III. The ProtoBulgar Calendar
By Peter Dobrev
The double specification of the events in the Nominalia of the Bulgarian Princes and their importance in deciphering the unclear calendar terms
Mathematical translation of the calendar terms of Nominalia
Where the special names in the calendar of Isperih come from?
The ancient peoples of the East and the arithmetic of the ProtoBulgarians
The double specification of the events in the Nominalia of the Bulgarian Princes and their importance in ieciphering the unclear calendar terms
The Nominalia of the Bulgarian princes is a chronological list, in which each event (besides the first one) is specified twice  by the duration of the rule of the prince and by the specification of the year of his birth/the year of his ascension to the throne.
This double specification makes it relatively easy to discover the points of accidental errors in the duration or in the year of ascension to the throne. Unfortunately, this possibility was not used in its full yet.
The first year of the first prince  AVITOHOL, was DILOM, and the first year of the last ruler of this series  UMOR, was likewise DILOM. Fortunately to us, this last ruler is also mentioned in the Byzantine chronicles  the year of his accession is 765 AD. That offers us the possibility to locate the year of the eastern cyclic calendar to which the Bulgarian cyclic year DILOM corresponded. According to the eastern cycle 765 AD is the year of the Snake and therefore the legendary progenitor of the Bulgars Avitohol ascended the throne in the year the Snake. Thus, the beginning of the Bulgarian chronicle can be reliably determined.
Like
every progenitor Avitohol appears in the Nominalia with his full life span.
Following the old tradition, he was attributed an unusually long life of 300
years. We can compare him with the patriarchs of the Bible, with the progenitors
of the Celts and many other peoples.
Avitohol is followed by another legendary personality  Irnik, whose life span
was, likewise, unusually long  150 years. The year of birth of this ruler was
again DILOM (snake) and corresponds completely to the features of the Bulgarian
cyclic calendar  adding 300 years to the year of birth of Avitohol (Dilom) we
arrive to Dilom again. All calculations up to now were correct and it is easy to
check them.
The twelveyear animal cyclic calendar of the ProtoBulgarians
The successor of Irnik  GOSTUN reigned for only two years. He ascended the throne 150 years after Irnik and, accordingly, his starting year was not Dilom but DOHS. According to the cyclic calendar DOHS corresponds to the wild boar. Here, however, pops up an inaccuracy of half a year, which could not explained by the previous researchers.
KUBRAT, called in the chronicle Kourt, follows after Gostun. His year was SHEGOR  the year of the bull after the cyclic calendar, because two years after the year of the wild pig starts the year of the bull.
Kubrat's reign was followed by several years of disturbances, combined in the three years rule of BEZMER. BEZMER appears 60 after Kubrat  five full 12years cycles. That is why his year is the same the Kubrat's  SHEGOR.
ISPERIH is the next after BEZMER. He appears is the year VER, which is the year of the Dragon. Like the previous progenitors Isperih was listed on the Nominalia with his full life span of 61 years. But from the text it can be inferred that the year VERENIALEM against his name is not the year of his birth, but the year in which he crossed Danube and created Bulgaria. That is seen particularly clearly from the text preceding his name. In it it is reported that the five previous princes ruled for "515 years on the other side of Danube and then came Isperih on this side of Danube". The newest research points out that 680 AD and not 681 AD was the year of the foundation of Bulgaria. It is in agreement with the Nominalia as 680 AD, the year of the crossing of the Danube, was the year of the VER (Dragon).
Isperih is the last ruler listed with his whole life span listed in the Nominalia, the next rulers are given with the span of their reign. That is quite logical since they did not resume the state but just governed.
From here on the next periods of rule are likewise expressed correctly, and it was only the bad orientation of the previous translators, that tried to explain the whole Nominalia with the help of the Turkic languages, that led to the general conception that the data in this section were coincidental or false. In reality, there is a only one and insignificant copying inaccuracy in the whole second section.
The inaccuracy in question is the the name of the successor of Tervel  Tvirem instead of TVIREMAK or TVIRELAK.
Starting with DILOM the previous researchers had no difficulties determining DOHS to be the year of the wild boar, SHEGOR to be the year of the bull, VER  the year of the dragon, TOH  the year of the cock, SOMOR  the year of the mouse, and IMENSHEGOR  the year of the horse. But they have completely neglected the names of the months in the calendar. As a result the calendar terms remained generally untranslated.
According the previous translations it followed that Gostun reigned for 1.5 years and Isperih at least 62.5 and not 61 years. Similar discrepancies appeared for Sevar, who was assigned to reign for 16 instead of 15 years, and also for Kormisosh, from whom they took one year off. Vineh was "deprived" of almost the whole seventh year of his rule. Great was also the confusion with the inscriptions from the village of Chatalar, whose datings deviated for almost an year from the Byzantine date of the 15th Indict.
