomic assemblies doesn't change. Everything that exists {C}because of the same reasons as Exa Pico is a [life]. The difference between {C}both is only in what kinds of waves constitutes each of them. Each one of {C}the waves that we know also forms part of a bigger wave range, whose highest {C}point are the waves that expand from Exa Pico (pic. 3).

At2 p143 the flow of the waves in the world

The Flow of the Waves in the World

The waves represented here are an schematic diagram of the supposedly infinite {C}waves that expand from Exa Pico, which is on a upper rank in comparison {C}to the star clusters, stars, and planets, among other things, and we can {C}see how each one of the lower ranks inherit one part of these waves when {C}they are created. In other star clusters there are also other planets, which {C}means that they might have entirely different waves in their composition {C}from the ones that Ar Ciel has. Furthermore, if the "father" part doesn't have an specific wave as its component, then, its "children" parts won't {C}inherit it either. For example, if a sun doesn't have N-Waves on its composition, the planets orbiting it won't have N-Waves either. Following this line {C}of thought, we can see that being apart in this universe by a relatively {C}short distance doesn't go against the common sense. However, given how vast the universe is, there might be infinite places where the scientific paradigms existent on Ar Ciel might not be applied.

The Existence Called the "Voice"

The human atomic assemblies have a vertical area of influence of approx. 2 meters, which is where their own Static D-Waves enter into effect to mold their bodies. However, the humans surprisingly have also another extremely great power. This power is the [Voice]. The voice changes the Static D-Waves, and produces Dynamic H-Waves. As we said before, the Static H-Waves are [Will], and releasing the voice is an act of expanding the area of influence of the atomic assemblies by several hundreds of meters temporarily. And furthermore, the humans also have sensors capable of perceiving any kind of Dynamic H-Waves, as long as they are lower than 20.000 Hz. These sensors are what we call the [Ears]. Under Wave Science, the Ears are thought of as a prepared instrument that acts as a checksum for confirming the Dynamic H-Waves (Will) that we ourselves release.

The H-Waves - "Will" and "Feelings"

If we can call the Static H-Waves the [Will], then we can also call the Dynamic H-Waves the [Feelings]. Because the human atomic assemblies are comprised of Static H-Waves, the humans also have a Will, as we can prove under Wave Science.

According to the researches conducted in Sol Ciel, it has been explained that the humans are able to express Dynamic H-Waves in a range that goes from 1 Hz to 5.28x10^11 Hz. However, if they were to become waves from the highest frequencies, their H-Waves (feelings) would need to increase their strength in extremely great quantities. As for an example of things would be raise to raise the strength of the H-Waves, we can say things such as the instinctive (potential) [earnest feelings] and [impulsive feelings], which are what in the end produce Dynamic H-Waves containing great quantities of energy.

We can try to think about what kind of influence its exercised by the voice of a person causing interferences in the Will of others. When both read the same sentence aloud, one reading it with strong feelings, and the other one reading it plainly, the former one will resound more to the hearts of the people. Basically, it's because the Dynamic H-Waves of the first person {C}were spread in the [words filled with feelings], and the more feelings they {C}contain, the stronger is the energy they will have when they clash with {C}the Static H-Waves of the receiver, meaning this will create wave interferences. {C}Because of the judgement that all of the people generally make from their {C}own viewpoints, we will notice with our eyes what we call the [movement] {C}(the interferences of the Dynamic D-Waves), however, though we normally {C}say that [I'm moved], we are also conscious that we can't see the moving {C}of the heart (the interference of the Dynamic H-Waves)

Still, the Static H-Waves can be moved by many other things besides the {C}voice. For some familiar examples, we could say the books or the movies. {C}All of these can be either inorganic substances or atomic assemblies, but {C}all of them are created by the humans, and both produced the human wave interferences, and they are what end forming the Static H-Waves. All of this can be resumed in that the [Will] and the [Feelings] are H-Waves, and they are present in every thing we can see.


