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    Equipment Dualizing Guide by Wii306

    Version: 1.10 | Updated: 06/26/12 | Printable Version | Search Guide | Bookmark Guide

    ******************************************************************************
    Tales of Graces f
    
    Equipment Dualizing Guide, Version 1.10
    
    By Wii306
    ******************************************************************************
    
    ---------------
    Version History
    ---------------
    
    Version 1.10, 06/26/12
    -In addition to the charts, listed all combinations for getting each 
    individual quality.
    -Added dual qualities to the effects table.
    -Made a correction to the formula for determining Rank 6 qualities.
    -Added a new method for getting an item worth 200k+.
    -Added a few more tips on gem extraction.
    -Various other minor corrections and edits.
    -Added this version history section.
    
    Version 1.00, 04/21/12
    -The original.
    
    
    =================
    Table of Contents
    =================
    I. Introduction
    II. How to Dualize - Step by Step
      IIA. Enhancing Equipment
        IIA1. Qualities
        IIA2. Effects 
          IIA2a. Upgrading Effects on Equipment
          IIA2b. Dual Effects
      IIB. Tempering Equipment
        IIB1. Increasing CC through Tempering
      IIC. Extracting Gems
      IID. Upgrading Gems
        IID1. Fusing Gems
        IID2. Gem Polishing
      IIE. Converting Equipment
    III. Determining Resell Value
    IV. References
      IVA. Qualities
      IVB. Effects
      IVC. Quality Combinations
      IVD. Quality-Effect Pairs
    V. Shard Drops
      VA. Locations by Quality
      VB. Locations by Ability
    VI. General Tips and Tricks
    VII. Frequently Asked Questions
    VIII. Credits
    IX. Contact Info & Legal
    
    ===============
    I. Introduction
    ===============
    
    If you want your characters to become as powerful as they can, and if you want
    to tackle the higher difficulties on your first run through the game, 
    upgrading your weapons and armor through dualizing becomes very important. 
    However, the in-game tutorials don't do a very outstanding job of explaining
    all of the details of every step in the equipment dualizing process. I hope 
    this guide will make it easier for you, the reader, to best plan out what 
    needs to be done in order to optimally upgrade your equipment. I also hope 
    that the guide will serve as a useful reference for anyone who wants to
    perform any equipment dualizing, even if they are already familiar with the 
    basics of how it all works.
    
    Let's begin!
    
    
    =================================
    II. How to Dualize - Step by Step
    =================================
    
    The meat of this guide! This will be a step-by-step walkthrough of everything
    you need to know to get started with dualizing, from upgrading weapons to 
    extracting and refining gems. Read through this if you're new to dualizing
    and want to know the ins and outs of how it all works, or feel free to jump
    to any section if there is a particular aspect of dualizing that you are 
    confused with. This section was written with the assumption that you have no 
    knowledge of how the dualizing system works, although it is also interspersed 
    with discussions of some of the more complicated, "hidden" mechanics that even
    a seasoned dualizer might find interesting. 
    
    ------------------------
    IIA. Enhancing Equipment
    ------------------------
    
    The first step in upgrading any weapon or armor is to enhance it, or to 
    dualize it with a shard. Every shard has two important attributes that you're
    going to want to pay attention to: the "Quality" (e.g. Cool or Noble), and the
    "Effect" (e.g. Attack or Rise) & its associated level (e.g. [2]). All pieces 
    of equipment have a quality, and they also sometimes come with an effect. I'll 
    talk about qualities first, and then I'll go on to talk about effects, since 
    the two are sort of unrelated and can be treated more or less independently - 
    at least for the simplest cases of dualizing. I'll point out exceptions to 
    this claim as they come up (which will be rather soon, as it turns out).  
    
    ...............
    IIA1. Qualities
    ...............
    
    This is the primary attribute you want to focus on if you care about making 
    the most powerful WEAPON or ARMOR possible. The quality of the weapon/armor 
    that results from dualizing your equipment with your shard directly determines
    what stats will be boosted upon dualizing. For example, if you end up with a 
    "Noble" weapon, it will gain 3 P.Atk, 2 C.Atk, and 6 Acc. Note that weapons 
    only gain the stat boosts for P.Atk, C.Atk, and Accuracy, whereas armors only 
    gain the stat boosts for P.Def, C.Def, and Evasion. To check what stats will
    be boosted, just select the equipment and shard in the dualizing menu to bring
    up the preview screen, then scroll over to the stats screen with Square. You 
    can also refer to section IVA of this guide for a table listing what each 
    quality does. These boosts are permanent - they persist even after the 
    equipment's effect has been extracted. (Extraction will be covered in section 
    IIC.)
    
    All qualities have a "rank" assigned to them that's determined by the number 
    of letters in their name. I will use the following convention: a Rank 1 
    quality is one with four letters in its name, a Rank 2 quality is one with 
    five letters in its name, and so on until Rank 7 (ten letters). 
    Unsurprisingly, higher-ranking qualities tend to give greater stat boosts than
    lower-ranking qualities, so you usually want to increase the rank of your 
    equipment each time you dualize.  
    
    There is a somewhat complicated formula that determines the rank of the weapon
    or armor that results from dualizing a piece of equipment with a shard.  I'll 
    break it into three cases:
    
    1. If you dualize an equipment and shard of DIFFERENT rank, the resulting 
    equipment will take on the lower-ranking quality. (e.g. Cool + Olden -> 
    Cool). It does not matter whether the lower quality is on the equipment or on 
    the shard.
    
    2. If you dualize two things of EQUAL rank, the resulting equipment will have 
    a different rank.  If their ranks are less than 5 (less than eight letters), 
    the rank either goes up by one (e.g. Keen + Cool -> Noble), or it becomes Rank
    6 (e.g. Keen + Hard -> Tolerable). If their ranks are 5, the rank will 
    decrease or become Rank 6.  If their ranks are 6, the rank will stay at 6. The
    quality that results is strictly determined by the two qualities you start 
    with (except in cases where you end up with a Rank 6 quality). All of the 
    combinations are summarized in the charts in Section IVC.
    
    3. There are some exceptions that yield special, Rank 7 "cameo" qualities. For
    example, "Cool" + "Noble" -> "Guyabulous." To gain access to these qualities 
    through dualizing, you must have purchased the "Unlock Qualities" feature from
    the Grade Shop during a New Game +. A list of how to make these qualities can 
    also be found in Section IVC.
    
    As you can see, the final quality of your equipment is directly determined by
    the starting qualities of your original equipment and your shard. It doesn't 
    matter which quality is on which item.  If you're ever unsure about what a 
    particular combination of qualities will yield, you can always select the two 
    items in the dualizing menu and see what quality the preview window shows you.
    Also, if the resulting quality is of a higher rank than the starting 
    qualities, its name will appear in Orange in the preview window.
    
    Note that in some cases, if you are dualizing a weapon and shard with the same
    quality rank, the effect will level up instead of the rank. This is the 
    primary exception to my previous claim that qualities and effects can be 
    treated more or less independently. This can actually be a very useful feature
    if you care about gem extraction more than you care about upgrading the weapon
    in question. Check Section IIA2a for a more detailed explanation of how this 
    works.
    
    .............
    IIA2. Effects
    .............
    
    Effects are a bit unusual in that they are only transiently attached to the 
    weapon/armor that you dualize with. If you want to continue upgrading your 
    equipment beyond +1, you must first extract the effect from it, which 
    essentially means transferring the effect to a gem. Thus, this is the 
    attribute that you want to focus on if you want to make the most effective 
    GEMS possible (more on that in section IIC - stay tuned).
    
    Each effect has a name and a level.  The name tells you what the effect does: 
    for example, the Petrify effect increases damage against enemies weak to 
    petrification, while the Reinforce effect increases your rate of CC recovery.
    The level (i.e. [#]) is an indicator of how effective the effect is, from 1 to
    10 (*) - higher levels correspond to greater passive bonuses.  The level 
    directly determines the numerical value of the effect's bonus: or example, the
    Attack[2] effect always gives +17 P.Atk, while the Attack[3] effect always 
    gives +24 P.Atk.  (It should be noted that Rise shards only give 1 additional 
    minimum CC every 3 levels, and Exceed shards only give 1 additional maximum CC
    every 2 levels.  It would be pretty overpowered otherwise!)  In any case, you 
    can look through the shard's item description (with Square) to determine 
    exactly what stat boosts the shard gives. I have also summarized what each 
    effect does at each level in the table in section IVB.
    
    The way in which effects are transferred from shards to weapons is usually 
    pretty simple. Once you dualize a weapon with a shard, that shard's effect 
    gets added to the weapon. After dualizing, you can check all of its effects by 
    scrolling through the weapon description. If the weapon already has an effect 
    (i.e. from Converting, unique weapons, or previous rounds of dualizing), then 
    it will end up with two effects. All weapons, armors, and gems can have a 
    maximum of two effects.
    
    Skip ahead to the section IIC gem extraction if you want to find out why 
    effects are more important for gems than for weapons and how to make the best 
    use of them. It may sound like I'm downplaying the significance of shard 
    effect with respect to weapons and armor - I am not entirely justified in 
    doing so. As it turns out, effects are very important for your weapons/armor 
    if you do NOT plan on extracting the gem.  Say you've gotten up to +40 and 
    you're sick of dualizing. Then you want the last shard you dualize with to be 
    one with a good effect, because that effect will stick around on the equipment
    and provide its passive bonus to you.  So know when you're going to stop 
    dualizing, and plan accordingly!
    
    IIA2a. Upgrading Effects on Equipment
    -------------------------------------
    
    Of course, there are additional levels of complexity in the system. Some 
    combinations of quality and effect will actually increase the level of the 
    effect by one. This ONLY occurs if the initial effect is level 3 or lower. In 
    all such cases, the quality can be on either item you are dualizing with, but 
    then the effect must be on the other. The resulting equipment will keep the 
    quality in question. In order for effect upgrading to occur, the starting 
    items must be of a compatible quality and effect. The two items can be a 
    weapon and a shard (during enhancing), a weapon and a weapon (during 
    extraction), or a gem and a gem (during fusion). For a full list of which 
    qualities are compatible with which effects, see section IVD.
    
