Here's the result of my research on the relationship between the attribute of the day of the week and synthesizing, and the relationship between moon ages and synthesizing.
BASIC THEORY:
In general, the following is popular belief.
On the day of Light (?uΛ?v), we are more likely to succeed in synthesizing.
On the day of Darkness (?uˆÅ?v), we are more likely to fail in synthesizing.
If you use a cystal with an attribute which is the same with the attribute of the day of the week that day, you are more likely to succeed in synthesizing.
If you use a cystal with an attribute which is strong to the attribute of the day of the week that day, you are more likely to succeed in synthesizing.
* Strong Attribute (more likely to succeed):
Crystal ?@?¨?@Attribute of Day
‰Š?@?¨?@•X
•X?@?¨?@•—
•—?@?¨?@“y
“y?@?¨?@—‹
—‹?@?¨?@?…
?…?@?¨?@ˆÅ
ˆÅ?@?¨?@Œõ (Unclear)
Œõ?@?¨?@ˆÅ (Unclear)
If you use a cystal with an attribute which is weak to the attribute of the day of the week that day, you are more likely to fail in synthesizing.
* Weak Attribute (more likely to fail):
Crystal ?@?¨?@Attribute of Day
‰Š?@?¨?@?…
•X?@?¨?@‰Š
•—?@?¨?@•X
“y?@?¨?@•—
—‹?@?¨?@“y
?…?@?¨?@—‹
ˆÅ?@?¨?@Œõ (Unclear)
Œõ?@?¨?@ˆÅ (Unclear)
On the day of Full Moon (?u–žŒŽ?v), you are more likely to succeed in synthesizing HQ (High Quality) items.
ADVANCED THEORY:
If you synthesize on the previous day of the attribute of the crystal you use, you are more likely to succeed in synthesizing HQ items.
For example, if you want to synthesize HQ items with a Fire Crystal (?u‰Š‚̃NƒŠƒXƒ^ƒ‹?v), you had better do it on the day of Darkness (?uˆÅ?v).
On the previous day (?u“ñ?\˜Z–é?v) or the following day (?uŽO“úŒŽ?v) of the New Moon (?u?VŒŽ?v), you are more likely to succeed in synthesizing HQ items.
The lunar age varies every 7 day:
–žŒŽ?@?¨?@?\˜Z–é?@?¨?@‹?‘ÒŒŽ?@?¨?@‰ºŒ·‚ÌŒŽ?@?¨?@
“ñ?\“ú—]ŒŽ?@?¨?@“ñ?\˜Z–é?@?¨?@?VŒŽ?@?¨?@ŽO“úŒŽ?@?¨?@
Žµ“úŒŽ?@?¨?@?㌷‚ÌŒŽ?@?¨?@?\“ú–é?@?¨?@?\ŽO–é?¨?@–ž ŒŽ?@
Lunar Age Calender:
http://www3.big.or.jp/~wanpaku/FFXI/vtime.cgi
REFERENCES:
—j“ú‚Ì?‡”Ô (order of the days of a week)
[‰Î]?¨[“y]?¨[?…]?¨[•—]?¨[•X]?¨[—‹]?¨[Œõ]?¨[ˆÅ]
Relationship of Each Attribute:
?@?@?@?@?@?@?@?@?@‰Š
?@?@?@?@?ª?@?@?@?@?@?@?@?@?«
?…?@?@?@?@?@?@?@?@?@?@?@?@?@?@?@?@•X
?@?@?@?@?@?@?@?@?@Λ
?ª?@?@?@?@?@?ª?@?@?@?@?«?@?@?@?@?@?«
?@?@?@?@?@?@?@?@?@ˆÅ
—‹?@?@?@?@?@?@?@?@?@?@?@?@?@?@?@?@•—
?@?@?@?@?ª?@?@?@?@?@?@?@?@?«
?@?@?@?@?@?@?@?@?@“y