ARM Backup/Settei book translations/Wave Theory section

==For Experienced Players: [Wave Science] Lecture==
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Here we will approach the deepest side of the world setting through the [Wave Science] from Sol Ciel, which states that "Everything is made from [Waves]!
==Introduction to Waves==
===The Structure of Matter and the Static D-Waves===
Matter is constructed from the complex entwining of multiple waves, which can have frequencies ranging from 1 to ∞ Hz. These particular waves are called [Static D-Waves (Static Detail Waves)], and they are characterized by always remaining at rest. The strength, directionality and spectra (frequency component) of the wave frequencies' energy act upon the microscopic points where each Static D-Wave rests, which is what make possible the change of matter from solid to liquid and gas.
[Graph:]
This is the FFT analysis and disassembly of the spectrum in the Z-Axis of the wave component that acts upon the steel frame's microscopic point.
The sum of the measurement errors is equal to the strength and directionality of the Dynamic Waves that act upon this microscopic point. These are the Dynamic D-Waves.
There are thousands to millions of waves with different frequencies in a single microscopic point. Their characteristics are what give shape to matter.
[End Graph]
===The Magic and the Dynamic D-Waves===
Every single kind of paranormal power has its origin in the [Dynamic D-Waves (Dynamic Detail Waves). The Dynamic D-Waves that constantly appear and disappear are also the [ridges] that produce measurement errors in 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. If we take a look at a diagram of space coordinates stagnated with Static D-Waves, we would see there are measurement errors in their power fields and spectra components, but if we check the time axis for these same waves, we would see a different type of waves that constantly spread and converge in a way similar to undulation. These measurement errors become a surplus energy, and their unstable centers of power serves as the source of magic.
===The Power of the Voice and the H-Waves===
While sounds normally exist only in a frequency band that goes from 50 to 20000 Hz, whenever a living creature emits its voice they also output waves with an even higher frequency to a greater or lesser extent. These special waves that are unrelated to the D-Waves are called H-Waves, and are commonly known as the [Waves of Feelings].
The H-Waves are also split between [Dynamic H-Waves (Dynamic Hymmno Wave)] and [Static H-Waves (Static Hymmno Wave)], with the former corresponding to the singing voice and feelings, while the latter are said to be the source of life (life energy). Given that the H-Waves and D-Waves exist in different dimensions, the H-Waves cannot affect the material world by themselves, but under the supposition that they exist as well as the D-Waves in the frequency ranges that go from the lowest to the highest bands, their frequency components can be negotiated through the [Songstones] to be converted into D-Waves.
Name
(Abbrev.) 	Dynamic D-Wave
(DDW) 	Static D-Wave
(SDW)	Dynamic H-Wave
(DHW) 	Static H-Wave
(SHW)
Forms 	Dynamic energy 	Matter 	Songs (Song Magic), feelings	Life energy
Nature 	Distortion of matter 	Matter itself 	Songs, brainwaves 	Cosmosphere
Kinetic Energy Level	High 	Low 	High 	Low
Wave Type 	Ether wave 	Ether wave 	Astral wave 	Astral wave
Wave Nature 	Radiation, continuous motion	Continuous rest	Radiation, continuous motion	Continuous rest
===The Role of the Songstones===
The Songstones contain two different components called [Grathnode] and [Parameno]. Paramenos reacts to the presence of Dynamic H-Waves by absorbing them and transmitting their energy to the neighboring Grathnode component. The Grathnode component then reacts to the distortion in the crystal's internal D-Wave composition by absorbing these Dynamic D-Waves, and once the absorbed energy has crossed the crystal's critical point, it emits these distortions upon its surroundings. This Dynamic D-Wave emission becomes the power to create matter from nothing. As the Grathnode component won't emit any energy except for the amount that exceeds the crystal's own critical point, it is quite frequent to find in nature crystals that have quite an amount of distortions absorbed into itself. Therefore, if a Songstone crystal is broken at the same time a sound is emitted, its emissions will always be similar in nature to sonic waves.
