# Coligny calendar

The Coligny calendar is a bronze plaque with an inscribed calendar, made in Roman Gaul in the 2nd century CE. It lays out a five-year cycle of a lunisolar calendar, each year with twelve lunar months. An intercalary month is inserted before each 2.5 years. The lunar phase is tracked with exceptional precision, adjusted when necessary by a variable month, and the calendar uses the 19-year Metonic cycle to keep track of the solar year. It is the most important evidence for the reconstruction of an ancient Celtic calendar.
It was found in 1897 in France, in Coligny, Ain (46°23′N 5°21′E﻿ / ﻿46.383°N 5.350°E﻿ / 46.383; 5.350, near Lyon), along with broken pieces of a bronze statue of a life-size naked male holding a spear, likely Roman Mars. It was engraved on a bronze tablet, preserved in 73 fragments, that was originally 1.48 metres (4 ft 10 in) wide by 0.9 metres (2 ft 11 in) tall, equivalent to 5 x 3 Roman feet. It is written in Latin inscriptional capitals and numerals, but terms are in the Gaulish language. Based on the style of lettering and the accompanying statue, the bronze plaque probably dates to the end of the second century, although the copying errors indicate the calendar itself is much older. It is now held at the Gallo-Roman Museum of Lyon-Fourvière.
Eight small fragments of a similar calendar were found at the double-shrine of Villards-d'Héria. It does not have the holes of a peg calendar that the Coligny calendar does, but otherwise has the same notations. It is now held in the Musée d'Archéologie du Jura at Lons-le-Saunier.

## List of months

The names of the twelve lunar year months are reconstructed as Samonios, Dumannios, Rivros, Anagantios, Ogronios, Cutios, Giamonios, Simivisonnios, Equos, Elembivios, Edrinios, and Cantlos. The names occur in the form SAMONI (gen.), DUMANNI, RIVRI etc. in the internal notations of the calendar. The name of the first intercalary month is unknown being on a lost fragment, the second is reconstructed as[ S]antaran[...], [R]antaran[...], [B]antaran[...], or Antaran[...].
Mid Samonios refers to summer (Gaulish samo-,< *sṃHo-3)$^{:267}$ while Mid Giamonios refers to winter (Gaulish giamo-). These two months divide the calendar into summer and winter seasons of six months, each season led off by a festival of several days marked with IVOS. This indicates an early version of the same traditional seasons as seen in later Celtic contexts: “For two divisions were formerly on the year, viz., summer from Beltaine (the first of May), and winter from Samuin to Beltaine”.
It is not possible to align the Coligny lunar months accurately with modern solar months, but allowing for variation across the years it is likely that the month of MID SAMONIOS began around May–June.
| Value | Name | Days | Etymology | Interpretation |
| I-1 | Unknown | 30 | Unknown meaning | Intercalary One |
| 1 | Samonios | 30 | Samo- is Gaulish for summer.$^{:267}$ | May–Jun |
| 2 | Dumannios | 29 | Compare to Latin fūmus. Delamarre suggests "month of fumigations."$^{:154}$ | Jun–Jul |
| 3 | Rivros | 30 | Compare to Old Irish remor (stout, thick, fat) and Welsh rhef (thick, stout, great, large). Delamarre suggests "fat month." | Jul–Aug |
| 4 | Anagantio | 29 | Delamarre suggests "month of ritual ablutions." | Aug–Sep |
| 5 | Ogronios | 30 | Delamarre suggests a month of cold or winter | Sep–Oct |
| 6 | Cutios | 30 | Delamarre suggests a month of invocations | Oct–Nov |
| I-2 | [.]antaran[...] | 30 | Unknown meaning | Intercalary Two |
| 7 | Giamonios | 29 | This name is derived from giamos, the Gaulish word for winter. mi gam is Old Irish for November, according to Cormac's Glossary. | Nov–Dec |
| 8 | Simivisonnios | 30 | Simi could mean half, so "half the course of the sun."$^{:274}$ | Dec–Jan |
| 9 | Equos | 29 or 30 | Possibly a month of horses or livestock.$^{:165}$ | Jan–Feb |
| 10 | Elembivios | 29 | Month of the stag.$^{:161–162}$ | Feb–Mar |
| 11 | Edrinios | 30 | Compare with Old Irish áed (fire, "heat).$^{:34}$ | Mar–Apr |
| 12 | Cantlos | 29 | Delamarre suggests "month of chanting." | Apr–May |