    This concept is best illustrated with an example:
    Suppose you have an Keen Iron Sword and a Cold Attack[3] Shard.  Normally, you
    would expect the combination of Keen and Cold to yield a Rigid quality. 
    However, because Keen and Attack form a quality-effect pair, the Attack 
    shard's effect will be upgraded instead, from [3] to [4]. The sword will 
    maintain its Keen quality. So the net result of this dualizing is a keen Iron
    Sword+1 with the effect Attack[4].
    
    This is a very useful feature if you have a lot of low-level shards lying
    around (particularly in the early-mid game), and I encourage you to take 
    advantage of it. It also takes priority during gem extraction (see section
    IIC), so it can be used to extract the lower-level effect from a weapon. 
    Useful for getting a weapon with two high-level effects!
    
    IIA2b. Dual Effects
    -------------------
    Some effects can be combined into new "dual" effects. Your first item must
    have one effect, and your second item must have the other. For this to occur,
    two conditions must be met: 
    
    1) The resulting quality must be of a specific kind (all Rank 5) that depends 
    on the dual effect you are aiming for. Alternatively, the required Rank 5 
    quality can also be on one of the starting items (and the resulting item will
    keep that Rank 5 quality), in which case both of the effects to be combined 
    must be on the other item.
    
    2) The two original effects must be within one level of one another. The level 
    of the dual effect will be equal to the higher of the two initial levels.
    Note: this second condition may not be as set in stone as I once thought. More
    testing is required, but it seems like effects two levels apart can be put
    together as well.
    
    Note that if a gem already has a dual effect and you try to add a new version
    of the same type of dual effect to it, the new effect will overwrite the old 
    one, even if it is at a lower level.
    
    Dual Effect | Required Effects | Required Quality |
    ===================================================
    Warrior     | Attack + Defense | Fabulous         |
    ---------------------------------------------------
    Sorcerer    | Mind + Resist    | Dazzling         |
    ---------------------------------------------------
    Assassin    | Aim + Evade      | Perilous         |
    ---------------------------------------------------
    Valiant:    | Attack + Mind    | Poignant         |
    ---------------------------------------------------
    Paladin:    | Resist + Evade   | Vigorous         |
    ---------------------------------------------------
    Hunter:     | Aim + Defense    | Gracious         |
    ---------------------------------------------------
    
    For example, combining a Magical Attack[3] Ice Coffin+1 with an Epochal 
    Defense[4] shard will produce a Fabulous Warrior[4] Ice Coffin+2.
    
    (This is the second exception to the "treat qualities and effects 
    independently" rule, for those out to make me eat my words.)
    
    ------------------------
    IIB. Tempering Equipment
    ------------------------
    
    If you use a piece of upgraded equipment in battle, it will eventually become 
    tempered. There is a set probability that the equipment will be tempered at 
    the end of each battle, and it varies from item to item, so just keep fighting
    battles when this happens. It will often take between 5-10 battles for a 
    weapon or armor to be tempered. Remember that the item has to be equipped in 
    order for it to have a chance of tempering. Tempered weapons will receive a 
    passive percent bonus to damage dealt, and tempered armors will give a percent 
    reduction to damage received. The value of this tempering bonus is solely 
    determined by the equipment's quality. Once a piece of equipment has been 
    tempered, its name will be highlighted in orange in the item/dualizing menu.
    
    .....................................
    IIB1. Increasing CC through Tempering
    .....................................
    
    The tempering bonus is also related to the CC a weapon gains as you upgrade 
    it. Upgraded weapons get passive, permanent bonuses to both minimum and 
    maximum CC as you upgrade them more and more. The way minimum CC is upgraded 
    is simple: each weapon can gain four boosts to minimum CC: at +30, +60, +90, 
    and +99.
    
    Maximum CC is a bit more complicated. The number of times the maximum CC can 
    be boosted depends on the weapon you are trying to upgrade: a Long Sword can 
    be upgraded 12 times to a maximum of 19 CC, whereas a Phact Phantasia can only 
    be upgraded 5 times to a maximum of 20 CC.
    
    The point at which the maximum CC will increase varies and depends on the 
    cumulative tempering bonus, which the game keeps track of each time you 
    upgrade a weapon. The total cumulative tempering bonus that you need to reach
    is equal to the product of the weapon's current minimum and maximum CC. For 
    example, since a Long Sword starts off with 5-7 CC, you will need to reach a 
    cumulative tempering bonus of +35% or more. This can be accomplished by first 
    making a Cool +1 weapon (+4%), followed by Noble (4% + 6% = 10%), followed by 
    Guyabulous (10% + 18% = 28%), followed by Barbed (28% + 8% = 36%). At that 
    point, the maximum CC of the weapon will increase, and the cumulative 
    tempering bonus counter will reset. Note that the cumulative tempering bonus 
    you need to reach increases each time either your minimum or your maximum CC 
    increases.
    
    
    Perhaps more importantly, tempering allows you to extract a gem from the 
    weapon. If you want to keep on upgrading the same piece of equipment, this 
    becomes very important. Which brings us to the next section...
    
    
    --------------------
    IIC. Extracting Gems
    --------------------
    
    You may have noticed that once you've upgraded a piece of equipment once, the 
    game won't allow you to dualize it with any more shards, even after it has 
    been tempered. In order to continue upgrading a piece of equipment, you must 
    first extract an effect from it by dualizing it with another piece of tempered
    equipment. Note that the equipment does not have to have the same name - so 
    you can dualize a Steel Bladearang+2 with a Rune Shotstaff+1.  (However, you 
    can not dualize weapons with armor.) This will take away the higher-level 
    effect from each piece of equipment and combine them into a single gem. Each 
    weapon will lose one effect, even if one weapon has the two highest-level 
    effects overall. The weapons will NOT disappear after dualizing - they each 
    will merely lose an effect.
    
    These gems can be equipped in the 4th slot of your Equipment screen, where 
    items like Poison Charms go. The only stat boosts that gems give are whatever
    the effects say (with the exception the Rank 7 gems - scroll down a bit for 
    an explanation of that). Gems also have a Rank associated with them, A 
    through S, with S being the highest.  The Gem Rank depends on the sum of the
    levels of all abilities on the gem. If they add up to 2, the Gem will be Rank
    A; if they add up to 3, the Gem will be Rank B, and so on until Rank S, where
    they add up to 20 ([*]/[*]).  (This bit of information is really only 
    important except if you care about completing the Dualizing/Collector's Book.)
    
    There are a few special cases that you should probably familiarize yourself
    with:
    
    -If the highest-level effect on both pieces of equipment is the same and at 
    the SAME level, that effect will be upgraded by 1. If they have any additional
    effects between them, it will then take the next-highest effect. This means 
    that if the two pieces of equipment are identical, then both effects will be 
    extracted, and both will be upgraded. 
    For example, dualizing a Rise[4]Att[3] weapon with another Rise[4]Att[3] 
    weapon will result in a Rise[5]Att[4] gem, as well as two weapons with no 
    effects. This is ideal if you want to optimize your gems in the least possible
    number of steps.
    
    -If the highest-level effect on both pieces of equipment is the same but at a
    DIFFERENT level, it will take the higher-level effect of the two and leave 
    behind the other. If the weapon with the lower level of that effect has a 
    second effect, then it will take that effect; otherwise, the gem will only 
    have one effect. 
    For example, dualizing an Aim[3]Freeze[2] weapon with an Aim[2] weapon will 
    yield an "AIM-AIM" gem that only has the effect Aim[3], but the Freeze[2] and 
    Aim[2] effects will remain on their respective weapons. 
    This can be a very useful feature to take advantage of because it allows you 
    to obtain two effects on ANY weapon - not just ones that started with an 
    effect.
    
    -If an effect on one piece of equipment is compatible with the quality of the
    other (see Section IIA2a), that effect will be extracted preferentially, even 
    if it is not the highest-level effect. You can take advantage of this fact to
    get rid of the innate low-level effects on some equipment. For example, 
    dualizing a Holy[4]/Reinforce[6] Shrine Maiden's Garb with an Evade[5] Blouse 
    that has the Sunny quality will net you a Holy[4]/Evade[5] gem, leaving you 
    with a Shrine Maiden's Garb with Reinforce[6]. You are no longer stuck with a 
    level 4 effect on the Shrine Maiden's Garb!
    
    -Tiebreakers: If a weapon has two different effects that are tied in level 
    (for example, Freeze[3]Rise[3]), the effect that ends up being extracted 
    varies. I'm not exactly sure how it works, but I am prety sure that it depends 
    on the effect that will be extracted from the other weapon.  This means that 
    in such a case, you might be able to choose a weapon with an effect that 
    allows you to retain Rise[3], while some other effect might allow you to 
    retain Freeze[3], depending on your preference. It would just require some 
    experimentation. From what I've been able to gather, as far as being extracted
    goes, it seems as though the effects that are unique to weapons/armors always
    take precedence over the ones that can be found on shards. So for example, 
    for a Killer[4]/Attack[4] weapon, Killer[4] will be preferentially extracted.
    
    
    As far as gem qualities go, you do not need to worry about them in most cases.
    Since there are no inherent stat boosts associated with gems (i.e., excluding 
    those conferred by the gem's effects), ending up with a Rank 1 gem quality is 
    no different from ending up with a Rank 5. For example, equipping a gem with 
    the Barbatosan quality will NOT give you +15 to all stats because, as 
    explained in Section IIA1, the quality only affects the stat boost that is 
    applied directly to the weapon/armor when it is upgraded. 
    
    With that said, I can think of three exceptions where you might actually care 
    about gem quality:
    
    1. Quality always affects resell value, so if you intend to sell the gem, try 
    shooting for qualities with high resell inheritance / resell multiplier 
    values.  See section III for more information on how resell value is 
    determined.
    
    2. If you equip a gem with one of the Rank 7 qualities, the special effects of
    those qualities WILL take effect. For example, equipping a Barbatosan gem 
    will prevent you from using items (even though it doesn't give you any stats).
    
    3. When fusing gems, the effect-upgrading rules that depend on compatible
    effect-quality pairs (see section IIA2a) still apply.  The same holds for 
    creating dual abilities, which also requires specific qualities (see section 
    IIA2b).
    
    If you care about any of these, then gem qualities are determined in the same 
    way that weapon qualities are. It is based entirely on the qualities of the 
    two gems you begin with.
    
    
    -------------------
    IID. Upgrading Gems
    -------------------
    
    There are two ways to make the effects on a gem more powerful: gem fusion and
    gem polishing.
    