===H-Wave Bands===
As the Static H-Waves are what give form to the minds of humans and Reyvateils, it is possible to decipher even their emotions and concrete feelings by analyzing them. The device that systematizes this process is the Dive Machines. To summarize the basic process through which Song Magic is crafted, the Dynamic H-Waves emitted by the Diver (human) cause undulations in the Reyvateil's Static H-Waves, with these distortions becoming Dynamic H-Waves, or a new Song. The Static H-Waves are divided into the following frequency bands:
▼Individual Consciousness Fields...This band reaches at most the 116000000 Hz point, and it is the region where it is possible for an individual to be conscious of their own actions. It is also known as the [Cosmosphere], and it is possible to Dive in it.
▼Hymn Code...A band located approximately at 100 Hz above the 116000000 Hz point, which is characterized by the fact that no matter how much a person's feelings change, it will never change its shape. The First Era engineers took notice of this band's stability during the development of the Pureblooded β-Types and decided to add a prerecorded tag to the [FFT Spectrum] corresponding to it. Therefore, saying a Hymn Code is actually ordering the Tower to compare the FFT Spectrum of the Reyvateil that owns that Code against the record of her Spectrum stored in the Tower. This band is generally never passed down as genetic information, so the Third Generations do not have their FFT Spectra recorded within the Tower (in other words, they do not have Hymn Codes that were recorded into the Tower). There are rare cases like Aurica who did inherit a Hymn Code, but this is only because the Tower misrecognized them for another individual.
▼Shared Consciousness Fields...The region located in the highest wave frequencies, where the individual is unable to assert any sort of control and it is instead drawn in by other people's feelings, and their own feelings are affected by the feelings of others. This band can be used to exert control over others, which is why the Reyvateils' own Shared Consciousness Fields were created in shallow layers. During the events that led to the end of the Second Era, the Reyvateils started seething with hostility toward all humans regardless of who they were, but this was because the distrust each Reyvateil held toward the humans was greatly amplified, which caused them to lose control of themselves to the point of unconsciously attacking humans as a whole.
[Graph]
FFT Spectrum (Extract from the δ Time Axis)
FFT Spectrum of a Reyvateil (Static H-Waves)
Individual Consciousness Fields Shared Consciousness Fields
 Hymn Code
FFT at Time of Singing a Lv. 8 Song Magic (Dynamic H-Waves)
Audible Band (Carrier Wave Band) Individual Consciousness Fields Shared Consciousness Fields
Enzyme (Static D-Waves)
Low Density (Gases) Middle Density (Liquids) High Density (Solids)
Iron (Static D-Waves)
Low Density (Gases) Middle Density (Liquids) High Density (Solids)
Dragonferno (Dynamic D-Waves)
Low Displacement Middle Displacement High Displacement 
[End Graph]
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==Dive==
===Dives as Proven Under Wave Science===
The area in which Diving is possible starts at the lowest wave frequencies, where Soulspace Level 1 is located (approximately in the 20000 Hz range), while Level 9, the highest one, is located in the highest frequencies (approximately in the 110000000 Hz range). Trying to interfere into wave bands any higher than that point could not only bring about the risk of destroying the Reyvateil's own mind, but it would also affect the minds of the Reyvateils that exist in points slightly higher to the Diver, and the Diver's own mind as well. As consciousnesses with a low wave frequency receive a great impact from consciousnesses with high wave frequencies, and it is necessary that the intervening wave frequencies of the Diver become so close to the wave frequencies of the intervened Reyvateil that they seem indistinguishable from each other, if the Diver is unable to interfere into the Reyvateil using the purest feelings (high-frequency Dynamic H-Waves) they hold for her, the Diver's mind will be devoured by the Reyvateil (the Diver will be unable to return to the real world). In order to avoid this danger, the concept of the Cosmosphere being divided into levels and the creation of the safety device known as the Mind Guardians were created in order to protect both the Reyvateil herself and the Diver.
===Paradigm Shifts and Limits to Diving===
When the Dynamic H-Waves of the Diver cause a remarkable peak on the Reyvateil's Dynamic H-Waves, the Reyvateil's own waveforms undergo a large undulation and a Paradigm Shift materializes. When the waves change into finer (higher frequency) waveforms, they are compelled to go a level higher within the coordinates shown in the FFT Spectrum. So in summary, a Paradigm Shift is the act in which a Reyvateil's waveforms are elevated to a higher frequency. The elevation of the Diver's consciousness triggers an elevation of the Reyvateil's consciousness, which makes it a process in which both grow together.