## The lunar month

The Coligny calendar as reconstructed consisted of 16 columns and 4 rows, with two intercalary months given half a column each, resulting in a table of the 62 months of the five-year cycle. The 5 years of the calendar plaque is part of a Metonic cycle of 19 years, although it could also be extended to a 30-year cycle. The full length of the calendar is still being debated.
| IC1 1. | Riu 4. | Gia 8. | Aed 12. | Riu 16. | Gia 20. | Aed 24. | Riu 28. | IC2 32. | Equ 35. | Sam 39. | Ogr 43. | Equ 47. | Sam 51. | Ogr 55. | Equ 59. |
| IC1 1. | Ana 5. | Sim 9. | Can 13. | Ana 17. | Sim 21. | Can 25. | Ana 29. | IC2 32. | Ele 36. | Dum 40. | Qut 44. | Ele 48. | Dum 52. | Qut 56. | Ele 60. |
| Sam 2. | Ogr 6. | Equ 10. | Sam 14. | Ogr 18. | Equ 22. | Sam 26. | Ogr 30. | Gia 33. | Aed 37. | Riu 41. | Gia 45. | Aed 49. | Riu 53. | Gia 57. | Aed 61. |
| Dum 3. | Qut 7. | Ele 11. | Dum 15. | Qut 19. | Ele 23. | Dum 27. | Qut 31. | Sim 34. | Can 38. | Ana 42. | Sim 46. | Can 50. | Ana 54. | Sim 58. | Can 62. |
Each lunar year has a 12 lunar months, six months of 30 days and five of 29 days, although not in 29/30 pairs, and one variable month of 29 or 30 days. A synodic month has 29.53 days, so the calendar overcomes any slight slippage or temporary imbalance by the month of MID EQVOS having either 29 or 30 days as required to keep the calendar in sync with the lunar phase.
The Coligny calendar is designed to keep perfectly in sync with the lunar phase, with a tolerance of less than 24 hours. Its internal notations are organised according to the phase of the moon.
At the end of the 19-year Metonic cycle, the calendar has overrun the 62-month lunar point by 0.312 days. This would be fixed by reducing an EQUOS month from 30 days back to 29 once every 61 years.
If the plaque was part of a 30-year calendar, it overruns the lunar phase by 0.151 days. This requires a day to be removed (by turning a 30-day EQUOS into a 29-day) roughly once every 198 years. However, the internal months show a larger variation in accuracy for the lunar phase, nearly 48 hours (1.44 to −0.65 ), making the ability to track the lunar phase of 30-years notably less accurate.

## The solar year

The calendar is based on the Metonic cycle, a period of 19 years after which the sun and moon complete their phase within about two hours, 0.087 days, of each other. This is created by 4 Coligny plaques, with the first year dropped.
All the days and their notations are luni-solar and move around within a space of 36 days.
| | cycle 1 | cycle 1 | cycle 1 | cycle 1 | cycle 1 | cycle 2 | cycle 2 | cycle 2 | cycle 2 | cycle 2 | cycle 3 | cycle 3 | cycle 3 | cycle 3 | cycle 3 | cycle 4 | cycle 4 | cycle 4 | cycle 4 | cycle 4 |
| | y1 | y2 | y3 | y4 | y5 | y1 | y2 | y3 | y4 | y5 | y1 | y2 | y3 | y4 | y5 | y1 | y2 | y3 | y4 | y5 |
| int1 | 0 | | | | | 29 | | | | | 29 | | | | | 29 | | | | |
| SAM | 0 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 |
| DUM | 0 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 |
| RIU | 0 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 |
| ANA | 0 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 |
| OGR | 0 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 |
| CUT | 0 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 |
| int2 | | | 30 | | | | | 30 | | | | | 30 | | | | | 30 | | |
| GIA | 0 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 |
| SIM | 0 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 |
| EQU | 0 | 29 | 29 | 29 | 30 | 30 | 29 | 29 | 29 | 30 | 30 | 29 | 29 | 29 | 30 | 30 | 29 | 29 | 29 | 30 |
| ELE | 0 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 |
| AED | 0 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 |
| CAN | 0 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 |
The calendar itself must count in whole days, so 6940 days overruns the sun by 0.398396 and the moon by 0.311620 days.
The functioning of the calendar relies on the lunar months staying in sync with the lunar phase, so the calendar is already adjusting for any lunar difference through the use of the variable day in EQVOS. To keep in sync with the solar year it only needs to adjust for the difference of 0.087 days. Every 276 years this adds one day, but as all the notations are luni-solar and move around within 36 days, this extra solar day would be unnoticeable for many centuries. Eventually the calendar would require a 30-day lunar month to be skipped once every 6,536 years.