    .................
    IID1. Fusing Gems
    .................
    
    Two gems can be fused by dualizing them with one another. Fusing two gems 
    works almost identically to extracting a gem from two pieces of equipment.  
    When two gems are dualized with one another, as with equipment, you will 
    end up with a gem with two effects. However, in this case, you will lose both 
    starting gems, which means that as many as two effects can be lost 
    permanently. Additionally, as with equipment, the higher-level effect from 
    each gem will be the one that is inherited.
    
    If the two starting gems share a highest-level effect, and that effect is at 
    the same level on both, then fusing will increase the level of that effect by 
    1. If the common effect is at a different level on the two gems, then the 
    higher-level effect takes priority. In both cases, the next-highest effect 
    will become the second effect on the gem. All remaining effects will be 
    discarded. The following examples are illustrative:
    
    Rise[4]Att[3] + Rise[4]Def[2] -> Rise[5]Att[3] 
    (Rise is upgraded because the levels match; the next-highest effect is also
    inherited. Def[2] is lost.)
    
    Rise[6]Att[3] + Rise[4]Def[2] -> Rise[6]Def[2] 
    (Rise[6] takes priority as the highest-level effect; the second effect from 
    the other gem inherited even though it is lower than Att[3]. Rise[4] and 
    Att[3] are lost.)
      
    What this means is that you'll benefit most from fusing identical gems, 
    because that will allow both effects to be upgraded (as with equipment). 
    As with equipment (starting to see a trend here?), tiebreakers are handled in 
    mysterious ways that I do not fully understand.
    
    ...................
    IID1. Gem Polishing
    ...................
    
    The second way to upgrade gems is through gem polishing, which is much more 
    straightforward. After completing the sidequest with Marian in Yu Liberte 
    (available in the market district after Hubert joins the party), she will 
    offer to polish gems for you, for a price. Simply put, this will increase the 
    level of each effect on the gem by one. For example, a Rise[3]/Aim[2] gem will
    become a Rise[4]/Aim[3] gem. Note that a [*]/[*] gem can only be obtained 
    through dualizing - Marian will only polish up to level 9. The process is 
    pretty expensive for high-level gems, and it requires that you wait several 
    minutes in real-time. But this is by far the easiest, least confusing way to 
    get to that coveted [9]/[9] gem.
    
    You can speed up the process by giving her certain food items, which can be 
    done about once every 3 minutes. 
    Pumpkin Pudding: -30% 
    Peach Parfait:   -25% 
    Grape Parfait:   -20%
    Banana Pie:      -15%
    Apple Pie:       -5%
    
    
    -------------------------
    IIE. Converting Equipment
    -------------------------
    
    The last way in which you can upgrade a weapon is to convert it into an 
    entirely different weapon by dualizing it with the appropriate crystal (or 
    some other material, in the case of the joke/ultimate weapons). Every basic 
    weapon (Iron, Steel, Rune, Battle, Platinum, Mythril, Rare) can be upgraded in
    this way; many armors can be converted as well. Converted weapons generally 
    have superior stats and a lower minimum CC but higher maximum CC than the 
    corresponding original weapons. (Once again, the exceptions are the joke/
    ultimate weapons - those all have higher minimum CC as well.) Converted 
    armors always have superior stats to the base armor.  
    
    Converted weapons/armor also all come with a new, predetermined effect, and 
    they have a predetermined quality as well (so you might experience a drop in 
    quality by converting a highly upgraded weapon). Some of these effects are 
    unique to converted equipment (i.e. they aren't found on shards), but they can
    still be extracted onto gems. This is also the easiest way to get two effects 
    onto a weapon that doesn't start with an effect.
    
    Interestingly enough, when you convert a weapon, its upgrade counter will be 
    reset to 0. Better yet, a fraction of the quality-derived stat boosts gained 
    by upgrading the base weapon will be inherited by the converted weapon. (I 
    want to say it's half, but I haven't done any exact calculations.) What this 
    means is that, if you want to get the most powerful weapon possible, it might 
    pay to dualize the base weapon to +99 (or some arbitrarily high number), then 
    convert it so that it inherits a sizeable stat boost, then dualize it to +99 
    again.
    
    
    =============================
    III. Determining Resell Value
    =============================
    
    One of the most frequently asked questions about dualizing is: How do I figure
    out / optimize the resell value of my upgraded equipment? What in the world do
    these resell multiplier and resell inheritance values mean?  I'll do my best 
    to answer this.  Full credit to this answer goes to the editors of the 
    Japanese Tales of Graces wiki for teasing out these hidden formulas - I 
    probably would have never been able to figure this out on my own. 
    
    There are basically 6 variables you need to keep track of when determining 
    resell value.  I will abbreviate them as follows:
    
    V = the original value / selling price of the item
    
    M = the resell multiplier, which depends on the weapon's quality
    
    I = 1 + the resell inheritance for each step in the dualizing process 
    (cumulative), which depends on each quality the weapon has passed through 
     
    A1 = Depends on the level of the first effect.  Only the level matters; not 
    the type of effect. 
    A2 = Depends on the level of the second effect. Use the following key:
    [no effect] = 1.0, [1] = 1.2, [2] = 1.3, [3] = 1.4, [4] = 1.5, [5] = 1.6, 
            [6] = 1.8, [7] = 2.0, [8] = 2.5, [9] = 3.0, [*] = 5.0
    
    S = The status of the weapon.  S = 1.0 if the weapon has not been upgraded or 
    has had its gem extracted; S = 1.2 if the weapon has been upgraded (name will 
    be blue); S = 1.5 if the weapon has been tempered (name will be orange).
    
    
    Then, simply put:
    
    Resell value = V * M * I * A1 * A2 * S
    
    
    Let's walk through an example for the Dreamer's Flange, a popular resell item. 
    Let's say this Flange is tempered, +3, with the effects Attack[6] and Rise[4],
    and it has gone through the following quality progression:
    Epochal (default) -> Stuffy -> Magical-> Poignant.
    
    V = 5,880                     (selling price of the Dreamer's Flange)
    M = 5.0 (for Poignant)
    I = 1 + 140% + 160% + 150%    (resell inheritance for Stuffy, Magical,  
      = 5.5                        and Poignant, respectively)
    A1 = 1.8                      (level [6])
    A2 = 1.5                      (level [4])
    S = 1.5                       (tempered)
    
    Resell value = 5,880 * 5.0 * 5.5 * 1.8 * 1.5 * 1.5 = 654,885
    (Fun fact: Even with no effects, the Dreamer's Flange would be worth 242,550 
    gald if you follow this progression. More than enough to make the final 
    offering in the Zhonecage.)
    
    And that's it!  As you can see, the tricks to maximizing resell value are to:
    1) Maximize Resell Inheritance at each step in the dualizing process.
    2) Only worry about maximizing the Resell Multiplier at the end. 
    3) Aim for high-level effects if possible.
    4) Temper your weapon before selling it.
    
    (Note: I haven't tested any of this out myself yet, and some of it does seem a
    bit unintuitive - particularly the way the Resell Inheritance factors in. I'll
    probably get around to sorting all this out eventually, but take it with a 
    grain of salt until then. From what little testing I've done, it seems that 
    this formula may overestimate the value of the item a bit.)
    
    
    ==============
    IV. References
    ==============
    
    This reference section includes all of the information tables and charts 
    relevant to this guide.
    
    
    --------------
    IVA. Qualities
    --------------
    
    These tables list all qualities, the stat boosts they give to weapons (P.Atk,
    C.Atk, and Acc) or armors (P.Def, C.Def, and Eva) when a weapon/armor of the
    given quality is created, and any special effects the quality may have.
    
    Key:
    PATK  = Physical Attack
    CATK  = Cryas Attack
    ACC   = Accuracy
    PDEF  = Physical Defense
    CDEF  = Cryas Defense
    EVA   = Evasion
    Temp  = Tempering Bonus
    Mult  = Resell Multiplier
    Inher = Resell Inheritance
    
    Ranks 1-4:
    
    Name      |PATK|CATK|ACC |PDEF|CDEF|EVA |Temp|Mult|Inher|Special Effect*
    ==============================================================================
    Keen      |4   |3   |2   |3   |2   |2   |4%  |2.0 |+40% |Boosts Attack
    ------------------------------------------------------------------------------
    Hard      |2   |2   |3   |4   |3   |2   |4%  |2.0 |+20% |Boosts Defense
    ------------------------------------------------------------------------------
    Cool      |3   |4   |2   |2   |2   |3   |4%  |2.4 |+20% |Boosts Mind
    ------------------------------------------------------------------------------
    Cute      |2   |2   |3   |3   |4   |2   |4%  |2.6 |+15% |Boosts Resist
    ------------------------------------------------------------------------------
    Rapt      |2   |3   |4   |3   |2   |2   |5%  |1.6 |+50% |Boosts Aim
    ------------------------------------------------------------------------------
    Oily      |3   |2   |2   |2   |3   |4   |5%  |2.5 |+40% |Boosts Evade
    ------------------------------------------------------------------------------
    Buff      |4   |4   |0   |4   |4   |0   |5%  |1.5 |+55% |Boosts Vitality
    ------------------------------------------------------------------------------
    Cold      |0   |3   |5   |0   |3   |5   |5%  |2.5 |+40% |Boosts Speed
    ------------------------------------------------------------------------------
    Grand     |6   |3   |2   |4   |3   |3   |6%  |2.3 |+60% |Boosts Gain
    ------------------------------------------------------------------------------
    Noble     |3   |2   |6   |4   |4   |3   |6%  |2.5 |+70% |Boosts Absorb
    ------------------------------------------------------------------------------
    Suave     |3   |6   |2   |4   |3   |3   |5%  |2.2 |+55% |Boosts Blessing
    ------------------------------------------------------------------------------
    Olden     |3   |3   |4   |3   |2   |6   |6%  |1.5 |+90% |Boosts Tension
    ------------------------------------------------------------------------------
    Sunny     |3   |4   |3   |2   |6   |3   |6%  |1.8 |+85% |Boosts Holy
    ------------------------------------------------------------------------------
    Rigid     |4   |3   |3   |6   |3   |2   |7%  |1.0 |+95% |Boosts Rescue
    ------------------------------------------------------------------------------
    Wicked    |8   |3   |2   |5   |4   |3   |7%  |2.2 |+90% |Boosts Poison
    ------------------------------------------------------------------------------
    Barbed    |2   |8   |3   |5   |3   |4   |8%  |2.1 |+90% |Boosts Paralyze
    ------------------------------------------------------------------------------
    Frosty    |4   |3   |5   |2   |3   |8   |7%  |2.3 |+90% |Boosts Freeze
    ------------------------------------------------------------------------------
    Stuffy    |3   |2   |8   |5   |3   |4   |6%  |1.0 |+140%|Boosts Burn
    ------------------------------------------------------------------------------
    Formal    |3   |4   |5   |8   |2   |3   |7%  |2.7 |+100%|Boosts Petrify
    ------------------------------------------------------------------------------
    Solemn    |3   |4   |4   |3   |8   |2   |7%  |2.6 |+100%|Boosts Slow
    ------------------------------------------------------------------------------
    Untamed   |8   |0   |7   |3   |3   |7   |9%  |3.5 |+90% |Boosts Revenge
    ------------------------------------------------------------------------------
    Gallant   |3   |3   |9   |3   |3   |9   |7%  |3.5 |+140%|Boosts Refresh
    ------------------------------------------------------------------------------
    Haughty   |7   |8   |0   |7   |7   |0   |9%  |3.0 |+150%|Boosts Refill
    ------------------------------------------------------------------------------
    Sketchy   |6   |9   |0   |4   |5   |4   |8%  |2.0 |+30% |Boosts Rise
    ------------------------------------------------------------------------------
    Magical   |5   |4   |4   |0   |9   |6   |4%  |3.5 |+160%|Boosts Exceed
    ------------------------------------------------------------------------------
    Epochal   |9   |3   |2   |9   |2   |3   |8%  |4.5 |+10% |Boosts Reinforce
    ------------------------------------------------------------------------------
    *For all qualities ranked 1-4, if you dualize an item of that quality with a
    second item that carries a specific effect, that effect will be upgraded in
    the resulting item.  Refer to section IIA2a.
    
