The moon and the Proclamation of Christmas

Here's the Proclamation of Christmas sung to the Solemn Tone in Latin at this year's Midnight Mass at St. Peter's:



I've been looking into the rather strange general intro to the Proclamation - this year it's Octavo Kalendas Ianuarii, luna undecima - and have finally understood what's going on here.

Here's the deal:  the Proclamation will always start out with "Octavo Kalendas Ianuarii" because Christmas Day is the eighth day of the Calends of January.  Here's the explanation of how Calends and other relative days are figured,  at Wikipedia:

The Calends (Latin Kalendae "the called", gen. plural -arum), correspond to the first days of each month of the Roman calendar. The Romans assigned these calends to the first day of the month, signifying the start of the new moon cycle.^{[citation needed]} On that day, the pontiffs would announce at the Curia Calabra the rest days for the upcoming month, and the debtors had to pay off their debts that were inscribed in the calendaria, a sort of accounts book. The date (in this calendar system) was measured relative to days such as the Calends, Nones or Ides, for example, in modern terms, three days past Calends would be the 4th of the month. This sort of system would be used to date documents, diary entries, etc.

Computation of the days of the month from Calends can be done using the following verses:

Principium mensis cujusque vocato Kalendas:
Sex Maius nonas, October, Julius, et Mars;
Quattuor at reliqui: dabit Idus quidlibet octo.

meaning that the first day is called the Calends; six days later is the Nones of May, October, July and March; four days later for the remaining months; and the Ides is eight days after that.^[1]

To find the day of the Calends of the current month, one counts how many days remain in the month, and add two to that number. For example, April 22, is the 10th of the Calends of May, because there are 8 days left in April, to which 2 being added, the sum is 10.^[2]

So, December 25 is the 8th of the Calends of January, since there are six days following it before January begins.  Then, add two.   (This all has something to do with  the difference between the average number of days in a solar month - 30.41 days - and the length of the lunar cycle - 29.54 days; I haven't quite figure this out yet, but it's not necessary in order to explain what's happening with the announcement.  But this sort of thing is, no doubt, why the Julian calendar replaced this system.)

The phrase following "Octavo Kalendas Ianuarii" will vary each year; the number there - this year luna undecima, two years ago luna decima nona - is a count of how many days have passed since the last New Moon.    Per this "Moon Phases" calendar, you can see in 2012, the new moon did indeed occur 11 days before December 24, and in 2010 it did indeed occur 19 days before Christmas Eve.

So the announcement in English for this year is this:

"The eighth of the Calends of January, 11 days after the last New Moon."

It seems that this kind of announcement, "the Martyrology," was and in some places still is made at every service of Prime - the first office of the day - for the following day.    ("The following day," of course, begins later that same day with Vespers.)  It normally - as far as I know at the moment - listed the martyrs for that day (and the saints who died on that day, which date is typically chosen for their feast day), along with the date and at least sometimes the phases of the moon.

Here's a typical listing from Divinum Officum for July 18, 2012 (chosen at random), first in Latin, then in English:

Martyrologium (anticipated)

Quartodecimo Kalendas Augusti Luna vicesima nona Anno 2012 Domini

Sancti Vincentii a Paulo, Presbyteri et Confessoris, Congregationis Presbyterorum Missionis et Puellarum Caritatis Fundatoris, caelestis omnium caritatis Societatum Patroni; qui in Domino obdormivit quinto Kalendas Octobris.
Colossis, in Phrygia, natalis sancti Epaphrae, quem sanctus Paulus Apostolus concaptivum appellat. Hic, ab eodem Apostolo Colossis Episcopus ordinatus, ibidem, clarus virtutibus, martyrii palmam, pro ovibus sibi commendatis, virili agone percepit; cujus corpus Romae, in Basilica sanctae Mariae Majoris, conditum est.
Treviris sancti Martini, Episcopi et Martyris.
Hispali, in Hispania, passio sanctarum Virginum Justae et Rufinae, quae, a Praeside Diogeniano comprehensae, primo equulei extensione et ungularum laniatione vexatae, postea carcere, inedia et variis torsionibus sunt afflictae; tandem Justa in carcere spiritum exhalavit, Rufinae vero cervix, in confessione Domini, confracta est.
Cordubae, in Hispania, sanctae Aureae Virginis, beatorum Adulphi et Joannis Martyrum sororis; quae aliquando in apostasiae crimen a Mahumetano Judice inducta est, sed mox, facti poenitens, iterato certamine, hostem effuso sanguine superavit.
Romae sancti Symmachi Papae, qui, a schismaticorum factione diutius fatigatus, demum, sanctitate conspicuus, migravit ad Dominum.
Veronae sancti Felicis Episcopi.
Apud Scetim, Aegypti montem, sancti Arsenii, Romanae Ecclesiae Diaconi; qui, Theodosii tempore, in solitudinem secessit, ibique, virtutibus omnibus consummatus et jugi lacrimarum imbre perfusus, spiritum Deo reddidit.
In Cappadocia sanctae Macrinae Virginis, filiae sanctorum Basilii et Emmeliae, atque sororis item sanctorum Episcoporum Basilii Magni, Gregorii Nysseni et Petri Sebastensis.
V. Et álibi aliórum plurimórum sanctórum Mártyrum et Confessórum, atque sanctárum Vírginum. 
R. Deo grátias.

Martyrologium (anticipated)

On the morrow we keep the feast of the holy Confessor Vincent of Paul, who slept in the Lord upon the 27 th day of September, and whom Pope Leo XIII. proclaimed the patron before God in heaven of all charitable societies throughout the whole Catholic world which derive their origin in any way from his institution, [in the year 1660.] 
July 19th anno Domini 2012 The 29th Day of Moon were born into the better life 

The holy Epaphras, whom the holy Apostle Paul doth call his own fellow prisoner. He was ordained by the same Apostle Bishop of Colossi, where, illustrious for graces, he gained the palm of martyrdom in manly contending on behalf of the sheep committed to his care. His body is buried at Rome, in the Church of St Mary the greater. 
At Seville, in Spain, the holy Virgins Justa and Rufina. They were arrested under the President Diogenian. They were first racked and tormented by being torn with hooks, and afterwards afflicted with imprisonment, starvation, and divers tortures in the end Justa gave up the ghost in prison, and Rufina had her neck broken for confessing the Lord, [at the end of the third century.] 
At Cordova, the holy Virgin Aurea, who for a time fell away, but repented of what she had done, and in a renewed combat prevailed against the enemy by the shedding of her blood, [in the year 856.] 
At Trier, the holy martyr Martin, Bishop [of that see, in the year 210.] 
At Rome, the holy Pope Symmachus, who long suffered through the deeds of the schismatics, and at length passed away, famous for holiness, to be ever with the Lord, [in the year 514.] 
At Verona, holy Felix, the Bishop. 
At Mount Skete, in Egypt, holy Arsenius, a Deacon of the Church of Rome, who in the time of Theodosius betook himself to the desert, where he gave up his soul to God, finished in all graces and plentifully wet with tears, [in the year 450.] 
In Cappadocia, the holy Virgin Macrina, sister to holy Basil the Great and Gregory of Nyssa, [in the year 379.] 
V. And elsewhere many other holy martyrs, confessors, and holy virgins.
R. Thanks be to God.

I'm sure that's much more than you ever wanted to know.  But that's what's happening there - and it's really interesting that the Church is still using this, since the Julian calendar was introduced in 46 BC....

(A pretty impressive aspect of this, BTW, is that the coder at the Divinum Officum site has integrated a phases of the moon function into his/her script!  Well done, I must say.)