What the measurements show
From 1930 to 2035 the noon longitude on this date has run from about nineteen and four fifths degrees of Virgo to roughly twenty one and a fifth. The dividing line at twenty degrees falls near the lower end of that range, so the majority of years are past it and a minority are not.
The variation comes from the leap year cycle. Each ordinary year the date arrives about six hours ahead of the Sun's previous position and the longitude creeps up, then a leap day resets it. The whole oscillation is a little over a degree wide, and it happens to be centred close enough to twenty degrees that no single answer covers every year. A birth time shifts the figure further, since the Sun moves close to a degree in a day.
The two bands and their rulers
If the Sun had not yet reached twenty degrees, the birthday belongs to the middle band, which the Chaldean order assigns to Venus and the triplicity scheme assigns to Mercury. Traditional readings of the Venus version emphasise arrangement, craft and material care rather than analysis.
If it had passed twenty degrees, the final band applies. The Chaldean order gives that to Mercury, the ruler of Virgo itself, and older texts treat it as the sign at its most concentrated, where method and discrimination are least diluted by anything else. The triplicity scheme names Saturn there instead, which shifts the reading towards endurance and structure. All four of these are inherited conventions, and none is settled by anything observable.
Nothing here is in doubt about the sign
It is worth being unambiguous. The Sun leaves Virgo around 22 or 23 September, nine or ten days after this date, and enters it three weeks before. The ingress instants move by hours from year to year, which is nowhere near enough to reach 13 September.
So this birthday is Virgo in every year, at every hour, in every time zone. The uncertainty described above is entirely internal to the sign. That is a different kind of question from the one dates near a boundary raise, and conflating the two is one of the more common errors in popular writing about birthdays.
Resolving it, and what remains
To settle the band you need the year first and the hour second. The widget above computes the Sun's longitude for your own birth details and reports the figure directly, along with how far it stood from the nearest sign boundary, which on this date will be a comfortable distance.
What it cannot settle from a date alone is the rest of the chart. The Moon has two candidate signs on any 13 September and occasionally three. The rising sign has all twelve, decided by the clock and the latitude. Those placements do more to separate one person's chart from another's than the sun sign ever does, and they are the reason a birthday page can only take you so far.
What this page can do is be accurate about its own limits. The sign is certain, the band is conditional, and the remainder waits on details only you have.
Questions people ask about this
Is 13 September in the second or third decan?
Usually the third, but not in every year. The Sun sits within about a degree of the twenty degree line, so the answer depends on the birth year and the hour.
Is 13 September definitely Virgo?
Yes. The sign ends around 22 or 23 September, more than a week later, and the boundary moves only by hours between years.
How do I tell which band I was born in?
Compute the solar longitude for your own year, time and birthplace using the widget above. Anything below twenty degrees is the middle band and anything above it is the final one.
What rules the final decan of Virgo?
Mercury in the Chaldean order, which also rules the sign, and Saturn under the triplicity method. Both attributions are conventions inherited from different traditions.
Does the time of day really matter here?
It can. The Sun advances close to a degree a day, so in the years where noon lands near twenty degrees a morning birth and an evening birth fall on opposite sides.
Why do other pages give one decan flatly?
Because they work from a fixed date table rather than a calculation. A table cannot represent a boundary that shifts within a date, so it picks the more common case and drops the rest.