### A full cycle of 19 or 30 years

The calendar can perform as a 30-year cycle, by extending the 19-year Metonic cycle to use six 5-year cycles, with a 30-day intercalary month dropped once every 30 years. But whether it was a 19-year or 30-year calendar is unknown.
Pliny stated that the Celts treated 30 years as an ‘age’, and this period is seen many times in stories. But it does not necessarily follow that the calendar was then based on a 30-year cycle. If the calendar was a 30-year cycle, the luni-solar swing would be 46 days, meaning that the timing of festivals would often be inappropriate to their seasonal nature. For example, Lugnasad might find itself in the middle of the busy harvest.
In a 30-year calendar, the moon finishes only 0.1515 days earlier than the calendar, requiring a day to be removed from EQVOS every 199 years. But the lunar/solar difference is larger at 1.4172 days, requiring a 30-day month to be skipped every 198 years. This relatively fast slippage against the solar year would also add to the already large luni-solar swing, for a total of 75 days before a possible adjustment, further aggravating the solar discrepancy, and displacing seasonal festivals by up to two and a half months. This slippage and inaccuracy indicates that the Coligny calendar is more likely to be a practical 19-year calendar rather than a 30-year cycle.

## The start of the lunar month

The calendar month is broken into two halves with the term ATENOVX between them. The first half-month has 15 days (called a cóicthiges ‘fifteen-days’ in Old Irish, coicís in modern Irish). The second half-month has either 15 days, or 14 days with the term DIVERTOMV placed over the space for the 15th day. The notation patterns act as though this 'virtual' 15th day is present.
Pliny reported that the Celtic month began on the ‘6th day of the new moon’.
    The mistletoe, however, is but rarely found upon the oak; and when found, is gathered with rites replete with religious awe. This is done more particularly on the sixth day of the moon, the day which is the beginning of their months and years, as also of their ages, which, with them, are but thirty years. This day they select because the moon, though not yet in the middle of her course, has already considerable power and influence; and they call her by a name which signifies, in their language, the all-healing.
Classical writers counted from the day of the first visible moon, so the 6th day would be the first quarter moon, Day 1, the start of the calendar's month. The quarter moon with its D-shape is the only moment in the lunar phase that is easily identifiable by eye. The internal notations of the calendar confirm Pliny's statement, with a focus on the middle triplet of days in each half-month, days 7-8-9 (the full moon) and days 7a-8a-9a (the dark invisible moon).
The first coicise tracks the gibbous moon, the phase in which the moon is more than half full, it's brightest half. The second coicise tracks the crescent moon, the darker half. Notations, which will govern activities, usually focus in the first, brighter, coicise when the moon has ‘considerable power and influence’. Every odd day in the darker coicise is marked as ‘inauspicious day’.

## Full Reconstruction

A full reconstruction of the calendar by McKay (2020) includes the latest information about the intercalary notations and the triple marks. Olmsted (2001) offers a previous reconstruction, which usefully aligns the notations with photographic images. RIG III (1986) presented an earlier in-depth description of terms with a reconstruction.

