This thread is a compilation all the information I've gathered floating BG and elsewhere.
If you want to add to the list, which I will try to keep updated, please post the following:
Base Gear (NQ or HQ?)
Synergy Tier (NQ/HQ1/HQ2/HQ3)*
Augment Results
For Kirin's Osode/Kirin's Pole, post which scrap was used
*On the armor augments, you can determine the synergy tier by the amount of cinder you get at the end relative to NQ. NQ is 100 cinder, HQ1 is 110 (+10%), HQ2 is 120 (+20%), and HQ3 is 130 (+30%)
To fully develop the list, it would be helpful to post all your results, not just the best results you kept. If you remember augments but don't remember HQ tier, etc., post anyway and I'll try to fit it in where it makes sense.
Materials synth results are:
Seal -> Scrap
NQ (4), HQ1 (6), HQ2 (8 ), HQ3 (12)
Abjuration -> Tatters
Head: NQ (10), HQ1 (12), HQ2 (14), HQ3 (18 )
Body: NQ (12), HQ1 (14), HQ2 (16), HQ3 (20)
Hands: NQ (6), HQ1 (8 ), HQ2 (10), HQ3 (14)
Legs: NQ (8 ), HQ1 (10), HQ2 (12), HQ3 (16)
Feet: NQ (4), HQ1 (6), HQ2 (8 ), HQ3 (12)
Each piece has a piece-specific pool of four possible stats and one HQ-guaranteed augment which only and always appears in some amount on any tier HQ result. The range of values for the HQ-guaranteed augment shifts up by 1 when the base armor used is the +1 version of that piece of armor. Additionally, the maximum values for each of the other four frequent augments for that piece typically shift up by 1 when the base armor used it +1.
Additionally, there is a non-specific random pool of from which augments are randomly chosen which all pieces have in common.
For each augment I have the possible amount of the stat in parentheses if I've only seen it once, or a range if I've seen it multiple times with different results. There seems to be a lot of overlap between HQ1 and HQ2, but it's still difficult to say for sure whether those two completely overlap or not.
NQ: One augment
HQ1: Exclusive HQ augment + one additional augment
HQ2: Exclusive HQ augment + one additional augment
HQ3: Exclusive HQ augment + one or two additional augments (usually two, >90%)
The augment is chosen from one of the two following pools. The chance of each augment coming from the "1 in 4" pool goes up slightly with result tier (NQ: ~60%, HQ1/2: ~70-75%, HQ3: ~80%).
"1 in 4" pool: This pool is specific to each piece of armor
For the "1 in 4" pool, the possible range and average values of the augments go up with higher tier HQs.
Note: The highest augment values in the common pools shown below are typically only possible with the HQ base armor.
"Random" pool: This pool is the same for each piece of armor and the possible values of the augments do not go up with higher tier HQs. The possible augments in the random pool are:
Resist Fire, Earth, Water, Wind, Thunder, Ice, Light, or Darkness: (1-9)
Resist Blind, Bind, Sleep, Slow, Stun, Silence, Gravity, Virus, Paralyze, or Poison: (1-5)
M.atk./M.acc/Atk./Acc/R.atk/R.acc/Eva./M.Eva.: (1-8 )
STR/DEX/INT/MND/CHR/VIT/AGI: (1-5)
HP/MP: (1-31)
For augments chosen from the random pool, the chance of getting a stat augment (bottom three lines above, as opposed to a resist augment), goes up significantly with HQ tiers:
NQ: ~5% stat augments when augment is chosen from random pool
HQ1/2: ~20% stat augments when augment is chosen from random pool
HQ3: ~50% stat augments when augment is chosen from random pool
Much of the information below, with the exception of the potential values of the augments, is consolidated on the BG Wiki page for synergy augments:
Tatter and Scrap Synergy Augments (BG Wiki)
NOTE: The values for the augments listed as common for each piece are not separated based on the quality of the base piece (normal or HQ). The maximum values of the ranges typically represent the maximum values found on HQ versions of the pieces. Typically, subtract 1 for the maximum values of the ranges that can be obtained on NQ pieces. For example, Cure Potency goes up to 4% on Zenith Pumps+1 and 3% on Zenith Pumps, Store TP goes up to 6 on Armada Hauberk and 5 on Adaman Hauberk, etc.