    Ranks 5 and 6:
    
    Name      |PATK|CATK|ACC |PDEF|CDEF|EVA |Temp|Mult|Inher|Special Effect*
    ==============================================================================
    Fabulous  |3   |4   |10  |6   |5   |4   |9%  |4.0 |+140%|Required for Warrior
    ------------------------------------------------------------------------------
    Dazzling  |4   |5   |6   |10  |3   |4   |7%  |5.0 |+1%  |Required for Sorcerer
    ------------------------------------------------------------------------------
    Perilous  |10  |3   |4   |5   |4   |6   |10% |3.0 |+200%|Required for Assassin
    ------------------------------------------------------------------------------
    Poignant  |3   |10  |4   |6   |4   |5   |8%  |4.0 |+150%|Required for Valiant
    ------------------------------------------------------------------------------
    Vigorous  |4   |5   |6   |4   |3   |10  |9%  |3.0 |+170%|Required for Paladin
    ------------------------------------------------------------------------------
    Gracious  |5   |5   |6   |4   |10  |3   |8%  |3.5 |+90% |Required for Hunter
    ------------------------------------------------------------------------------
    Worthless |1   |1   |1   |1   |1   |1   |5%  |0.5 |10+% |N/A
    ------------------------------------------------------------------------------
    Tolerable |2   |2   |2   |2   |2   |2   |5%  |0.5 |10+% |N/A
    ------------------------------------------------------------------------------
    Easygoing |3   |3   |3   |3   |3   |3   |4%  |0.5 |10+% |N/A 
    ------------------------------------------------------------------------------
    Diffident |4   |4   |4   |4   |4   |4   |4%  |0.5 |10+% |N/A 
    ------------------------------------------------------------------------------
    Impartial |5   |5   |5   |5   |5   |5   |3%  |0.5 |10+% |N/A 
    ------------------------------------------------------------------------------
    Competent |6   |6   |6   |6   |6   |6   |3%  |0.5 |10+% |N/A 
    ------------------------------------------------------------------------------
    Unadorned |7   |7   |7   |7   |7   |7   |2%  |0.5 |10+% |N/A 
    ------------------------------------------------------------------------------
    Concealed |8   |8   |8   |8   |8   |8   |2%  |0.5 |10+% |N/A 
    ------------------------------------------------------------------------------
    Deficient |9   |9   |9   |9   |9   |9   |1%  |0.5 |10+% |N/A 
    ------------------------------------------------------------------------------
    Pointless |10  |10  |10  |10  |10  |10  |1%  |0.5 |10+% |N/A 
    ------------------------------------------------------------------------------
    *Each Rank 5 quality is required to obtain a specific dual effect.  Refer to 
    section IIA2b. Rank 6 qualities have no additional effects.
    
    Rank 7:
    
    Name      |PATK|CATK|ACC |PDEF|CDEF|EVA |Temp|Mult|Inher|Special Effect*
    ==============================================================================
    Garrtastic|4   |5   |10  |2   |2   |15  |4%  |5.0 |+10% |10% chance to avoid
              |    |    |    |    |    |    |    |    |     |physical attacks
    ------------------------------------------------------------------------------
    Barbatosan|15  |15  |15  |15  |15  |15  |20% |5.0 |+50% |Item usage disabled
              |    |    |    |    |    |    |    |    |     |
    ------------------------------------------------------------------------------
    Lukerrific|10  |12  |7   |7   |8   |9   |11% |5.0 |+50% |1/2 damage to Human-
              |    |    |    |    |    |    |    |    |     |enemies
    ------------------------------------------------------------------------------
    Bruiserine|10  |0   |0   |10  |0   |0   |10% |5.0 |+50% |Iron stance on first 
              |    |    |    |    |    |    |    |    |     |hit received
    ------------------------------------------------------------------------------
    Lonimazing|15  |10  |0   |20  |5   |2   |15% |5.0 |+50% |Recovers 10% of 
              |    |    |    |    |    |    |    |    |     |damage from females
    ------------------------------------------------------------------------------
    Nataliated|2   |5   |20  |5   |10  |15  |13% |7.0 |+50% |End-of-battle Gald 
              |    |    |    |    |    |    |    |    |     |+20%
    ------------------------------------------------------------------------------
    Nanalystic|2   |10  |15  |6   |7   |10  |12% |5.0 |+50% |Accuracy x2
              |    |    |    |    |    |    |    |    |     |
    ------------------------------------------------------------------------------
    Guyabulous|12  |13  |10  |5   |5   |20  |18% |5.0 |+50% |Damage from females
              |    |    |    |    |    |    |    |    |     |causes petrification
    ------------------------------------------------------------------------------
    Genisimile|5   |5   |5   |5   |5   |5   |5%  |5.0 |+50% |Flare Shot damage x2 
              |    |    |    |    |    |    |    |    |     |(for Hubert)
    ------------------------------------------------------------------------------
    Kyleicious|12  |12  |22  |12  |12  |22  |13% |5.0 |+50% |Damage done to Reala  
              |    |    |    |    |    |    |    |    |     |reduced to 1
    ------------------------------------------------------------------------------
    Eugenelike|12  |8   |1   |15  |2   |5   |16% |5.0 |+50% |10% chance to avoid 
              |    |    |    |    |    |    |    |    |     |cryas damage
    ------------------------------------------------------------------------------
    Caiusesque|4   |4   |4   |3   |3   |3   |9%  |5.0 |+50% |8x damage to bears 
              |    |    |    |    |    |    |    |    |     |
    ------------------------------------------------------------------------------
    *The special effects of the Rank 7 qualities take effect as long as you have
    an equipment with that quality equipped.  This includes gems.
    
    
    ------------
    IVB. Effects
    ------------
    
    This chart covers all effects that can be obtained from shards. I have not 
    included effects that are unique to certain weapons and armor (although I may
    in a future update.)
    