The result was a series of ambiguities in the translations of the Bulgarian Nominalia, the errors appeared in the Bulgarian history textbooks and created a distorted picture of history.
In the case of the names of the months the translations were only hypothetic  the Bulgarian word TVIREM was, for example, equated with the TurcoTatarian TOKUZINCHI (via the Chuvashian TAHARAMASH), CHITEM  with ETINCHI, VECHEM with JUCHINCHI etc. The months of the ProtoBulgarian calendar obviously did not coincide with their TurcoTatarian counterparts.
In order to overcome this very serious problem it was necessarily to abandon the previous translation models and to look for another, more adequate model.
As the possibilities of mathematics were not sufficiently used so far, we wanted to apply a purely mathematical interpretation of the names the years and months, relying on the relations between the numerical data of the Nominalia alone.
Mathematical
translation of the calendar terms of Nominalia
The Nominalia of the Asparuh Bulgars is an excellent field for the application
of mathematics. Its information is exclusively numerical  a line of connected
one to another numbers.
The previous translation attempts relied on coincidence, the unclear calendar terms were interpreted not by mathematical calculations, but on the basis of a priori considerations about the similarity of the ProtoBulgarian calendar with Turkic and Mongolian calendars. And these considerations were very arbitrary, i.e. it was assumed that TVIREM means 9, VECHEM  3, CHITEM  7, etc. and after that followed the attempts to calculate the periods of rule of the individual princes. That led to contradictory results but nobody knew where (in which term) the errors laid.
Since we know the exact periods of rule of the princes, we must follow to other way round  to calculate the points on the twelveyears cycle corresponding to the calendar expressions. I decided to check whether it was possible to find an unique and logical mathematical solution to that problem. It was shown that such a mathematical solution exists and that it is unique. So we can be convinced that each calendar term of the ProtoBulgarians is a part of a harmonious system, which forms the basis of ProtoBulgarian calendar dates. The mathematical solution supplied the following translation of the ProtoBulgarian calendar terms:
Year 
Month 
SOMOR  Mouse 
ALEM  first 
SHEGOR  Bull 
TUTOM  second 

CHITEM  third 
DVAN  Hare 
TVIREM  fourth 
VER  Dragon 
VECHEM  fifth 
DILOM  Snake 
SHEHTEM  sixth 
TEKU  Horse 



TOH  Cock 
ELEM  tenth 
ETH  Dog 
ENIALEM  eleventh 
DOHS  Wild boar 
ALTEM twelfth, literally last 
So, the mathematical decoding of the Nominalia detected, for example, that the year DILOM and the month TVIREM correspond to the year of the SNAKE, the fourth month of the cyclic calendar. The procedure was applied successively to all calendar terms, it pointed that TOH ALTOM was the year of the cock, the twelfth month. Likewise, TEKUCHITEM was determined to be the year of the horse, the third month  only this translation satisfied all conditions of the Nominalia.
The scholars working on the Nominalia accused the unknown VIIIth c. writers of being imprecise and having often entered false years and months. By these accusations they tried to excuse their own inaccurate translations. In fact, the authors of the Nominalia were quite precise  both the periods of rule and the years of ascension (or the life span) of all Bulgarian princes were perfectly correct.
The only, and easy to overcome, inaccuracy which crept into the Nominalia was due to later transcribers. The late XVXVIth c. transcribers had the month ENIELEM, in which Isperih (Asparuh) assumed the throne, written as ENIALEM. They have also inadvertently changed the dates of the successor of Tervel by copying the expression TVIREMAK LET as TVIREM KH LET, but both errors are easily spotted mathematically. In the case of Isperih by the fact that writing his month as ENIELEM we obtain the right correspondence between his first year and Tervel, and in the second case  by the fact that only the return of the letter K to its place (before L) fits to the other history records about Tervel.
Let us look at one example, which best illustrates the mistakes of the previous investigators. 61 years are entered against the name of Isperih. These 61 years made hard the life of those, who those tried to decipher the name calendar with the help of the Turkic calendar. Assuming that VER  the year of Isperih's ascension, corresponded to the Tatarian word VJORE (wolf), and that the year of ascension of his successor Tervel was the year of the sheep (for a long time the term TEKU was translated in this way), they concluded Isperih ruled for 65 and not for 61 years.
Rarely, the Turcologists shifted the first year of Isperih to the year of the dragon, although the dragon was LUN and not VER in the Turkic calendar. But again, the years did not fit, now they had 63.5 years for the reign of Isperih. Similarly, the shift of the ascension of Tervel to the year of the horse did not help, because between the first month of the dragon and the seventh month of the horse (as TEKU CHITEM was translated) there were 62 years and six months and not 61 years. It seemed as if the authors of the Nominalia were quite ignorant about Isperih  the central figure of their work.