Dives end at Level 9. At Level 9 there is a small low-frequency band that corresponds to the Hymn Code zone, and it is impossible to interfere in frequencies any higher than it under normal circumstances. Therefore, Divers cannot emit Dynamic H-Waves to interact with frequencies any higher than Level 9 regardless of how much they may sympathize with any Reyvateil.
[Graphs]
Example of a Dangerous Dive (What would happen if a low-leveled consciousness accessed a high-leveled Cosmosphere)
Consciousness at the time of interference (Dynamic H-Waves) Challenged Band
Eroded by the Reyvateil, the mind of the
Diver is strained, and finally, collapses.
Individual Consciousness Fields
Example of a Safe Dive 1 (Lukewarm Relationship)
Consciousness at the time of interference (Dynamic H-Waves) Challenged Band
As they are in the same region, they are in balance.
They cause no effect upon each other.
Individual Consciousness Fields
Example of a Safe Dive 2 (Lukewarm Relationship)
Consciousness at the time of interference (Dynamic H-Waves) Challenged Band
 
 -> Paradigm Shift
 The Diver gives to the Reyvateil
 a positive influence.
Individual Consciousness Fields
[End Graphs]
===The Duties of the Dive Shops===
Whenever a remarkable consciousness difference appears between the Diver and the Reyvateil, it is necessary to conduct an emergency suspension. Therefore, the Dive Operators have the duty of constantly monitoring the [FFT Spectra] of the people involved. Cases that would require such actions would be situations in which either the Reyvateil's waveforms or the Diver's consciousness suffer a striking drop. For example, if Aurica told Lyner [Come live in the Soulspace] and Lyner even thought [I'd be okay with that], this would cause a critical situation in which Lyner's waves would drop in frequency and Aurica's high-frequency waves would erode them. Therefore, the Dive Operators must always monitor the waveforms to keep such dangerous situations from occurring, though they are unable to see in any way what concrete events transpire within the Cosmosphere.
===The Reason for Dives Into Humans Being an Impossibility===
The structure of the Reyvateil minds, the [FFT Spectrum] is a waveform circuit designed by the humans, and the device (Dive Machine) for safely and meticulously examining it was designed at the same time as it. So if a human was examined through a Dive Machine, generally nothing would happen (there is a one-in-a-million chance of it destroying that person's mind though). So to Dive into a human, it would be necessary to analyze in detail the structure of the humans' Soulspace Map (Static H-Waves), but as only the analysis of the Dynamic H-Waves was completed during the First Era, the Soulspace Map of the humans was left an unknown. The reason for why it is possible to Dive into the Reyvateils who are hybrids with the humans during the Third Era is because their human Static H-Wave component is left undisturbed by the Dive Machine, as the replication of it they have as part of their Reyvateil structure is the only section that is drawn out to be examined.
==Reyvateil Anatomy==
===The Spectrum Gene===
The existence that has the central role in configuring a Reyvateil's body is called the [Spectrum Gene]. This is an aggregation of Dynamic H-Waves that has a spectrum of a specific wave frequency, which gives form to a regular tetrahedron that maintains a 60° angle: the [Triangular Nuclear Loop]. Each Triangular Nuclear Loop contains the [Standard Spiritual Frequency] that serves as the individual clock to each Reyvateil, and its timing serves as the basis for the formation of the Reyvateil's Static H-Wave FFT Spectrum.
The Spectrum Gene has an exceedingly low capacity for storing information, so whenever a clone is created, the combination of Parameno, Grathnode and the Triangular Nuclear Loop coupled with the effect of multiple [undulations] such as infinitesimal interference measuring errors will keep the new individual from being identical to the one that served as its basis. Therefore, they will not be completely identical despite being called clones.
