In
'Pour une astrologie de l'événement', p.19 to 25, Danièle Jay gives more explanations on the role of the Syzygy.
I will try to report as faithfully as possible what she says in her book.
"The ASC is a place of light..."
To rectify this degree, astrologers can try to solve this problem with 3 solutions among other ways.
1) Hermes trustine
"Vettius Valens in Anthology, I, 23-24 and III,13 said that the natal Moon correspond to the ASC of birth.
Please note that Al-Daya defines the conception time with the drop of the sperm (Commento al Centiloquio tolemaico, aphorism LI, translated from arabic by Giuseppe Bezza, Ed. Mimesis, Milano, 2013)
The process would be very practical, except that most of us are unaware of the moment, day and hour, of conception, which rarely corresponds to the moment of the sexual encounter."
2) the Namudar
See Note 19 here of Deb
https://www.skyscript.co.uk/centiloquium1.html
A method from Ptolemy.
"Namudar, a Persian term which means 'one who shows'.
After having determined the ruling planet of sygygy preceding birth, according to the five prerogatives (essential dignities) as defined in Book I,
it will be necessary to see what degree this planet will hold in the sign it occupies at the time of birth. Such will be this degree, we will judge that a similar one will rise above the horizon (Tetrabiblos III, 2 tr Nicolas Bourdin)."
"Giuseppe Bezza and Marco Fumagalli have explained this passage, by evoking an
isorhythmia. There is no question of attributing to the ASC the same degree as the planet which governs the Sygygy but of attributing to it a similar degree, that is to say having the same proportion (isorhythmia) in its sign as the ruler of syzygy in his house. If Jupiter, for example, ruler of a syzygy, would be in Pisces and placed in the middle of the house which welcomes him at the time of the nativity, while the ASC would be in the middle of his zodiacal sign, we could consider the time of birth to be correct. If this were not the case, we would move the ASC (or the MC if its degree was closer to that of Jupiter), until this proportionality is accomplished."
3) Primary directions
I think you are familiar enough on their use to rectify a chart.
Danièle Jay says that this is the most certain of all.
"The quality of our life will be defined in order as per Ptolemy in Tetrabiblos III,11, Bourdin by the Sun, the Moon, the ASC, the
Syzygy, Fortuna and their rulers."
"The sun warms, the moon humidifies: together they create the optimal conditions for life."
"Their union before birth, by conjunction or opposition, must be consulted to judge the existence promised to the child. The Syzygy will give us valuable indications as to the climate which will determine its
health. She will have a say in the question of
longevity. The ruler of the syzygy will allow us to know, among other factors, whether or not, the death will be accidental."
"As for Fortuna, it represents the amount of light of the Moon in the local sphere."
"Once we ascertain that the 5 elements described by Ptolemy are looked at by benefics they will provide good conditions for the life of the child."
And Danièle Jay concludes by saying
"Planets are strong by their celestial positions when in good or friendly places; oriental to the Sun and fast in motion; by their angularities"
"Planets are weak when in places contrary to their nature; occidental to the Sun and slow in motion; falling from the Angles".
"Concerning the timing of events, angular or matutine planets to the Sun or the ASC are swifter and begin earlier. Vespertines act later in their effects."
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So it appears that the Syzygy provides a quality to our life in the background. I find a parallel with the Sygygy in meteorology to know what the season of our life will look like. Will it be sunny or rainy!
I haven't found anything about a transiting or progressed syzygy but your question raises an interesting point. Like we do for a prenatal Syzygy, should we look at it in our annual revolution to get a feel of the kind of weather we will be facing for the year (figurative). And we could start to look at the planet ruling the Syzygy.
Best to you,
Ouranos