## Sample month

MID SAMONIOS of year 2 is the only month out of 62 that has been preserved without any gaps. Currently, most of the patterns of the various notations are known, even if their significance may not be understood. Because of this, most days on the calendar can be reconstructed with confidence.
The month begins with M[ID] SAMON[I] MAT, the 'month of SAMONIOS lucky'.
The double circle "◎" in the table indicates the peg-hole for marking the current day, followed by a Roman numeral for the day's number in the half-month.
All days here were originally marked as M D 'lucky day' because SAMONIOS is marked as a MAT month in its header, but this will often be subsequently overwritten by other notations D 'day' (neutral), D AMB 'unlucky day', or N 'night' as they are added in turn.
The notations are usually visually aligned on the D or N. Terms are often shortened, and the spelling is non-standard and often varies.
Next are occasional triple-marks of the form ƚıı ıƚı or ııƚ, in that order before major movements and overwriting. These follow the same offset pattern as the PRINNI notations, and likely divide the daytime into three periods.
Days 5 and 11 in the upper coicise and each odd day (except day 1a) in the lower coicise are marked with D AMB 'inauspicious day'. Day 9a will end up having its D AMB overwritten by N INIS R.
The notation N INIS R occurs in this month on days 8a and 9a. The significance of this nighttime term in unknown.
The name of the following month, DVM(ANNI), is marked on days 1, 3, 8 and 1a. This tracks the swapping of these days' notations (all of them) with the following month DUMANIOS days 1, 8, 1a and 2a where the notations from SAMONIOS have SAMONI added in their turn. Day 2a, first swapped with DUM day 2a, then undergoes another anomalous swap with SAM day 3. Days with notations that have been moved are always marked with their originating month's name (and day name if different).
The notation PRINNI LOUD sits in months marked MAT, at the first day of the first month (Samonios), the second day of the second MAT month (Rivros), and so on for 8 instances. Another PRINNI LOUD originally at SAMONIOS day 1 has been swapped with DVMANNIOS day 1 below it .
The Day 2a(17) is marked with TRINVX SAMO, and this term also has SINDIV IVOS 'festival this (one) day' added to it in years 1 and 4. This means that this day's notations have been swapped with day 3 (TRINVX) of SAMONIOS, after first being swapped with DVMANNIOS day 2a, whose notations now sit at SAMONIOS day 3 ƚıı D DVM IVO. (SAMONIOS day 2a's original notations are found in turn at DUMMANIOS day 2a).
Days 1–3 are marked with a sequence of IVOS, a term interpreted as "festival". This run of IVOS started on the last two days of the previous month CANTLOS, days 13a-14a, so the whole festival lasts for 5 days. This probably equates with the festival of Beltaine, although these sorts of specific terms are not used on the calendar, festivals only being marked with runs of IVOS.
Finally, Day 1 has its 'day' terms overwritten by a single N, without changing the rest of its notations. Originally, it started off with ƚıı M D, was swapped with DUM day 1 receiving D DUMANI, had an IVOS added to give D DUMANI IVOS, and now has that D overwritten by a single N to end up with N DUMANI IVOS. This single N indicates that the notations of SAMONIOS day 1 in this year 2, D DUMANI IVOS, have been used to help create the notations of Intercalary Two day 1.

## The Notations

Several different notations, each with their own pattern, are placed sequentially on the 12 lunar months of the calendar, interacting according to certain rules with the notations before them, often replacing them. After the basic notations are set, many days’ notations are then moved to other days, creating visual chaos. Finally, the days of the intercalary months are filled with notations copied from certain days in the 12 yearly months.
The notations, their patterns and interactions have gradually over the last century been identified by several key researchers, and what follows is a general, but not comprehensive, overview of each notation.

### Numbering the days

Each month has two halves. The first half has days numbered from I to XV (1 to 15). The second half has either I–XV (1–15), or I–XIIII (1–14) with the 15th day marked with DIVERTOMU. The term ATENOVX is placed between the two half-months. The patterns of the notations act as though the 30th day is always present. This means that in practice some months only have 29 days, but conceptually, all months have 30 days.

### MAT and ANM months and their days

Months of 30 days were marked MAT (except EQVOS), months of 29 days were marked ANM(AT) (except Intercalary One). MAT and ANM(AT) have been read as "lucky" and "unlucky", respectively, based on comparison with Middle Welsh mad and anfad and Old Irish mad and ni-mad.
the MAT and ANM months :
| | SAMONIOS season | SAMONIOS season | | GIAMONIOS season | GIAMONIOS season |
| 1 | mat | SAM | 7 | anm | GIA |
| 2 | anm | DUM | 8 | mat | SIM |
| 3 | mat | RIV | 9 | anm | EQU |
| 4 | anm | ANA | 10 | anm | ELE |
| 5 | mat | OGR | 11 | mat | EDR |
| 6 | mat | CVT | 12 | anm | CAN |
Six months are marked in their header as MAT ‘good, auspicious’, and six months as ANM[AT] ‘not good’. The summer season has 4 MAT months, and the winter season only has 2 MAT months. The summer season needs more auspicious time for all its activities. The months do not run in 29/30 pairs.
For months marked as MAT, all days are initially given M D, a good or auspicious day. Days of the months marked as ANM are given just D, a neutral day. The terms M D and D refer to daylight hours and are in apposition to N for night. Any type of notation marked with N (night) will overwrite the full daytime notation, including the triple mark, M D, D, or D AMB.