===The Reyvateil Body===
The Reyvateil body is basically composed from the same proteins that build the human body, but it also uses Grathnode compounds and Parameno compounds in order to protect the Triangular Nuclear Loop and to link together the H-Wave component (mind) and the D-Wave component (body). These compounds are materials that maintain a perfect balance and never have waveform displacements, similar to the Hymn Crystals. The Reyvateil constantly emit Dynamic H-Waves that have their [Spiritual Standard Frequency] as their source, and the Parameno and Grathnode contained in their bodies convert them into D-Waves, which results into the preservation of their material form (body). Therefore, it would be no exaggeration to say that the Reyvateil bodies themselves are produced by [Song Magic] as well. This is why it is said that the [Reyvateils at their core are made from sounds].
===Special Characteristics for Life Span and Growth===
As explained previously, the Reyvateil body is created by magic, and if the Triangular Nuclear Loop maintaining it could sing eternally, it would retain an eternal youth. So in summary, the reason why the Pureblooded β-Types suffer next to no changes until the 150th year that is said to be the limit for their Triangular Nuclear Loops' life spans is because they were programmed by the humans in this fashion so their abilities wouldn't deteriorate. However, at childhood their bodies are formed as they grow, just like the humans do. This is because, while the Reyvateil body starts just as a Triangular Nuclear Loop, it continues creating its own body little by little, which translates to physically enlarging it (making it grow) and maturation of its own waveforms (which translates to mental maturation and learning). The [Hexagons] that serve as the Triangular Nuclear Loop's hinges contain Dynamic H-Waves that decrease in energy whenever the Reyvateil undergoes growth, and when their energy is completely depleted, the bodily growth will stop entirely. This is why it is said that the [Triangular Nuclear Loop] reaches its critical state when the Reyvateil is approximately of 18 years in age.
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===What Happens in the Bodies of the Third Generations===
The reason why the Life Extending Agent is necessary for the Third Generations lies in the [Triangular Nuclear Loop]. Third Generations have the same body as the humans, but they also possess Reyvateil traits that attempt to construct their bodies through magic. However, given the Third Generations do not possess a [Triangular Nuclear Loop] that can generate Dynamic H-Waves, the [HD-Conversion Ring] that serves as one of the functions of the LPM (Reyvateil Life Preservation Mechanism) activates upon all zones of their bodies and starts causing their Static H-Waves to undulate (distorts them) to convert them into Dynamic H-Waves, with the result that it destroys their own bodies. The Dynamic H-Wave amount that the Reyvateil body demands gradually increases more and more until they reach 18 years, and once they have matured, the destructive power on the H-Waves will surpass the body's own capacity to replenish the consumed waveforms, causing their death.
Diquility is a mass of [Static H-Waves] that have no special properties, but possess a high purity. By Installing it, the HD-Conversion Ring will prioritize it as the source for the creation of Dynamic H-Waves, transforming it into energy. Given that it will lose its effects after three months because the distortion on the Static H-Waves will have magnified too much, this is why it it said that [Diquility is a life extending agent that must be applied once every three months].
[Graph]
Structure of a Pureblooded β-Type
Natural
Life Force
The Nuclear Triangular Loop
Creates Dynamic H-Waves
Because there is a normal proportion of waves,
the HD Conversion Ring does not activate
LPM
Parameno Compound
Grathnode Compound
Output of Dynamic D-Waves
Construction of the Physical Body
Structure of a Third Generation
(without a Nuclear Triangular Ring)
Diquility
(Life Extending Agent)
To preserve the life of the Reyvateil,
it emit Dynamic D-Waves while
snatching away life force.
Natural
Life Force
LPM
Parameno Compound
Grathnode Compound
Output of Dynamic D-Waves
Construction of the Physical Body
===Installs and Grathnode Crystals===
The Cosmosphere has a checksum mechanism that verifies if the feelings are being transmitted to the Tower normally. To verify that the feelings are in fact being transmitted to the Tower in a 100%, if there isn't enough power to correspond to the feelings' strength, the mechanism sends off a feedback correction with the demands that must be obeyed so the energy may be sent normally. The Install is an act to deceive this [checksum]. For example, if we had the feelings [I want to save with a power of 10!] and we Installed a Grathnode Crystal called [Power Up+3], the checksum would misunderstand the feelings as [I want to save with a power of 13!]. As only a power of 10 is being sent from the Cosmosphere, a feedback correction stating [It is missing 3!] would be sent, but the energy would be forcefully sent anyways. As this makes Reyvateils use a power that they would normally be unable to use, it places a large burden on them. This creates a large discrepancy between the checksum and the Cosmosphere's feelings, with the consequence it dramatically increases the Reyvateil's mental fatigue.