    ==============================================================================
             |                 |                   Effect Level                  |
    Name     |Effect           |1   |2   |3   |4   |5   |6   |7   |8   |9   |*   |
    ==============================================================================
    Attack   |Physical Attack  |+10 |+17 |+24 |+31 |+38 |+45 |+52 |+59 |+66 |+73 |
             |up               |    |    |    |    |    |    |    |    |    |    |
    ------------------------------------------------------------------------------
    Defense  |Physical Defense |+10 |+17 |+24 |+31 |+38 |+45 |+52 |+59 |+66 |+73 |
             |up               |    |    |    |    |    |    |    |    |    |    |
    ------------------------------------------------------------------------------
    Mind     |Cryas Attack up  |+10 |+17 |+24 |+31 |+38 |+45 |+52 |+59 |+66 |+73 |
             |                 |    |    |    |    |    |    |    |    |    |    |
    ------------------------------------------------------------------------------
    Resist   |Cryas Defense up |+10 |+17 |+24 |+31 |+38 |+45 |+52 |+59 |+66 |+73 |
             |                 |    |    |    |    |    |    |    |    |    |    |
    ------------------------------------------------------------------------------
    Aim      |Accuracy up      |+10 |+17 |+24 |+31 |+38 |+45 |+52 |+59 |+66 |+73 |
             |                 |    |    |    |    |    |    |    |    |    |    |
    ------------------------------------------------------------------------------
    Evade    |Evasion up       |+10 |+17 |+24 |+31 |+38 |+45 |+52 |+59 |+66 |+73 |
             |                 |    |    |    |    |    |    |    |    |    |    |
    ------------------------------------------------------------------------------
    Vitality |Maximum HP up    |+100|+190|+280|+370|+460|+550|+640|+730|+820|+910|
             |                 |    |    |    |    |    |    |    |    |    |    |
    ------------------------------------------------------------------------------
    Speed    |Movement speed up|+10 |+15 |+20 |+25 |+30 |+35 |+40 |+45 |+50 |+55 |
             |                 |    |    |    |    |    |    |    |    |    |    |
    ------------------------------------------------------------------------------
    Gain     |Recover HP with  |+50 |+80 |+110|+140|+170|+200|+230|+290|+290|+320|
             |each kill        |    |    |    |    |    |    |    |    |    |    |
    ------------------------------------------------------------------------------
    Absorb   |Recover HP when  |+8  |+12 |+16 |+20 |+24 |+28 |+32 |+36 |+40 |+44 |
             |hit              |    |    |    |    |    |    |    |    |    |    |
    ------------------------------------------------------------------------------
    Blessing |HP recovery      |+10%|+14%|+18%|+22%|+26%|+30%|+34%|+38%|+42%|+46%|
             |effect up        |    |    |    |    |    |    |    |    |    |    |
    ------------------------------------------------------------------------------
    Tension  |Recover HP with  |+30 |+40 |+50 |+60 |+70 |+80 |+90 |+100|+110|+120|
             |each critical hit|    |    |    |    |    |    |    |    |    |    |
    ------------------------------------------------------------------------------
    Holy     |Automatic HP     |+15 |+20 |+25 |+30 |+35 |+40 |+45 |+50 |+55 |+60 |
             |recovery         |    |    |    |    |    |    |    |    |    |    |
    ------------------------------------------------------------------------------
    Rescue   |Chance to recover|+12%|+16%|+20%|+24%|+28%|+32%|+36%|+40%|+44%|+48%|
             |HP when dire     |    |    |    |    |    |    |    |    |    |    |
    ------------------------------------------------------------------------------
    Poison   |Hit Pois weakness|+20%|+24%|+28%|+32%|+36%|+40%|+44%|+48%|+52%|+56%|
             |-> damage up     |    |    |    |    |    |    |    |    |    |    |
    ------------------------------------------------------------------------------
    Paralyze |Hit Para weakness|+20%|+24%|+28%|+32%|+36%|+40%|+44%|+48%|+52%|+56%|
             |-> damage up     |    |    |    |    |    |    |    |    |    |    |
    ------------------------------------------------------------------------------
    Freeze   |Hit Frz weakness |+20%|+24%|+28%|+32%|+36%|+40%|+44%|+48%|+52%|+56%|
             |-> damage up     |    |    |    |    |    |    |    |    |    |    |
    ------------------------------------------------------------------------------
    Burn     |Hit Burn weakness|+20%|+24%|+28%|+32%|+36%|+40%|+44%|+48%|+52%|+56%|
             |-> damage up     |    |    |    |    |    |    |    |    |    |    |
    ------------------------------------------------------------------------------
    Petrify  |Hit Petr weakness|+20%|+24%|+28%|+32%|+36%|+40%|+44%|+48%|+52%|+56%|
             |-> damage up     |    |    |    |    |    |    |    |    |    |    |
    ------------------------------------------------------------------------------
    Slow     |Hit Slow weakness|+20%|+24%|+28%|+32%|+36%|+40%|+44%|+48%|+52%|+56%|
             |-> damage up     |    |    |    |    |    |    |    |    |    |    |
    ------------------------------------------------------------------------------
    Revenge  |Chance to recover|8%  |11% |14% |17% |20% |23% |26% |29% |32% |35% |
             |CC when hit      |    |    |    |    |    |    |    |    |    |    |
    ------------------------------------------------------------------------------
    Refresh  |Chance to recover|24% |30% |36% |42% |48% |54% |60% |66% |72% |78% |
             |CC when dodging  |    |    |    |    |    |    |    |    |    |    |
    ------------------------------------------------------------------------------
    Refill   |Recover CC with  |+1  |+1  |+2  |+2  |+3  |+3  |+4  |+4  |+5  |+5  |
             |each kill        |    |    |    |    |    |    |    |    |    |    |
    ------------------------------------------------------------------------------
    Rise     |Minimum CC up    |+1  |+1  |+1  |+2  |+2  |+2  |+3  |+3  |+3  |+4  |
             |                 |    |    |    |    |    |    |    |    |    |    |
    ------------------------------------------------------------------------------
    Exceed   |Maximum CC up    |+1  |+2  |+2  |+3  |+3  |+4  |+4  |+5  |+5  |+6  |
             |                 |    |    |    |    |    |    |    |    |    |    |
    ------------------------------------------------------------------------------
    Reinforce|CC recovery rate |+20%|+24%|+28%|+32%|+36%|+40%|+44%|+48%|+52%|+56%|
             |up               |    |    |    |    |    |    |    |    |    |    |
    ------------------------------------------------------------------------------
    Warrior  |P.Atk and P.Def  |+8  |+12 |+16 |+20 |+24 |+28 |+32 |+36 |+40 |+44 |
             |up               |    |    |    |    |    |    |    |    |    |    |
    ------------------------------------------------------------------------------
    Sorcerer |C.Atk and C.Def  |+8  |+12 |+16 |+20 |+24 |+28 |+32 |+36 |+40 |+44 |
             |up               |    |    |    |    |    |    |    |    |    |    |
    ------------------------------------------------------------------------------
    Assassin |Accuracy and     |+8  |+12 |+16 |+20 |+24 |+28 |+32 |+36 |+40 |+44 |
             |Evasion up       |    |    |    |    |    |    |    |    |    |    |
    ------------------------------------------------------------------------------
    Valiant  |P.Atk and C.Atk  |+8  |+12 |+16 |+20 |+24 |+28 |+32 |+36 |+40 |+44 |
             |up               |    |    |    |    |    |    |    |    |    |    |
    ------------------------------------------------------------------------------
    Paladin  |C.Def and Evasion|+8  |+12 |+16 |+20 |+24 |+28 |+32 |+36 |+40 |+44 |
             |up               |    |    |    |    |    |    |    |    |    |    |
    ------------------------------------------------------------------------------
    Hunter   |Accuracy and     |+8  |+12 |+16 |+20 |+24 |+28 |+32 |+36 |+40 |+44 |
             |P.Def up         |    |    |    |    |    |    |    |    |    |    |
    ------------------------------------------------------------------------------
    
    
    -------------------------
    IVC. Quality Combinations
    -------------------------
    
    These charts show all of the qualities that result from dualizing together
    two qualities of the same Rank. To use them, simply find the quality of the
    first item in the left-most column, find the quality of the second item in
    the top-most row, and then find the cell corresponding to that row and 
    column in the chart.  
    
    Also, before you use this chart, make sure that you are not using a quality-
    effect pair that will lead to an effect upgrade (as described in section 
    IIA2a).  Effect upgrades always supercede quality rank upgrades, leaving the
    quality unchanged, even if the effect is already above level 3 and as a result
    isn't actually upgraded.
    
    Rank 1 + Rank 1:
     
         || Keen  | Hard  | Cool  | Cute  | Rapt  | Oily  | Buff  | Cold  |
    =======================================================================
    Keen || Grand | Rank6*| Noble | Noble | Sunny | Suave | Rigid | Rigid |
    -----------------------------------------------------------------------
    Hard || Rank 6| Rigid | Rigid | Suave | Buff  | Grand | Rigid | Grand |
    -----------------------------------------------------------------------
    Cool || Noble | Rigid | Noble | Rank 6| Sunny | Noble | Sunny | Suave |
    -----------------------------------------------------------------------
    Cute || Noble | Suave | Rank 6| Olden | Olden | Noble | Olden | Sunny |
    -----------------------------------------------------------------------
    Rapt || Sunny | Buff  | Sunny | Olden | Grand | Rank 6| Rigid | Sunny |
    -----------------------------------------------------------------------
    Oily || Suave | Grand | Noble | Noble | Rank 6| Suave | Grand | Olden |
    -----------------------------------------------------------------------
    Buff || Rigid | Rigid | Sunny | Olden | Rigid | Grand | Rigid | Rank 6|
    -----------------------------------------------------------------------
    Cold || Rigid | Grand | Suave | Sunny | Sunny | Olden | Rank 6| Noble |
    -----------------------------------------------------------------------
    
    Rank 2 + Rank 2:
    
             || Grand    | Noble    | Suave    | Olden    | Sunny    | Rigid    |
    =============================================================================
    Grand    || Stuffy   | Stuffy   | Barbed   | Formal   | Rank 6   | Solemn   |
    -----------------------------------------------------------------------------
    Noble    || Stuffy   | Barbed   | Barbed   | Rank 6   | Stuffy   | Frosty   |
    -----------------------------------------------------------------------------
    Suave    || Barbed   | Barbed   | Frosty   | Frosty   | Wicked   | Rank 6   |
    -----------------------------------------------------------------------------
    Olden    || Formal   | Rank 6   | Frosty   | Wicked   | Solemn   | Wicked   |
    -----------------------------------------------------------------------------
    Sunny    || Rank 6   | Stuffy   | Wicked   | Solemn   | Formal   | Formal   |
    -----------------------------------------------------------------------------
    Rigid    || Solemn   | Frosty   | Rank 6   | Wicked   | Formal   | Solemn   |
    -----------------------------------------------------------------------------
    
    Rank 3 + Rank 3:
    
             || Wicked   | Barbed   | Frosty   | Stuffy   | Formal   | Solemn   |
    =============================================================================
    Wicked   || Magical  | Epochal  | Haughty  | Magical  | Gallant  | Magical  |
    -----------------------------------------------------------------------------
    Barbed   || Epochal  | Epochal  | Sketchy  | Untamed  | Rank 6   | Haughty  |
    -----------------------------------------------------------------------------
    Frosty   || Haughty  | Sketchy  | Sketchy  | Rank 6   | Sketchy  | Magical  |
    -----------------------------------------------------------------------------
    Stuffy   || Magical  | Untamed  | Rank 6   | Untamed  | Gallant  | Haughty  |
    -----------------------------------------------------------------------------
    Formal   || Gallant  | Rank 6   | Sketchy  | Gallant  | Gallant  | Untamed  |
    -----------------------------------------------------------------------------
    Solemn   || Magical  | Haughty  | Magical  | Haughty  | Untamed  | Haughty  |
    -----------------------------------------------------------------------------
    
    Rank 4 + Rank 4:
    
             || Untamed  | Gallant  | Haughty  | Sketchy  | Magical  | Epochal  |
    =============================================================================
    Untamed  || Perilous | Dazzling | Perilous | Vigorous | Gracious | Rank 6   |
    -----------------------------------------------------------------------------
    Gallant  || Dazzling | Vigorous | Rank 6   | Dazzling | Poignant | Vigorous |
    -----------------------------------------------------------------------------
    Haughty  || Perilous | Rank 6   | Poignant | Perilous | Gracious | Perilous |
    -----------------------------------------------------------------------------
    Sketchy  || Vigorous | Dazzling | Perilous | Dazzling | Fabulous | Dazzling |
    -----------------------------------------------------------------------------
    Magical  || Gracious | Poignant | Gracious | Fabulous | Gracious | Fabulous |
    -----------------------------------------------------------------------------
    Epochal  || Rank 6   | Vigorous | Perilous | Dazzling | Fabulous | Fabulous |
    -----------------------------------------------------------------------------
    