### The notation D AMBRIX RI

D AMBRIX RI, usually shortened to D AMB, denotes an inauspicious day. It occurs only on Days 5 and 11 in the upper half-month, that being the period when the moon is more than half full, so it's mostly left free of inauspicious days. In the second half-month, D AMB is placed on every odd numbered day except Day 1, but this is explained by the traditional view that the unit 1 is neither odd nor even. The use of odd numbers as inauspicious is also seen with most months of 29 days being ANMAT ‘not good’. It is symptomatic of Celtic cultures, as the Romans held the reverse view, that odd numbers were auspicious.

### The triple marks

The triple marks are a series of ogham-like marks. They are first lain down each month in triplets over three days, ƚıı, ıƚı, or ııƚ, followed by three days with none. As they only occur with days marked with D (for daytime), and never N (for nighttime), they likely divide the daytime into three divisions.
The triple marks are by far the most complex notations, composed of three main patterns. They do not always repeat across the years. The first pattern assigns possible triplet positions which start on the same offset as the first PRINI term in the month, moving down a day in each of the following MAT or ANM months. The first triplet starts on Days 1-2-3 of SAMONIOS in Year 1, Days 2-3-4 in RIVROS, and so on following the MAT sequence of months. The equivalent sequence starts on Days 1-2-3 of GIAMONIOS in Year 3 and follows the ANM months, so mirroring one intercalary period to the other.
If a triplet cannot be completed before the end of a coicise because it starts on Days 14 and 15, or 14a and 15a, or just 14a of a 29-day month, then the triple marks changes to NSDS and DSNS. If a triplet starts only on day 15, or day 15a, then it changes to a single N.
A second pattern, again following the MAT/ANM sequence, determines which triplets of the first pattern will manifest from year to year. This means the triple mark on a day/month of one year may not be found on the same day/month in another year.
A third pattern adds another IIT on Day 21(6a), the last day of the visible moon, adding to another mark if already there, resulting in each Day 21 holding either TIT, ITT, or IIT.
The triple marks undergo many changes as other notations are added. Days with N forms of notation overwrite the whole ‘day’ notation, e.g. IIT MD becomes just N, while ITI D AMB becomes just N. Days are moved and exchanged, often overwritten and lost, intercalary borrowed days are marked with N, and so on. The result turns a complex pattern of triple marks into visual chaos.

### The notations PRINI LOUD and PRINI LAG

the PRINI LOUD and PRINI LAG pattern :
| month | month | MAT months PRINI LOUD day | MAT months PRINI LOUD day | ANM months PRINI LAG day | ANM months PRINI LAG day |
| 1 | SAM | 1 | 7 | | |
| 2 | DUM | | | | 5 |
| 3 | RIV | 2 | 8 | | |
| 4 | ANA | | | | 6 |
| 5 | OGR | 3 | | | |
| 6 | CUT | 4 | | | |
| 7 | GIA | | | 1 | 7 |
| 8 | SIM | 5 | | | |
| 9 | EQU | | | 2 | 8 |
| 10 | ELE | | | 3 | 9 |
| 11 | AED | 6 | | | |
| 12 | CAN | | | 4 | |
PRINI LOUD has the same MAT month offset, and PRINI LAG the same ANM month offset, as the triple marks. If it falls on a triple mark, it replaces it, along with any M D, D, or D AMB. The PRINI LOUD of SIM 5 is later overwritten by N INIS R. Exchanges will lead to some PRINI LOUD ending up in ANM months, and vice versa. PRINI LOUD does not only occur in the SAMONIOS season, and PRINI LAG does not only occur in the GIAMONIOS season – the SAMONIOS season of 6 months, and the GIAMONIOS season, both contain examples of PRINI LOUD and PRINI LAG.

### The notation N INIS R

The term N INIS R is scattered across the lunar year. The significance of its distribution is undiagnosed. All but three instances occur in the seven months of the SAMONIOS season plus the month of GIAMONIOS. It avoids the days marked with IVOS ‘festival’. As it occurs on seven nights when the moon is absent in the sky (the dark moon of 7a-8a-9a), and avoids the critical moments of the full moon of day 8 and the first visible moon of day 10a, it possibly refers to prognostication associated with stars.