[Graph]
Condition without an Install
Static H-Waves carried naturally by the Reyvateil <- Output of the "Power of 10" Feelings
 |
 V 
Composition and Transmission of Waves
 |
 V 
Checksum <- Checking if the Power is indeed 10. Recognized as normal.
 |
 V 
Transmission of Feelings to the Tower (Power of 10)
 |
 V 
Conversion into Power (Conversion into Dynamic D-Waves)
 |
 V 
Song Magic
Condition with an Install
Static H-Waves carried naturally by the Reyvateil <- Output of the "Power of 10" Feelings
 |
 V 
Feedback Correction
Due to the feedback correction,
a power that would naturally not be emitted is forcefully sent.
 |
 V 
Grathnode Crystal -> Checksum <- Convinced that the necessary power is 13. Recognized as abnormal
Grathnode Crystal +3
Grathnode Crystal
 |
 V 
The power is forcefully increased to 3.
The "3" feelings make the mind act
as if it actually had that power.
 |
 V 
Transmission of Feelings to the Tower (Power of 13)
 |
 V 
Conversion into Power (Conversion into Dynamic D-Waves)
 |
 V 
Magic
[Graph End]
===Install Port===
It isn't just the point of contact for carrying out the Installs, as it also serves as an I/O port that allows for interfering with the Reyvateil's Static H-Waves during a Dive (incidentally, it does not hurt during a Dive due to the fact that it is merely touched and scanned). As this is the part that completely exposes the Grathnode compound, it also fully exposes the Reyvateils' own feelings, reason why they instinctively cover it from other people's eyes.
==Hymmnos Language==
===The Hymmnos Language and the Causality of the Natural Laws===
The Hymmnos Language was invented by the ancient shamans. While their Hymmnos incantations had no effects as [words], there were many cases in which they detected particularly large waves in the ultra-high frequency bands (DHWs above the 200000 Hz range) just from the knowledge and experiences they had been bequeathed from antiquity. Furthermore, they learned through trial and error that their incantations could bring about effects, and naturally came up with words that would be used in deeds such as making rain fall. Strictly speaking, the many Dynamic Waves that were contained in these words would cause an effect on the waveforms of the atmosphere's moisture by changing their tendencies to condensation, so in simpler terms, it was no more than changing the Static Wave component to compel the atmosphere to contain water.
The energy a single person can emit on their own is quite weak and unable to bring about any sort of grand change, but they made it possible to enhance the effects by singing as large choirs composed by dozens of people. Furthermore, by making their consciousnesses synchronize with each other and make their pronunciation spectra resemble each other, they would cause resonances would be capable of bringing about extremely powerful effects. The fact that the Hymmnos make frequent use of multi-track choral singing in the Third Era is because these experiences were handed down into them.
===The [Tower of Origin] Interpreter===
The predecessor to Ar tonelico, the [Tower of Origin] was not compatible with the Hymmnos Language. The only thing the Tower of Origin could do was a fixed, simple sequential playback of a specific frequency, so creating solid matter from the air was no more than a dream inside a dream for it. At best, the only things it could do were produce sonic waves, water and formless energy. In order to manifest more complex magic, it needed instant-by-instant emotional spectra that were deployed on the Time Axis, or [Songs].
===The Songs and the ω-Spectrum (Time Axis Deployment)===
Whenever a Song is sung, the singer is capable of thinking up every single instant from the beginning to the end of that Song in their head. The movement of the Time Axis constructs a free high-dimensional world inside the singer's brain, and if they sing even a single instant of that Song, that instant will extend as a straight line, pulling from the singer's brain the entirety of the emotions and vocal spectra that exist upon the Time Axis. What makes this possible is that by combining the audible band (50 Hz to 20000 Hz) and the [Individual Consciousness Fields] that exist above the 20000 Hz range, it is possible to deploy the Time Axis. The audible band (Song) serves as a [carrier wave], so as soon as it can cross paths with and seize the Spectra from the Individual Consciousness Fields, it can be used to convey [feelings].