    Rank 5 + Rank 5:
    
    
             || Fabulous | Dazzling | Perilous | Poignant | Vigorous | Gracious |
    =============================================================================
    Fabulous || Fabulous | Noble    | Oily     | Grand    | Rank 6   | Suave    |
    -----------------------------------------------------------------------------
    Dazzling || Noble    | Rank 6   | Rank 6   | Stuffy   | Cute     | Cold     |
    -----------------------------------------------------------------------------
    Perilous || Oily     | Rank 6   | Rank 6   | Keen     | Cool     | Keen     |
    -----------------------------------------------------------------------------
    Poignant || Grand    | Stuffy   | Keen     | Poignant | Olden    | Rank 6   |
    -----------------------------------------------------------------------------
    Vigorous || Rank 6   | Cute     | Cool     | Olden    | Rank 6   | Noble    |
    -----------------------------------------------------------------------------
    Gracious || Suave    | Cold     | Keen     | Rank 6   | Noble    | Rank 6   |
    -----------------------------------------------------------------------------
    
    
    *Rank 6 qualities:
    
    As can be seen in the tables above, some quality combinations lead straight 
    to a Rank 6 quality. I did not specify which Rank 6 quality each combination
    yields in the tables because it actually does not strictly depend on the 
    starting qualities themselves.  Instead, when you are dualizing a piece of
    equipment with a shard, the Rank 6 quality you get is determined by the 
    following formula:
    
    N = floor((equipment rank + shard ability level)/3) + 1   (floor = round down)
    
    Equipment rank depends on the equipment itself.  While I am unsure of all of 
    the details about what determines equipment rank for the more unique weapons 
    and armor, I do know that the starting equipment is rank 0, Iron equipment is 
    1, Steel 2, Rune 3, Battle 4, Platinum 5, Mythril 6, and Rare 7. The shard 
    ability level should be self-explanatory.
    
    The quality then depends on the calculated value of N:
    N = 0 -> Worthless
    N = 1 -> Tolerable
    N = 2 -> Easygoing
    N = 3 -> Diffident
    N = 4 -> Impartial
    N = 5 -> Competent
    N = 6 -> Unadorned
    N = 7 -> Concealed
    N = 8 -> Deficient
    N = 9 -> Pointless
    
    If you are extracting or fusing gems, the formula is instead:
    N = floor((sum of levels of all effects on original items)/4
    
    Finally, when you are dualizing two Rank 6 items together, the resulting
    quality will be the one that corresponds to the lowest value of N above. For 
    example, Pointless (N = 9) + Unadorned (N = 6) -> Unadorned. 
    
    
    Rank 7 qualities:
    
    These ten-letter "cameo" qualities require special, unique combinations of 
    qualities of different Rank. They also require that you be on a New Game + and
    have purchased the "Unlock Qualities" option in the Grade Shop.
    
    Garrtastic = Sunny + Pointless
    Barbatosan = Perilous + Gallant
    Lukerrific = Barbed + Haughty
    Bruiserine = Oily + Grand
    Lonimazing = Stuffy + Poignant
    Nataliated = Suave + Dazzling
    Nanalystic = Untamed + Olden
    Guyabulous = Cool + Noble
    Genisimile = Keen + Magical
    Kyleicious = Rigid + Barbed
    Eugenelike = Solemn + Vigorous 
    Caiusesque = Competent + Untamed
    
    
    And finally, for convenience, I've compiled a list of all of the quality 
    combinations that allow you to attain each individual quality (for Ranks 1 
    through 6): 
    
    Keen:
     Perilous + Poignant
     Perilous + Gracious
    
    Hard:
     None
     
    Cool:
     Perilous + Vigorous
    
    Cute:
     Dazzling + Vigorous
    
    Rapt:
     None
    
    Oily:
     Fabulous + Perilous
    
    Buff:
     None
    
    Cold:
     Dazzling + Gracious
    
    Grand:
     Keen + Keen
     Hard + Oily
     Hard + Cold
     Rapt + Rapt
     Oily + Buff
     Fabulous + Poignant
    
    Noble:
     Keen + Cool
     Keen + Cute
     Cool + Cool
     Cool + Oily
     Cute + Oily
     Cold + Cold
     Fabulous + Dazzling
     Vigorous + Gracious
     
    Suave:
     Keen + Oily
     Hard + Cute
     Cool + Cold
     Oily + Oily
     Fabulous + Gracious
    
    Olden:
     Cute + Cute
     Cute + Rapt
     Cute + Buff
     Oily + Cold
     Poignant + Vigorous
    
    Sunny:
     Keen + Rapt
     Cool + Rapt
     Cool + Buff
     Cute + Cold
     Rapt + Cold
    
    Rigid:
     Keen + Buff
     Keen + Cold
     Hard + Hard
     Hard + Cool
     Hard + Buff
     Rapt + Buff
     Buff + Buff
    
    Wicked:
     Suave + Sunny
     Olden + Olden
     Olden + Rigid
     
    Barbed:
     Grand + Suave
     Noble + Noble
     Noble + Suave
    
    Frosty:
     Noble + Rigid
     Suave + Suave
     Suave + Olden
    
    Stuffy:
     Grand + Grand
     Grand + Noble
     Noble + Sunny
     Dazzling + Poignant
    
    Formal:
     Grand + Olden
     Sunny + Sunny
     Sunny + Rigid
     
    Solemn:
     Grand + Rigid
     Olden + Sunny
     Rigid + Rigid
    
    Untamed:
     Barbed + Stuffy
     Stuffy + Stuffy
     Formal + Solemn 
    
    Gallant:
     Wicked + Formal
     Stuffy + Formal
     Formal + Formal
    
    Haughty:
     Wicked + Frosty
     Barbed + Solemn
     Stuffy + Solemn
     Solemn + Solemn
    
    Sketchy:
     Barbed + Frosty
     Frosty + Frosty
     Frosty + Formal
    
    Magical:
     Wicked + Wicked
     Wicked + Stuffy
     Wicked + Solemn
     Frosty + Solemn
    
    Epochal:
     Wicked + Barbed
     Barbed + Barbed
    
    Fabulous:
     Sketchy + Maical
     Magical + Epochal
     Epochal + Epochal
     Fabulous + Fabulous
    
    Dazzling:
     Untamed + Gallant
     Gallant + Sketchy
     Sketchy + Sketchy
     Sketchy + Epochal
    
    Perilous:
     Untamed + Untamed
     Untamed + Haughty
     Haughty + Sketchy
     Haughty + Epochal
    
    Poignant:
     Gallant + Magical
     Haughty + Haughty
     Poignant + Poignant
    
    Vigorous:
     Untamed + Sketchy
     Gallant + Gallant
     Gallant + Epochal
    
    Gracious:
     Untamed + Magical
     Haughty + Magical
     Magical + Magical
    
    Rank 6:
     Keen + Hard
     Cool + Cute
     Rapt + Oily
     Buff + Cold
     Grand + Sunny
     Noble + Olden
     Suave + Rigid
     Barbed + Formal
     Frosty + Stuffy
     Untamed + Epochal
     Gallant + Haughty
     Fabulous + Vigorous
     Dazzling + Dazzling
     Dazzling + Perilous
     Perilous + Perilous
     Vigorous + Vigorous
     Gracious + Poignant
     Gracious + Gracious
     
    
    -------------------------
    IVD. Quality-Effect Pairs
    -------------------------
    
    As explained in section IIA2a, some combinations of quality and effect
    will actually increase the level of the effect by one, if the quality is one
    item and the effect is on the other. This table details which qualities 
    correspond to which effects. It essentially follows the order that the 
    qualities (Ranks 1 through 4) appear in the Quality Book and that the shards 
    appear in the Collector's Book.
    
    | Quality   | Effect    |
    =========================
    | Keen      | Attack    |
    -------------------------
    | Hard      | Defense   |
    -------------------------
    | Cool      | Mind      |
    -------------------------
    | Cute      | Resist    |
    -------------------------
    | Rapt      | Aim       |
    -------------------------
    | Oily      | Evade     |
    -------------------------
    | Buff      | Vitality  |
    -------------------------
    | Cold      | Speed     |
    -------------------------
    | Grand     | Gain      |
    -------------------------
    | Noble     | Absorb    |
    -------------------------
    | Suave     | Blessing  |
    -------------------------
    | Olden     | Tension   |
    -------------------------
    | Sunny     | Holy      |
    -------------------------
    | Rigid     | Rescue    |
    -------------------------
    | Wicked    | Poison    |
    -------------------------
    | Barbed    | Paralyze  |
    -------------------------
    | Frosty    | Freeze    |
    -------------------------
    | Formal    | Petrify   |
    -------------------------
    | Solemn    | Slow      |
    -------------------------
    | Untamed   | Revenge   |
    -------------------------
    | Gallant   | Refresh   |
    -------------------------
    | Haughty   | Refill    |
    -------------------------
    | Sketchy   | Rise      |
    -------------------------
    | Magical   | Exceed    |
    -------------------------
    | Epochal   | Reinforce |
    -------------------------
    
    
    ==============
    V. Shard Drops
    ==============
    
    Every normal battle has a chance of set chance of dropping one shard (and no
    more than one shard), and this chance depends on the difficulty on which you 
    are playing:
    
    | Difficulty     | Base Drop Rate |
    ===================================
    | Easy           | 20%            |
    -----------------------------------
    | Normal         | 24%            |
    -----------------------------------
    | Moderate       | 28%            |
    -----------------------------------
    | Hard           | 32%            |
    -----------------------------------
    | Evil           | 36%            |
    -----------------------------------
    | Chaos          | 40%            |
    -----------------------------------
    
    Additionally, this rate is modified based on the level difference between you 
    and your enemies. If your average party level is greater than the level of the
    most powerful enemy, the drop rate will decrease, and vice versa, as detailed 
    below:
    
    | Level Difference | Drop Rate Change   |
    =========================================
    | +/-20            | +/-10%             |
    -----------------------------------------
    | +/-10            | +/-5%              |
    -----------------------------------------
    | +/-2             | +/-1%              |
    -----------------------------------------
    | 0                | 0%                 |
    -----------------------------------------
    
    The drop rate decreases based on how many shards you have in your inventory.  
    If you have 100 or more total shards, the rate will be cut in half.  If you 
    have 150 or more, the rate will be decreased even further. If you have 190 or 
    more, the rate will essentially drop to 0%. Also note that, as with any other 
    material, you can never carry more than 15 shards with the same name (i.e., 
    the same effect - even if the levels differ).  
    