So far, we have seen that the themes of this lecture were the capacity the {C}humans have to see the D-Waves, and their ability of perceiving and emitting {C}H-Waves. However, this actually means that the human atomic assemblies are {C}not capable of emitting Dynamic H-Waves by themselves. {C}However, the humans found a solution to this with the discovery of the [Songstones]. {C}Because the Songstones are able to absorb with a good range the Dynamic {C}H-Waves from any given source, and after storing the energy of the [voice], {C}it can also release them converted into Dynamic D-Waves with an equally {C}good range, effectively manifesting that energy into the physical world, {C}and allowing them to be used. {C}Once the humans discovered the Songstones, they became able to create Dynamic {C}D-Waves at will, but unfortunately, its overall effects were too weak to {C}be used in a greater scope. It also was discovered that the Dynamic H-Waves {C}the humans released were filled with fluctuations, thus making them unable {C}to control the power their feelings could generate. This eventually led {C}to the creation of the [Reyvateils].

The Reyvateils and the Waves

Once the Humans realized their own limits, they began to research the H-Waves and D-Waves more deeply, and basing their theories on these two kinds of waves, they created the Reyvateils. And for maintaining the life cycle in their bodies, they made them so they needed only D-Waves and H-Waves, among the innumerable kinds of waves that may exist, to continue living. This is why they are a more simple version of the humans, who are constituted by seven different kinds of waves, and also, this is the reason behind being hard for the Reyvateils to come up with evil ideas. The reason behind this simplicity is related to being able to perform a process with extreme accuracy, making the Reyvateils so efficient that they effectively can't be compared with the Humans. Still, there are some phenomenon that are said to be impossible to cause in the human brains, and they can't happen in the Reyvateils either.

And from now, we shall be explaining about the Reyvateils as they are seen in an scientific way.

The main components that form the humans are the energies from seven different kinds of waves, with every one of these waves located in frequency bands that are between 1 Hz and 5.28x10^11 Hz. This also means that all the waves emitted by the humans, such as their vital energy, love, or any emotions, reach their limits at the 5.28x10^11 mark. No matter how much you fall in love, or how much enlightened you might be, the human waves can't cross the 5.28x10^11 frequency band, since that is a physical impossibility.

Because of this limit, the humans created the Reyvateils by scanning their own H-Waves, and made them similar to them, like if they were [clones of the humans, specialized in particular abilities].

And the memories and minds of the Reyvateils are preserved in Ar tonelico through a shape called the Cosmosphere, in which their Individual Consciousnesses are located in the frequency bands up to 1.16x10^8Hz, while any frequency band higher this is where their Common Consciousnesses are located. Furthermore, in all of the areas of the Cosmospheres, they are able to give a physical shape to all of their emotions, thanks to their direct connection to the Tower through the Parameno Discs. And more importantly, the Reyvateils are able to craft miracles called Song Magic (the conversion of Energy into Dynamic D-Waves through Ar tonelico) by sending their feelings to Ar tonelico (their Songs, which are essentially Dynamic H-Waves), which are created in response to their waves reaching a peak by cultivating their Cosmospheres.

And now, we will talk about the enhanced breed of Reyvateils created in Metafalss, the IPDs. They are different from the Standard Reyvateils by the fact that their Individual Consciousnesses were structered in a more shallow way, given that they are located in the frequency bands ranging from 2.0x10^4 Hz to 5.4x10^7 Hz. In the deeper bands, they were structured to have an special energy reserve called the E-Spot, which is their special characteristic as the [Reyvateils that were created to sing Metafalica](more details on page 91). However, having their consciousness limit lower than the other Reyvateils doesn't hamper at all the effects of their Song Magic. This, which was considered the biggest design failure of the IPDs, was discovered during their development stage, and ended being fixed thanks to the creation of the Hymmnos dialect used exclusively by the IPDs: the [New Testament of Pastalie].

And more importantly, they demonstrated that their Songs are more effective when compared to the ones used by the Standard Reyvateils, both time and effect-wise, since the IPDs could sing songs of {C}an specific level faster and with better effects than the ones used by the Standard Reyvateils of the same level.