The [Time Axis], the [Individual Consciousness Fields] and the [Energy] suffer complex tridimensional changes as they are entwined with each other, allowing for complex feelings and the manifestation of complex magic. These waves are what we know as the [FFT Spectrum]. And actually, by using the undulations of the heart in each microscopic δ-time unit and expanding each of their instants, the waves contained in them can manifest as a single magic. This deployment on the Time Axis that includes even undulations measured in microscopic time units across all time (which will not appear in the Third Dimensional space due to being Fourth Dimensional information) is called the ω-Spectrum.
===Hymmnos Vocabulary===
The Hymmnos vocabulary was made from the compilation of the shamans' rules of thumb, and it also had several additions made to it. As its name of [language of emotions] says, refining the pronunciations that would express a feeling the best, giving shape to the carrier waves (sound waves) that would allow to convey the waves of [feelings] for it (waves of over 20000 Hz) with the greatest efficiency, was how the Hymmnos word that translated to that [feeling] was created. The shamans had a great intuition, so even if we analyzed them scientifically, we would see that almost all the words have pronunciations (carrier waves) that are compatible with the feelings they carry, making theirs the best method. All the words that were created afterwards follow this same concept of making pronunciations that can carry feelings easily.
===The Purpose of Ar tonelico (the Tower)===
Ar tonelico manifests in the physical world the feelings of the Reyvateils. The Dynamic H-Waves contained in their Songs will produce a magical effect to a greater or lesser degree as long as there are Songstones nearby, but it would be extremely weak, not to mention that given that the Songstones' absorption capabilities worsen the more impure the crystal is, the singer would do nothing but exhaust herself without her feelings being properly conveyed. The Tower absorbs all the feelings in its Parameno part, and after amplifying them further through a feedback boost, it manifests them. So the Reyvateils using the resources of the supercomputer that the Tower is makes it possible for them to unleash great powers they could never use on their own.
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===Wave Transmission Methods===
The Reyvateils' waves are sent into the Tower through a Symphonic Power line located in their Cosmospheres called the [Tower of Life]. This gives them a direct connection, which means they can transmit their feelings to the Tower almost exactly as they felt them. It is due to this that the Reyvateils are able to send their requests for magic even if they aren't around the area of the Parameno Discs, and it was also the main reason that drove the development of the Reyvateils. If it was a human singing instead, the larger part of the waves they emit would be lost as they were transmitted through the atmosphere, making it next to impossible for the [Physical Parameno Discs] to receive them.
===Why Humans Cannot Use Song Magic===
The humans have large [fluctuations] in their Songs and emotions, so no matter how adept they might be at singing, they would never be able to craft and emit proper waves for them. Additionally, the majority of humans are also thinking of other things as they sing. Due to this, the feelings they put into the [sound] component is inconsistent with what they are actually feeling in their [minds], which generates large contradictions in the FFT Spectra and render them unable to convert them into Symphonic Power. Sincere and unwavering [feelings] are essential for the Songs, which is the second reason that drove the development of the Reyvateils. This is because a Reyvateil demonstrates an astounding concentration power whenever she sings, which means they will disregard any attacks they may receive and just keep singing, unable to stop or defend herself. The Pureblooded β-Types have next to no fluctuations, while the Third Generations have large amounts of them. This is what accounts for the difference in their abilities.
===Structure of the Hymmnos Words===
[Graphs]
Good Example: chs (chisu) Meaning: Transform / Feelings: I want to change!
 Feelings (Dynamic H-Waves)
 I want to change!
 The word is "chs" and the feelings
 are "I want to change!". Whenever it's pronounced,
 the carrier waves and the waves of the feelings match
 up, so the [power] to transform will be executed with maximum efficiency.
 
 chi su
 Audible Band (Carrier Waves)
Bad Example: chs (chisu) Meaning: Transform / Feelings: I'm hungry!
 Feelings (Dynamic H-Waves)
 I'm hungry!
 The word is "chs" and the feelings are
 "I'm hungry". Since the feelings and the
 carrier waves don't match up, that will only
 call forth a very weak power.