    The following items will double the drop rate for one battle when cooked: Fish
    & Chips, Curried Cod, and Miso-Glazed Cod (basically everything involving 
    Cod). The Book of Acquisition doubles the drop rate as well, and these all 
    stack.
    
    
    The level of any shards that drop depends on the highest level of the enemy 
    you are facing. Effect levels are centered around a certain value calculated
    from the following formula:
    
    N = floor((Highest Enemy Level) / 20) + 1
    
    If you have cooked Grape Parfait, N will be increased by an additional 1. (I
    am unsure if Grape Parfait has any effect on the qualities or types of effects
    that drop.)
    
    Of course, there is some random variation in what the effect level can be, but
    it is usually within 1 level of N.  (For example, if the enemies all level 50,
    N = 3, most shards will be level 2-4.) There are caps to the highest-level
    shard that can drop: on Easy, no shards above level 5 will drop, regardless of
    how high the enemy level is; on Normal, no shards above level 6 will drop;
    and so on. This means that level * (10) shards CAN drop on Chaos - i.e. there
    is no cap. Of course, it pays to play on higher difficulties either way 
    because enemy levels are higher.
    
    The qualities and effects of shards that drop depend solely on the area in 
    which you are fighting, not on the identity of the enemies themselves. In the 
    following two sections, I have compiled lists of convenient farming locations
    for every quality and effect that can be obtained on shards.
    
    
    ------------------------
    VA. Locations by Quality
    ------------------------
    
    The following is a list of a select few locations where shards of each quality
    can be found, complete with the percentage of all dropped shards that will 
    have the given quality.  Note that this is not a complete list of all drop 
    locations - I've just listed one convenient farming location from the main arc
    and all locations from the Zhonecage.  All information in this section comes 
    from the Japanese Tales of Graces wiki.  
    
    Keen: Lhant Hill (40%); Zhonecage 1, 9 (22%)
    Hard: North Lhant Road (40%); Zhonecage  2, 10 (22%)
    Cool: East Lhant Highroad (40%); Zhonecage 3 (22%)
    Cute: Lhant Hill - Cliffs (40%); Zhonecage 4 (22%)
    Rapt: Barona Catacombs (33%); Zhonecage 5 (22%)
    Oily: Lhant Hill - Cliffs (30%); Zhonecage 6 (22%)
    Buff: East Lhant Highroad (30%); Zhonecage 7 (22%)
    Cold: Strahta Desert - East (24%); Zhonecage 8 (22%)
    
    Grand: Strahta Craglands (19%); Zhonecage 1, 7 (19%)
    Noble: Strahta Craglands (19%); Zhonecage 2, 8 (19%)
    Suave: Strahta Desert(19%); Zhonecage 3, 9 (19%)
    Olden: Sandshroud Ruins (22%); Zhonecage 4 (19%)
    Sunny: Ghardia Shaft - Center (22%); Zhonecage 5 (19%)
    Rigid: Ghardia Shaft - Center (19%); Zhonecage 6 (19%)
    
    Wicked: Ghardia Shaft - Depths (14%); Zhonecage 1, 7 (17%)
    Barbed: Ghardia Shaft - Depths (17%); Zhonecage 2, 8 (17%)
    Frosty: Ghardia Shaft - Base (14%); Zhonecage 3, 9 (17%)
    Stuffy: Ghardia Shaft - Center (17%); Zhonecage 4, 10 (17%)
    Formal: Sandshroud Ruins (14%); Zhonecage 5 (17%)
    Solemn: Ghardia Shaft - Depths (11%); Zhonecage 6 (17%)
    
    Untamed: World's Eye (9%); Zhonecage 1, 7 (11%)
    Gallant: Ghardia Shaft - Depths (9%); Zhonecage 2, 8 (11%)
    Haughty: Sandshroud Ruins (9%); Zhonecage 3, 9 (11%)
    Sketchy: Ghardia Shaft - Base (9%); Zhonecage 4, 10 (11%)
    Magical: Ghardia Shaft - Base (5%); Zhonecage 5 (11%)
    Epochal: Ghardia Shaft - Center (5%); Zhonecage 6 (11%)
    
    Fabulous: World's Eye (3%); Zhonecage 1, 7 (5%)
    Dazzling: Sandshroud Ruins (3%); Zhonecage 2, 8 (5%)
    Perilous: Ghardia Shaft - Depths (3%); Zhonecage 3, 9 (5%)
    Poignant: Zhonecage 4, 10 (5%)
    Vigorous: Zhonecage 5 (5%)
    Gracious: Ghardia Shaft - Center (3%); Zhonecage 6 (5%)
    
    Worthless: Zhonecage 1 (3%)
    Tolerable: Zhonecage 2 (3%)
    Easygoing: Zhonecage 3 (3%)
    Diffident: Zhonecage 4 (3%)
    Impartial: Zhonecage 5 (3%)
    Competent: Zhonecage 6 (3%)
    Unadorned: Zhonecage 7 (3%)
    Concealed: Zhonecage 8 (3%)
    Deficient: Zhonecage 9 (3%)
    Pointless: Zhonecage 10 (3%)
    
    
    -----------------------
    VB. Locations by Effect
    -----------------------
    
    Like the previous section, but for effects this time. Since I figure that most
    people won't farm for shards until the end of the game, I've tried to select 
    more of the late-game locations. Each effect has listed, in this order: one 
    drop location from near the end of the main arc, all from the Zhonecage, and 
    one from the future arc. Including the early-game locations would be a 
    monumentally time-consuming task, so I repeat: this is NOT an exhaustive list,
    but it should suffice for late-game farming purposes. As far as I know, the 
    drop rate at each of these locations is unknown. It is possible that some 
    areas may drop shards with a given effect at a higher rate than others, as is
    the case with shard qualities - I just don't know which areas are the best for
    which shards.
    
    Attack: Ghardia Shaft - Base; Zhonecage 1, 2, 3, 10; Gustwork Ruins
    Defense: Ghardia Shaft - Base/Center; Zhonecage 4, 5, 6, 10; Gustwork Ruins
    Mind: Ghardia Shaft - Center/Depths; Zhonecage 1, 2, 3, 10; Gustwork Ruins
    Resist: Ghardia Shaft; Zhonecage 4, 5, 6, 10; Fendel Glacier Ruins
    Aim: Ghardia Shaft - Base/Center; Zhonecage 1, 2, 3, 10; Fodra's Core
    Evade: Ghardia Shaft; Zhonecage 4, 5, 6, 10; Gustwork Ruins
    Vitality: Bathus Citadel; Zhonecage 10; Arcadia Garden
    Speed: Bathus Citadel; Zhonecage 10; (no future drops)
    
    Gain: Bathus Citadel; (no Zhonecage drops); Lastalia Shaft: Depths
    Absorb: Snowshroud Ruins; Zhonecage 1, 2, 3; (no future drops)
    Blessing: Snowshroud Ruins; Zhonecage 1, 2, 3; Gustwork Ruins
    Tension: Humanoid Research Center; Zhonecage 1, 2, 3, 7, 8, 9; Arcadia Garden
    Holy: Humanoid Research Center; Zhonecage 7, 8, 9; Fendel Glacier Ruins
    Rescue: Bathus Citadel; Zhonecage 7, 8, 9; Strahta Desert Ruins
    
    Poison: Ghardia Shaft - Base; Zhonecage 7, 8, 9; (no future drops)
    Paralyze: Wallbridge Ruins; Zhonecage 7, 8, 9; Arcadia Garden
    Freeze:  Ghardia Shaft - Center; Zhonecage 7, 8, 9; Gustwork Ruins
    Burn: Ghardia Shaft - Center; Zhonecage 4, 5, 6; Lastalia Shaft: Base
    Petrify: Ghardia Shaft - Depths; Zhonecage 4, 5, 6; Gustwork Ruins
    Slow: Ghardia Shaft - Depths; Zhonecage 4, 5, 6; Gustwork Ruins
    
    Revenge: Snowshroud Ruins; Zhonecage 1, 2, 3; Eleth Research Laboratory
    Refresh: Bathus Citadel; Zhonecage 4, 5, 6; (no future drops)
    Refill: Humanoid Research Center; Zhonecage 7; Fodra's Core
    Rise: Ghardia Shaft - Base; Zhonecage 1, 2, 3, 8, 9; Strahta Desert Ruins
    Exceed: Ghardia Shaft - Center; Zhonecage 4, 5, 6; Fodra's Core
    Reinforce: Snowshroud Ruins; Zhonecage 7, 8, 9; Arcadia Garden
    
    
    ===========================
    VI. General Tips and Tricks
    ===========================
    
    This section just covers some of my final, disorganized ramblings on some 
    things I think might be helpful to people who are still getting used to how to
    approach and plan out the dualizing process. Some if it may be a little 
    redundant alongside the preceding sections, but I hope at least somebody will 
    find a few useful tidbits of information in here.
    
    
    -At some point, as you upgrade a weapon more and more, dualizing gets REALLY
    expensive. Unless you're rolling in gald at the end of the future arc, it may
    not really befeasible to get a weapon to +99, or to get all of your gems to 
    [9]/[9].  But every bit along the way makes a difference!
    
    
    -If you want to make really high-level gems, I would recommend using a cheap 
    weapon as a backbone. This will lower the dualizing costs pretty 
    significantly, without affecting your final product. Remember, the effects on
    the extracted gem are solely (in most cases) determined by the effects on the 
    shards you start with.  Plus, this way, you don't have to worry about 
    optimizing qualities because you'll be tossing the weapon out anyway!
    
    
    -If you want to keep an effect on a certain weapon while still upgrading that 
    weapon, this can be done. You just have to dualize with a shard that has a 
    higher-level effect. Recall that for equipment with two effects, it is the 
    higher-level effect that is extracted. For example, if you have Rise[4] on a 
    weapon and you don't want to get rid of it, you can dualize with a Petrify[5] 
    shard. When you get to the gem extraction step, the weapon will keep Rise[4], 
    and the gem will get Petrify[5]. 
    