The mathematical deciphering put the guessing to an end. It proved that the month written next to Isperih corresponds to the eleventh month of the year of the dragon, and the month next to Tervel  to the third month of the year of the horse. Counting on the twelveyear cycle, between the eleventh month of the dragon and the third month of the horse we have the whole numbers of 13, 25, 37, 61 etc. years. The authors of the Nominalia did not err writing 61 years next to Isperih  between the eleventh month of the dragon and the third month of the horse there are 61 years and four months.
The determination of exact meaning of the term ELEM (tenth) and its derivation ENIALEM (or ENIELEM)  eleventh, was very important for the solution of another mystery of the Nominalia. The Chatalar inscription from Omurtag says that it was made in the year SIGOR ELEM (written with Greek letters), i.e. in the year of the bull and the month ELEM. The Turkologists mistranslated SIGOR ELEM as the year of the bull, the first month  the first month of the bull corresponded to January of 821 AD; at the same time the inscription in Greek read that it was made in September of 821 (the 15th Byzantine indict began in September 821). The Greek date clearly showed that ELEM was not the first month and the solution of the mystery was quite simple  SIGOR, that is  SHEGOR ELEM, was October 821 and that is exactly the second month of the Byzantine 15th indict.
The mathematical deciphering places all calendar terms on their correct places. Let us examine briefly these so important for the Bulgarian history dates:
AVITOHOL. He assumed the throne in DILOMTVIREM (snake, fourth month). A legendary progenitor of the Bulgars, he lived for 300 years. Counting 300 years from the cyclic calendar we arrive in the year of the snake, fourth month in which, according to the Nominalia, was born Irnik.
IRNIK. The second progenitor. Born in DILOMTVIREM (snake, fourth month). Lived for 150 years. Counting 150 years we arrive in the year of the wild boar.
GOSTUN. A deputy. Reigned for 2 years staring in DOHS TVIREM (wild boar, fourth month). Continuing for two more years, we correctly reach KOURT (Kubrat).
KOURT (Kubrat). The renovator of Old Great Bulgaria. Starts in SHEGOR VECHEM (bull, fifth month), 60 years. Counting these 60 years we again arrive at the starting point, which is the beginning of the next ruler  BEZMER.
BEZMER. Governed for 3 years, starting from the bull, fifth month (SCHEGOR VECHEM).
ISPERIH. Founder of a new state and therefore entered in the Nominalia with his whole life span of 61 years, as the legendary AVITOHOL and the renovator KUBRAT. Ascended the throne in VERENIELEM (dragon, eleventh month).
TERVEL. Started in TEKU CHITEM (horse, third month) and ruled for 21 years.
TVIREMIK (or Tvirelik). He was mentioned in History of Paisij as as Trivelius. Ascended the throne in the year of the DVAN (hare) in the sixth month (SHEHTEM) and ruled for 6 years. Late transcribers introduced an error here.
SEVAR. The last of the clan DULO. He mounted the throne in TOH ALTOM (the year of the cock, twelfth month). Ruled for 15 years.
KORMISOSH. His first year of rule was SHEGOR TVIREM (bull, fourth month), and he ruled for 17 years.
VINEH. Ascended the throne in IMENSHEGOR ALEM (horse, first month). A second name for the year of the horse is not uncommon  many peoples had two or even three names for the same year of the cyclic calendar. Thus, the Tadjiks near Pamir have three different names for the year of the dog  SAK, VAFODOR and KUCHUK, and for the year of the wild boar  two (HUG and HUBON).
TELEC. Assumed the throne in SOMOR ALTEM (mouse, eleventh month) and governed for three years. In June 763 he suffered a catastrophic defeat and soon thereafter, not later than August, he was dethroned and probably murdered. From SOMORALTEM, which corresponds to the eleventh month of the year 760 AD, to August 763 there are two years and nine months, rounded by the authors of the Nominalia to three years.
INTERREGNUM. This period is inferred indirectly. The first year of the next ruler UMOR is DILOM TUTOM (snake, second month) which corresponds to February 765 AD. That is, since the deposition of TELEC (August 763) Bulgaria was governed for one year by a temporarily appointed person, or by an unpopular ruler, whose name was omitted by the authors Nominalia. Exactly in this period the Byzantines mention the unpopular SABIN, who saved his life by taking refuge in Constantinople. Obviously, his name was intentionally omitted after his infamous betrayal.
UMOR. This last ruler of Nominalia ascended the throne in DILOM TUTOM (snake, second month) and governed for 40 days. That fits exactly the information of the Byzantine sources, as in the summer of 765 AD the Byzantine emperor mounted a campaign against Bulgaria because of the deposition of Umor.