### The notations IVOS and SINDIV IVOS

The term IVOS ‘festival’ occurs in several runs of days of between three and nine days each, considered to mark each day of a festival. In all but two cases these festivals run from the end of one month into the beginning of the next. Four of these IVOS runs break the year into four-quarters, just as the four main Celtic festivals do in historic times, only here they are centered on Day 1 every three lunar months, rather than Day 1 of every three solar months as today.
There are also three other IVOS festivals on the calendar.
The term SINDIV IVOS ‘this day a festival’, occurs only three times – DUM 2a, SIM 9, and AED 25. These three special festival days must indicate something of exceptional importance in the year.

### The notation TIOCOBRIXTIO

TIOCOBRIXTIO is an exceptional term which only occurs on three days in the year – SIM 7, AED 8, and CAN 15. Whatever its significance, it marks days of exceptional importance.

### Movement of notations between days

At this point, most notations have been assigned their base position on the calendar. What happens next is a major feature of the calendar, the movement of one day's notations to a different day. This visually breaks up the patterns of the notations, making the calendar seem quite random. This exchanging of days according to several different patterns, is a major aspect of the calendar, involving a total of 870 days over 5 years.

#### EXCHANGES: swapping notations between two days

There are several patterns in which two days swap their notations.
* The first pattern only involves Day 1 in four pairs of months.
* The second pattern involves days other than Day 1, and uses a different set of four pairs of months to swap between. Days are swapped with the same day of a neighbouring month.
* A third pattern is called the anomalous swaps, where days are swapped between a different day of a month. This occurs just three times per year: between SAM 3 and SAM 2a, between RIV 4 and RIV 10a, and between RIV 8a and ANA 4.
As the notations of one day are moved to another, they take the information with them about their original position (presumably so that one day can be used to prognosticate for its swapped partner). As most movements are to the same day of the month, the day information is redundant, so only the month name (in the genitive) is added. But anomalous swaps between different days require both their original day name and the month to be added.

#### EXCHANGES: dragging notations between months

examples of dragging notations :
| YEAR 1 month/day | pre-drag | post-drag |
| GIAM 7 | PRINI LAG | MD SIMIVIS TIOCOBREXTIO |
| GIAM 8 | D | MD SIMIVIS |
| GIAM 9 | N INIS R | MD SIMIVIS SINDIV IVOS |
| SIMIVIS 7 | MD TIOCOBREXTIO | D EQVI |
| SIMIVIS 8 | MD | PRINI LAG EQVI |
| SIMIVIS 9 | MD SINDIV IVOS | D EQVI |
| EQUOS 7 | D | D ELEMB |
| EQUOS 8 | PRINI LAG | D ELEMB |
| EQUOS 9 | D EQVI | D ELEMB |
For the 12 lunar months after an intercalary month, the notations of the triplet of days 7-8-9 (the full moon) and 7a-8a-9a (the dark moon) in each month are dragged sequentially upwards to the previous month, like beads on a string. Their original month name is then added to the notations.
examples of dragging IVOS :
| YEAR 1 month/day | pre-drag | post-drag |
| OGRON 28 | D AMB | D AMB IVOS |
| OGRON 29 | MD | MD IVOS |
| OGRON 30 | D AMB | D AMB IVOS |
| CUTIOS 1 | MD | MD IVOS |
| CUTIOS 2 | MD | MD IVOS |
| CUTIOS 3 | MD | MD IVOS |
| CUTIOS 28 | D AMB IVOS | D AMB |
| CUTIOS 29 | MD IVOS | MD |
| CUTIOS 30 | D AMB IVOS | D AMB |
| GIAM 1 | MD SIMI IVOS | MD SIMI |
| GIAM 2 | MD IVOS | D |
| GIAM 3 | MD IVOS | D |
The notation IVOS is also sequentially dragged upwards a month in the post-intercalary year. However, it does not take all the other notations with it. This keeps the festival runs marked with IVOS intact. The same also applies to SINDIV IVOS.

### The notations of the intercalary months

The notations on the days of the intercalary months are created by a complex series of copies and merges of notations from certain days in the normal lunar months. Each day of an intercalary month sequentially copies a lunar month and the same day number, with its source month name added. At first 30 days are copied, and for days 1 to 18, their day number is replaced with a single N at the copied site. Secondly, a sequence of days 1 to 6 is again copied from a different year, and these are merged with the first. Thirdly, the days 7-8-9 and 7a-8a-9a which have been dragged from the following month are again merged with the copied notations. At which point, the calendar's notations are complete.