    You can also use your knowledge of this mechanic to extract abilities that are
    unique to certain weapons. For example, if you want to get Phact Phantasia's 
    Accel-Charge[3] onto a gem, all you have to do is dualize the weapon with a 
    level [1] or [2] shard, then proceed to the extraction step.
    
    
    -One strategy I sometimes like to use when designing gems is to shoot for 
    single-effect gems during the gem extraction process. This gives you a lot of 
    flexibility with what you can do with your gems later down the line. For 
    example, if you have two Exceed[4] shards, you can use them to enhance two 
    different weapons, then extract them together to get a single-effect XCEED-
    XCEED gem with Exceed[5]. You now have a gem that you can fuse with any other
    single-effect gem - without losing any effects in the process (since they
    only have one). It's a lot simpler than having two keep track of two effects
    at once, making sure that they will both get upgraded when you fuse the two
    gems. Of course, if you plan to use the gem immediately, then this approach is
    a bit less practical.
    
    
    -If you have some desired quality in mind but you don't know whether you have 
    the shards to get it, this is a trick that can help you: Go to the Dualizing 
    menu at a shop, and select the equipment you want to upgrade as your first 
    item.  Then go to your list of shards when you are prompted to select the 
    second item.  You should see a preview window on the left showing you what 
    equipment you'll end up with, including its quality. Now you can just scroll 
    through the list of shards by holding the control stick down. Stop if/when the
    quality you want to end up with shows up in the preview window. Also remember 
    that improved qualities/effects show up in orange (and previously undiscovered
    qualities show up in green), so you can use this trick to screen for 
    improvements as well. Bottome line here: make judicious use of the preview 
    screen in the dualizing menu!
    
    
    -Upgraded equipment always sells for more than base equipment. If you're short 
    on cash and are planning on selling some gear, try upgrading it to +1 with any
    junk shards you have lying around first (and tempering it if you have the 
    time).
    
    
    -It can sometimes pay to dualize with shards that have a lower quality than
    your equipment does. If your equipment is already at Rank 5, you may not want 
    to dualize with another Rank 5 shard because some of the Rank 6 qualities are 
    inferior to the lower-ranked ones, or perhaps because you care about the 
    resell value of your equipment. In this case, you can keep on dualizing with 
    Rank 4 shards, swapping back and forth between Ranks 4 and 5 each time you 
    upgrade your weapon.  
    
    
    ===============================
    VII. Frequently Asked Questions
    ===============================
    
    Q: How do I make an item worth 200,000+ gald?
    
    A: Refer to section III. 
    
    In order to get one of Asbel's titles and to progress in the bonus dungeon, 
    you're going to need to create a weapon worth a little over 200,000 gald. 
    This can be accomplished with some basic dualizing. Most people use a Dream 
    Flange with a Perilous quality because it can be obtained quite easily. To get
    a Dream Flange, obtain a Rare Shotstaff from Shot Cube level 12 or Gralesyde 
    stamp shop level 8. (You can sell your first Dream Flange at Gralesyde to get 
    it to level 8 so you can continue farming these for Gald.) Then dualize the 
    Rare Shotstaff with a High-Grade Crystal (Decaying Sword + Lump of Clay) to 
    convert it into a Dream Flange. Then just follow the steps in this guide to 
    keep upgrading it, being sure to shoot for high resell inheritance values 
    along the way and a final quality with a high resell multiplier. It pays to 
    end up with higher effects and to temper the weapon before you sell it as 
    well. I haven't done this myself yet, but I've read that a Dreamer's Flange+3 
    should be sufficient, even if you don't shoot for really high-level effects, 
    and the calculations seem to support this. This is also a pretty good way to 
    farm gald, assuming you have the shards and the stamp shop in Gralesyde.  
    
    To summarize, here are the upgrading steps you need to do:
    1) Obtain your Epochal Dreamer's Flange as described above.
    2) Dualize with any Stuffy Shard to get it to +1 Stuffy.  Temper and extract 
       the effect.
    3) Dualize with any Wicked shard to get it to +2 Magical.  Temper and extract.
    4) Dualize with any Gallant shard to get it to +3 Poignant.  Temper and sell.
    
    There are many other combinations of shard qualities that will get the 
    appropriate resell value.  But in all cases, I recommend using a Rank 3, then 
    a Rank 4, and finally a Rank 5 quality.
    
    Alternatively, there is a more straightforward way to obtain an item that will
    get you through the Zhonecage. However, it requires that you have gotten the 
    Turtlez shop to Rank 7 (which is not an easy feat in itself, mind you: you 
    need to spend or earn through selling a total of 378,000 gald at Turtlez 
    shops!). You will then be able to purchase Rare Swords. Dualizing these with a 
    Reticent Crystal (Legendary Metal + Earthen Pot) will net you an Isleberg with
    the Magical quality.  Dualizing that with just a single Gallant, Sketchy, or 
    Epochal shard that is LEVEL 6 or above will net you a Poignant or Fabulous 
    Isleberg+1. Once tempered, this Isleberg should be worth around 230,000 gald
    (for Poignant, level 6 second effect) which is just enough to get you into the
    10th floor of the Zhonecage.
    
    
    
    Q: Should I save my best shards in order to upgrade the best, end-game weapons
    and armor?
    
    A: Sure, to a degree. The weapon will keep the effect of the last shard you 
    use, so you may want to save your single best shard for your last dualizing 
    step. However, using lesser weapons doesn't matter if you're going to end up 
    extracting the effect onto a gem anyway. The quality is more important when 
    you're upgrading the weapon, so be sure to use your high-quality shards on 
    the weapons you intend to keep.
    
    
    Q: What are the best effects to put on weapons / armor / gems?
    
    A: If you (like me) enjoy stringing together long combos, Rise, Exceed, and 
    Reinforce shards are the way to go. Accuracy and evasion are actually some of
    the most important stats in this game (unlike in some other Tales games) 
    because they affect how long you stagger enemies or get staggered by them. 
    Most people recommend prioritizing these over the other stat-boosting effects 
    (P.Atk, C.Atk, P.Def, C.Def).  The weakness-exploiting shards (Poison, 
    Petrify, etc.) are really only useful if you want to design a weapon to beat a
    boss with a specific weakness. The healing shards (Gain, Tension, etc.) can be
    useful for the coliseum, where you have no dedicated healer. Play around with 
    them and see what suits your playstyle best. Experiment! Be creative!
    
    
    Q: What is the maximum level to which a weapon can be upgraded?
    
    A: +99 - You can upgrade any weapon or armor 99 times.  After that point, 
    additional dualizing will not yield any stat bonuses. You also get a grade 
    bonus equal to the highest level to which you've upgraded a piece of 
    equipment, so that's one incentive to getting it that high.
    
    
    Q: I upgraded my weapon once, and the game won't let me upgrade it again.  
    What gives?
    
    A: An upgraded weapon needs to be tempered and have its effect extracted 
    before you can upgrade it a second time.  Refer to the sections on tempering 
    (IIB) and gem extraction (IIC) for more details.
    
    
    Q: My weapon isn't tempering! How do I speed this process up?
    
    A: Refer to section IIB.
    
    Every weapon has a set chance of being tempered at the end of a fight, and 
    some take longer than others. There are several recipes that increase the 
    tempering rate for a single battle when cooked: Radish Steak, Marbled Radish 
    Steak, Radish Salisbury Steak, Radish Miso Soup, Daishi Stew, and Miso Stew. 
    Eat your radishes, and just keep at it! I also recommend trying to dualize 
    multiple pieces of equipment at once and fighting easy battles (at Lhant Hill)
    to speed up the process. The Book of Smithery also increases your tempering 
    rate, by 2x.
    
    
    Q: I can't get shards to drop! What can I do to increase the shard drop rate?
    
    A: Refer to Section V.
    
    Shards stop dropping after you reach a certain number of total shards. The 
    drop rate lowers by half when you have 100 shards, lowers by even more when 
    you hit 150, and drops to 0% when you have 190 shards. Also note that, as with
    all other materials, there is a limit of 15 shards for every type (every 
    effect). Furthermore, fighting enemies at a much lower level than you lowers 
    the drop rate substantially. This can be remedied by moving to a more 
    difficult area or raising the difficulty level (which passively increases the 
    drop rate in addition to raising enemy levels). If the drop rate still isn't 
    satisfactory after clearing out your inventory, then you can try cooking Fish 
    & Chips, Curried Cod, or Miso-Glazed Cod, or putting the Book of Acquisition 
    in your Mixer.  These all double the drop rate (and stack). Grape Parfaits in 
    particular make it more likely to obtain "rare shards" - i.e. shards with 
    high-level effects.
    
    
    Q: Where can I find <insert shard here>?
    
    A: Refer to Sections VA and VB. Those sections include a list of drop 
    locations for every quality and effect you could ever want. Note that high-
    ranking qualities generally have less base drop rates than lower-ranking
    qualities. I am not sure how drop rates for effects work out, but I would
    assume that Attack shards are more common than Reinforce shards.
    
    
    =============
    VIII. Credits
    =============
    
    I would like to extend thanks to the following people:
    
    -The wonderful editors of the Japanese Tales of Graces f Wiki, for teasing out
    many of the more hidden mechanics in the game and saving me from doing a lot
    of in-game field research/data collection.
    -Aselia, for doing a lot of the above data collection in English.
    -GameFAQs users animeloverzz, CeruleanGamer, CobraGT, cornett7, Cymerian, 
    Hikari62, magnum7979, oretsuaf, RitsuTainaka, Sephiroushin, Tarvosio, and 
    Wilksha for providing information and helping me clear up various odds and 
    ends about dualizing.
    -Namco Bandai, for developing this game.
    -GameFAQs, for hosting this guide.
    -And last but not least, the GameFAQs community and everyone who uses the 
    site, for giving me a reason to write this guide!
    
    
    ========================
    IX. Contact Info & Legal
    ========================
    
    If you want to contact me with any questions, feedback, corrections, or
    recommendations for improvement, feel free to send me a private message on 
    GameFAQs, or e-mail me at Wii306 AT gmail.com
    
    
    This document is copyrighted (c) 2012 by Wii306. 
    
    The guide was written specifically for www.gamefaqs.com.  It may not be 
    reproduced to any extent except for personal private use. Use of any 
    information obtained from this guide should be properly cited. No other sites 
    have permission to post this guide or to distribute it publicly, and 
    permission to do so will not be granted upon request.