The Atomic Nucleuses [Sing]

The Songs go through all the creation. This is because all of the atomic {C}assemblies [are singing], starting with Exa Pico and ending in the inorganic {C}substances. This is said to happen because [they are exposed incessantly {C}to the waves]. As paradoxical as this might sound, if the atomic assemblies {C}did not continue to sing, they would be unable to preserve the existence {C}of their child assemblies. {C}Taking an example from Song Magic, more precisely: Luca's restoration song magic [Triangle Tune]. While Luca sings the song, we can see the figure of a girl appear, but once Luca stops singing, the figure of the girl disappears in just an instant. This is because Luca stopped sending the Dynamic H-Waves that maintained the existence of Triangle Tune (or more strictly speaking, the Dynamic D-Waves that Ar tonelico released in response to her Dynamic H-Waves). And since the Dynamic D-Waves that formed her disappeared, she returns to the space (the sky) controlled by the [Dynamic D-Waves that are released from the great universe containing the Planet of Ar Ciel]. This is because Triangle Tune is not related anymore to the Will of Ar Ciel. All of the existences that are still over the Planet of Ar Ciel exist because of the Dynamic D-Waves that were produced by the singing of the Planet. All the other existences that may appear over it are allowed to be just because the Planet of Ar Ciel [allowed them to exist]. However, the Will of the Planet Ar Ciel will only recognize Triangle Tune as a friend during the time that Luca continues singing. That is why Triangle Tune cannot continue existing once Luca has stopped singing. Essentially, this is a law of nature, though the existence will not disappear only if its creator vanishes away. For example, a vacuum cleaner will not disappear, no matter if its inventor passes away. This is because, in the first place, the vacuum cleaner was created with the resources of Ar Ciel, so the inventor already made a mediation with the Will of the Planet. But from the viewpoint of the planet, the vacuum cleaner will end weathering because there wasn't any mediation about [preserving its vacuum cleaner {C}condition]? {C}Like this, all the things in the creation are singing. All of them, are {C}what forms this world shaped by the songs (pic. 4).

At2 p144 the love towards song magic trans

The Love Towards Song Magic

{C}An item, such the [Walking Gergo] created by Cloche, was created out from {C}the raw materials of Ar Ciel, so it has received all the love from this {C}star system. Because of that, no matter if Cloche dies or if Ar Ciel is {C}destroyed, it will continue existing. However, a Song Magic, such as [Triangle {C}Tune], is made from mechanical D-Wave interferences, and since it was created {C}from a disruption in the natural order of the Planet, it cannot receive {C}love from anything besides Luca. Because of that, Triangle Tune will disappear {C}as soon as Luca stops singing.

The Only Love of the Second Tower

The Second Tower, located in Metafalss, only continues existing because {C}it's exposed to the Dynamic D-Waves emitted from Sol Marta. Because the humans can perceive the D-Waves by various means, such as hearing and seeing, they settled down upon it, without even starting the doubt if this place was actually structured by just only D-Waves. However, in reality, this artificial structure does not exist over the Planet of Ar Ciel. And because it is an strange body that was not mediated with the love of Ar Ciel, it is supported only by Frelia's love. This means that if Frelia stopped singing {C}(supporting) it, this structure would return instantly to its original state {C}(in other words, it would vanish into thin air).

The Love of the World

The Planet of Ar Ciel, during more than 700 years has accepted an artificial {C}assembly of D-Waves among its own waves, and this is because of Frelia's singing. As long as Frelia continues singing, we can say that the Tower is a "friend" of the Planet of Ar Ciel. Over the Tower, we can see that plants grow like if there was land, and they are nurtured by water. Yes, this means that the Planet has accepted the strange Towers as if they were a natural part of it. This love that does not require any compensation is "the love of the world", which is represented at its peak by Exa Pico, which continues allowing the existence to all the things in the Universe.

Continuation: The Laws of the World

Now, we shall return to the start of the second section of this lecture: [The Laws of the World]. The atomic assemblies of both Exa Pico and the humans are exactly the same, the humans are formed by cells within their bodies, and as if it was to allow them to live as they wished, the laws of the world connect everything in an equal way. Exa Pico, and more precisely, Ar Ciel, exist because that is the Will of the Universe. And since Exa Pico is receiving the love of this [World], that means there should be others. That also means that there might be another atomic assemblies that were created like Exa Pico: by the Big Bang that gave birth to the Universe.


  1. Ar tonelico: A Reyvateil's Melody forums: Official Materials Collections Translation Project thread
  2. Ar tonelico: Official Materials Collection - Wave Science section, pages 114-117.

Ad blocker interference detected!

Wikia is a free-to-use site that makes money from advertising. We have a modified experience for viewers using ad blockers

Wikia is not accessible if you’ve made further modifications. Remove the custom ad blocker rule(s) and the page will load as expected.