Kirin's Osode, Byakko Scrap (HQ: Dual Wield)
Spoiler: show
Kirin's Osode, Genbu Scrap (HQ: Regen)
Spoiler: show
Kirin's Osode, Seiryu Scrap (HQ: Snapshot)
Spoiler: show
Kirin's Osode, Suzaku Scrap (HQ: Double Attack)
Spoiler: show
Kirin's Pole, Genbu Scrap (HQ: DMG, Common: VIT & Enhancing Magic Skill)
Spoiler: show
Kirin's Pole, Suzaku Scrap (HQ: DMG, Common: STR & Elemental Magic Skill)
Spoiler: show
Kirin's Pole, Seiryu Scrap (HQ: DMG, Common: AGI & Enfeebling Magic Skill)
Spoiler: show
Kirin's Pole, Byakko Scrap (HQ: DMG, Common: DEX & Summoning Magic Skill)
Spoiler: show
Byakko's Haidate (HQ: Store TP)
Spoiler: show
Byakko's Axe (HQ: DMG)
Spoiler: show
Genbu's Kabuto (HQ: Haste)
Spoiler: show
Genbu's Shield (HQ: Cure Potency)
Spoiler: show
Seiryu's Kote (HQ: Store TP)
Spoiler: show
Seiryu's Sword (HQ: DMG)
Spoiler: show
Suzaku's Sune-ate (HQ: Haste)
Spoiler: show
Suzaku's Scythe (HQ: DMG)
Spoiler: show
Zenith Crown (+1) (HQ: Magic Attack Bonus)
Spoiler: show
Dalmatica (+1) (HQ: Occasionally Quickens Spellcasting)
Spoiler: show
Zenith Mitts (+1) (HQ: INT)
Spoiler: show
Zenith Slacks (+1) (HQ: Song Spellcasting Time-)
Spoiler: show
Zenith Pumps (+1) (HQ: Summoning Magic Skill)
Spoiler: show
Adaman Celata (HQ: Dark Magic Skill)
Spoiler: show
Adaman/Armada Hauberk (HQ: Double Attack)
Spoiler: show
Adaman/Armada Mufflers (HQ: Haste)
Spoiler: show
Adaman/Armada Breeches (HQ: STR)
Spoiler: show
Adaman Sollerets (HQ: Pet: Haste)
Spoiler: show
Koenig Schaller (HQ: Fast Cast)
Spoiler: show
Koenig/Kaiser Cuirass (HQ: Physical Damage Taken-)
Spoiler: show
Koenig/Kaiser Handschuhs (HQ: Counter)
Spoiler: show
Koenig/Kaiser Diechlings (HQ: Magic Damage Taken-)
Spoiler: show
Koenig Schuhs (HQ: Regen)
Spoiler: show
Hecatomb Cap (+1) (HQ: Double Attack)
Spoiler: show
Hecatomb Harness (HQ: DEX)
Spoiler: show
Hecatomb Mittens (+1) (HQ: Critical Hit Damage)
Spoiler: show
Hecatomb Subligar (+1) (HQ: Critical Hit Rate)
Spoiler: show
Hecatomb Leggings (+1) (HQ: STR)
Spoiler: show
Shura Zunari Kabuto/+1 (HQ: Weapon Skill Damage)
Spoiler: show
Shura Togi (+1) (HQ: Haste)
Spoiler: show
Shura Kote (+1) (HQ: Counter)
Spoiler: show
Shura Haidate (+1) (HQ: Dual Wield)
Spoiler: show
Shura Sune-ate (HQ: Kick Attacks)
Spoiler: show
Crimson/Blood Mask (HQ: Magic Accuracy)
Spoiler: show
Crimson/Blood Scale Mail (HQ: Haste)
Spoiler: show
Crimson/Blood Finger Gauntlets (HQ: Snapshot)
Spoiler: show
Crimson/Blood Cuisses (HQ: Fast Cast)
Spoiler: show
Crimson/Blood Greaves (HQ: Blue Magic Skill)
Spoiler: show
Shadow Hat (HQ: Pet: Magic Atk. Bonus)
Spoiler: show
Shadow/Valkyrie's Coat (HQ: Magic Accuracy)
Spoiler: show
Shadow/Valkyrie's Cuffs (HQ: MAB)
Spoiler: show
Shadow/Valkyrie's Trews (HQ: Magic Attack Bonus)
Spoiler: show
Shadow/Valkyrie's Clogs (HQ: Singing Skill)
Spoiler: show
Shadow/Valkyrie's Helm (HQ: MP/Refresh)
Spoiler: show
Shadow/Valkyrie's Breastplate (HQ: Triple Attack)
Spoiler: show
Shadow/Valkyrie's Gauntlets (HQ: Double Attack)
Spoiler: show
Shadow/Valkyrie Cuishes (HQ: Haste)
Spoiler: show
Shadow/Valkyrie's Sabatons (HQ: Critical Hit Rate)
Spoiler: show