 
 chi su
 Audible Band (Carrier Waves)
[End Graphs]
==Song Magic==
===Reasons Behind the Physical Manifestation of Song Magic===
Magic is explained in Wave Science as follows: [By applying Dynamic D-Waves upon a target point, changes will occur upon the Static D-Waves that exist in said point]. Static D-Waves are what give form to matter, with low-frequency waves corresponding to gases and high-frequency waves being solids. Consequently, an application of high-frequency Dynamic D-Waves will produce Static D-Waves of high frequencies, which means it will produce [something] from nothing. This in itself is an advanced kind of magic.
===High-Load Index for Wave Frequency Difference===
Magic in which there is a large difference in the wave frequencies requires particularly strong feelings. For example, the energy necessary to produce matter or utterly annihilate it requires feelings with a proportionately high energy level to be generated, even taking the Tower's amplification in account. The simplest way to increase the energy level would be to craft the magic in a high-level Cosmosphere. Magic crafted in high-level Cosmospheres approach from their level of origin to the Tower whenever they are sung, meaning that given that the higher levels are closer to the Tower, their feelings are easier to transmit and the Tower can return them as high-energy Dynamic H-Waves.
[Graph]
 Sing
Actual Consciousness (Individual Consciousness Fields) H-Waves 
 (Cosmosphere) 
 
Having received a reply in the deeper parts,
a power output point is formed in this place.
Subconscious
Boundary Gate | Hymn Code (Gate)
 V 
 (Shared Consciousness Fields)
 
Administrator Clout<->Clout 
(Shurelia) 
 
 |
 V
 
 Logic Parameno Discs
 (Ar tonelico)
 
 |
 V
 
 Binary Field
 
 Grathnode Discs
 (Ar tonelico) 
 D-Waves
 |
 V 
 
 Song Magic
[End Graph]
==Hymn Crystals==
===What the Hymn Crystals Can Preserve===
The Hymn Crystals are Grathnode Crystals that possess no special qualities and that strictly speaking, possess distortions with equal energy amounts for all wave directionalities. If an Install was attempted using them, the distortions would all offset each other, which means they would cause no distortions on the Reyvateil's Static H-Waves (in summary, their GD value is zero).
The crystal maintains all distortion correction energies in equilibrium, so they would discharge no distortions upon the shape of the FFT Spectra that serves as the balance center for the energy, meaning their state is preserved forever. This preserved FFT Spectra that serves as the balance center itself is the [feelings], or [fully deployed Static H-Waves of the Reyvateil] that are recorded within the Hymn Crystal. The recorded mind of the Reyvateil itself then continues existing without destroying the crystal's internal balance.
===The Download Ceremony===
The reason why a Hymmnos Spell is chanted at the time of a Download is because power is borrowed from the Tower when the perfectly balanced waves are being recorded into the Reyvateil. If the Crystal was Installed normally, it would be [just like placing inside a feelings egg with shell and all], meaning it wouldn't be able to reach the Reyvateil's mind. In fact, the Hymmnos Spell for the Downloads is actually a command that carries out the process of not just accessing the Cosmosphere from the Binary Field, but also drawing out the preserved FFT Spectra and making it join with proper Static H-Waves.
===Why are Songs Crafted Instantly?===
The Song gushes forth as soon as the Download is complete. This is because all the axes (all wave frequency bands, all time bands) are instantly and completely overwritten by the FFT Spectra recorded in the Hymn Crystal, meaning that the Spectra's state changes to [in the process of crafting a Song]. If we looked at it from the receiving Reyvateil's viewpoint, to her it would seem like the Song was born... as if she had already had known it previously, a little bird born within her memories and feelings.
==Bonus Explanation: The Relationship Between Aurica and Mir==
Even among the people who possess Mir's genes, Aurica's Static H-Waves ended up having a large resemblance to Mir's own even in the highest frequencies of the Spectrum. Given that the wavelengths in their Hymn Code zones ended being so similar, Mir could easily open up Aurica's [Boundary Gate], manifest Viruses through her mind when she was at the Musical Corridor and also send the model data for Goddess Tyria into her Soulspace. What Shurelia referenced when she said that [Aurica might have a hole] was this similarity between their wavelengths.