## Footnotes

* ↑ "L'étymologie est transparent puisque le nom du mois et fait sur celui de l'hiver giamo-." — Delamarre (2003)$^{:179}$ [The etymology is transparent since the name of the month is made on that of the winter "giamo-".]
* ↑ EQVOS in year 1 and 5 is marked with 30 days, and the verse above the second intercalary month says Year 3 has 355 days, making EQVOS 30 days. Years 2 and 4 are on lost fragments but may have also been marked on the plaque as 30 days long. Early scholars struggled to fit values to EQVOS which would create a Metonic cycle, for example MacNeill suggested that Equos in years 2 and 4 may have had only 28 days, while Olmsted suggested 28 days in year 2 and 29 days in year 4. However, this issue was resolved when McKay re-evaluated the first intercalary as 29 days long allowing a pattern of 29 or 30-day months as normal and a correct Metonic cycle. The length of EQVOS may have been decided by a visual sighting of the first quarter moon which would start the next month. This gives a usual pattern of 30/29/29/29/30 days for EQVOS.
* ↑ The lunar month does not slip but remains perfectly tuned to the lunar phase, so the age of the calendar cannot be ascertained by any proposed slippage
* ↑ Unfortunately, because the calendar remains so steady and does not slip against the solar year except for a day every 276 years, this accuracy means that any slippage of perhaps a day or two against the solar year cannot be used to calculate how old the calendar is.
* ↑ The Latin text of the specific passage in Pliny is ... est autem id rarum admodum inventu et repertum magna religione petitur et ante omnia sexta luna, quae principia mensum annorumque his facit et saeculi post tricesimum annum, quia iam virium abunde habeat nec sit sui dimidia. — Pliny, Natural History 16.95 English translation by Bostock & Riley: "The mistletoe, however, is but rarely found upon the oak; and when found, is gathered with rites replete with religious awe. This is done more particularly on the sixth day of the moon, the day which is the beginning of their months and years, as also of their ages, which, with them, are but thirty years. This day they select because the moon, though not yet in the middle of her course, has already considerable power and influence; and they call her by a name which signifies, in their language, the all-healing."
* ↑ cf. Old Irish athnugud "renewal"
* ↑ The notations of each day/month are not always the same across all years, so the calendar cannot be simply filled out by copying a known day into the same day/month on a lacuna
* ↑ Because the day numbers are repeated in the upper and lower coicise, researchers use either the number with 'a' attached for the lower coicise, or continue on the sequence. For example, Day VI (6) in the lower coicise is given as either Day 6a or Day 21.
* ↑ unus non-est numerus sed ab eo crescunt numeri ‘one is not a number, but numbers grow from it’$^{:16}$
* ↑ A trace of the pre-Christian division of the day into three may be found here. For this is how Conchobor spends his time of kingship since he assumed sovereignty: as soon as he arises, settling the cares and business of the province, thereafter dividing the day into three, the first third of the day spent watching the youths playing games and hurling, the second third spent in playing brandub and fidchell and the last third spent in consuming food and drink until sleep comes on them all, while minstrels and musicians are meanwhile lulling him to sleep.
* ↑ For a full explanation of the patterns of the triple marks, see McKay (2018)
* ↑ Thurneysen (1899)$^{:530}$ suggested IVOS means "festival", although the etymology is obscure. The word ivos is also the Celtic word for "yew" – Rhys (1910),$^{:52}$ c.f. Ivo, īwaz, and Zavaroni$^{:97}$ suggested a meaning of "(con)junction", but neither meaning has found wide support.
* ↑ Exchanged days always occur between neighbouring months, but are not always between MAT and ANM months
* ↑ The anomalous swaps were partially identified by MacNeill in 1928,$^{:9}$ later by Duval & Pinault in 1986,$^{:267-340}$ Olmsted in 1988, and McKay in 2018.$^{:95}$
* ↑ The notation TRINVX SAMONI, found at SAM 2a, means that its notations were originally at SAMONIOS day 3 in the upper coicise. SAM 3 is the last day of the IVOS festival at the beginning of SAMONIOS, presumably the equivalent of the Beltaine festival. It is not associated with Samhain, being in the summer month of SAMONIOS. It is not a three-night festival, being explicitly marked as a daytime D ‘day’ and SINDIV IVOS ‘festival this (one) day’.