Wave Theory

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.

=Introduction to Waves=

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.

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.

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.

=Dive=

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.

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 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.

=Structure of the Reyvateils=

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 for the Static H-Wave FFT Spectrum of the Reyvateil. 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 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. 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. 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. 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 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].

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. 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.

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 did not bring about any effects out from the [Words] that were pronounced in them, actually, because of the knowledge and experience of the ancients ones, there were a lot of people that were able to feel the waves of super-ultra high frequencies (Dynamic H-Waves beyond the 200000 Hz range). 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. 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. 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 (Expansion 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. 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 three-dimensional 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. 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 four-dimensional 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. =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. 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 which 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.

=Hymmne Crystals (Hymn Crystals)=

The Storage Qualities of the Hymn Crystals
The Hymn Crystals are items similar to the Grathnode Crystals, but unlike them, they don't have any special qualities, and no matter how much energy they receive or which direction said energy comes from, they can't be interfered. If one of these crystals was Installed in a Reyvateil, the wave interferences would cancel each other, and it wouldn't affect the Static H-Waves of the Reyvateil at all (in short, it would reduce her GD* Value to 0). The interferences are balanced out by the energy from the crystal, and the power center that exists within the FFT Spectrum of the crystal doesn't allow the interferences to be discharged either, allowing the crystal to keep its form eternally. The power center that keeps the FFT Spectrum constant is what allows the Hymn Crystal to record the [Feelings] = [Complete Expansion of the Static H-Waves of the Reyvateil]. The one that records the feelings in the crystal is the heart of the Reyvateil, but the balance inside of the crystal is what allows them to continue existing without allowing any loss of feelings.


 * GD = Grathnode Damage.

The Download Ceremony
During the chanting of the Hymmnos Spell for the execution of the Download, a perfect equilibrium is kept for the waves that are being recorded in the Reyvateil's mind in that instant, because what keeps that balance is the power that is being borrowed from the Tower. If the Hymn Crystals were Installed like the normal Grathnode Crystals, [It would be like breaking the shell of a egg of feelings], and these feelings would never go through to the mind of the Reyvateil. Because of the drawing of that preserved FFT Spectrum, and furthermore, the precise overlapping of the Static H-Waves of the Reyvateil, this is not only the act of accessing to the Cosmosphere from the Binary Field, but also the result of the execution of this command, the Download Hymmnos Spell.

Why the Songs are Crafted Instantly?
When the download is complete, the song gushes forth by itself. This is because of the overwriting done by the FFT Spectrum that was recorded on the Hymn Crystal, expanding an entire spectrum of feelings on the time axis (in all the wave frequency zones, in all the time zones) in just an instant, and the Spectrum condition then becomes: [In process of crafting a song]. If we look at this through the perspective of the Reyvateil that downloaded the song, she feels like she had known the song from a long time ago, and within her own feelings and memories... the song is born, like an small bird.

=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.