The data, arranged in table look thus:
Ruler 
Year of 
Given in the Nominalia 
Duration 
Our 
Avitohol 
153 
Snake, 4th month 
300 
300 
Irnik 
453 
Snake, 4th month 
150 
150 
Gostun 
603 
Boar, 4th month 
2 
2 
Kourt 
605 
Bull, 5th month 
60 
60 
Bezmer 
665 
Bull, 5th month 
3 
3 
Isperih 
633 
Dragon, 11th month 
61 
61 
Tervel 
694 
Horse, 3rd month 
21 
21 
Tviremik 
715 
Hare, 6th month 
6 
6 
Sevar 
721 
Cock, 12th month 
15 
15 
Kormisosh 
737 
Bull, 4th month 
17 
17 
Vineh 
754 
Horse, 1st month 
7 
7 
Telec 
760 
Mouse, 11th month 
3 
3 
It was already said the that mathematical solution is unique. Let us then examine the particularity of this translation and have a closer look at the mysteries of the ProtoBulgarian calendar.
Let us compare this and the previous attempts for translation of the calendar terms of the Nominalia.
Name of the Month 
Mathematical translation 
Previous translation 
ALEM 
first 
first 
TUTOM 
second 
fourth 
CHITEM 
third 
seventh 
TVIREM 
fourth 
ninth 
VECHEM 
fifth 
third 
SHEHTEM 
sixth 
eighth 
ELEM 
tenth 
first 
ENIALEM 
eleventh 

ALTEM 
twelfth 
sixth 
The previously assumed names of the months were particularly incorrect. All months, except the first one  ALEM, were mistaken. The reason for that was the false belief of the previous translators that the ProtoBulgarians were Turkic people. They unconditionally tried to find the Turkic prototype behind each ProtoBulgarian name of the months  behind VECHEM  JUCHINCHI, behind CHITEM  ETINCHI, behind TVIREM  TAHAREMASH, etc. This play with the months undermined the mathematical base of the ProtoBulgarian calendar.
The names of the months were the weakest and, perhaps, fatal point of the past translations, their translations were much more erroneous than the translations of the names of cyclic years. It can be easily explained  the cyclic years were very helpful, it sufficed to guess the name of the first year of the Nominalia  DILOM (snake), in order to proceed correctly, almost automatically with the next records. Counting 150 years from DILOM (snake) they arrived to the year of the wild boar. Thus, it was correctly assumed DOHS is a wild boar, two more years led to SHEGOR (bull), etc. And although nowhere in the Turkic calendars names such as SOMOR, DVAN, VER, TEKU (as a horse) or IMENSCHEGOR were to be found, the translators obtained their correct meaning on a purely logical way, if even still believing in the Turkic origin of the ProtoBulgarian calendar.
In the case of the translation of the months, however, the situation was completely different, there were no additional clues to the correct interpretation and it produced a complete chaos. The large inconsistencies in the Turkic translations, were a very valuable symptom to us. The Bulgarian names of the months are not Turkic in origin, they come from a different numerical system.
Where the special names in the calendar of Isperih come from?
The ProtoBulgarian names of the months were as follows:
First month 
ALEM 
Second month 
TUTOM 
Third month 
CHITEM 
Fourth month 
TVIREM 
Fifth month 
VECHEM 
Sixth month 
SHEHTEM 


Tenth month 
ELEM 
Eleventh month 
ENIALEM 
Twelfth month 
ALTEM 
The solution is unique and the names of the months were derived by a purely mathematical way and not under the influence of any linguistic or historical hypothesis. It is interesting to see, which peoples in the world have (or had) a similar system of months.
We cannot find a similar system among the Turkic peoples and the Turkic languages. For them the first month was BIRINCHI, the second  IKINCHI, the third  JUCHINCHI, etc. But the mathematical solution could be an artificial system which do not exist anywhere in the world. If it is indeed so, if that system was not known not only by the Turkic but by any other peoples in the world, it would compromise completely our mathematical exercises with the calendar. The obtained solution, although attractive, would be then unrealistic from a linguistic and historical point of view.
In our quest for peoples which have (or had) a similar numerical system it would be appropriate to look first at one little known but particularly interesting area  the Pamirs and the Hindu Kush, because according to the documentary sources it was the place where the ProtoBulgarian people was formed. There one still meets the following cardinal numbers:
AL  one 
OLAM  first, initial, ALIN  front 
TU  two 
TUOM, DUOM  second 
CHIT  three 
CHITEM, CHITAM  third 
ZFIR  four 
ZVIREM  fourth 
VUCH, VOCH  five 
VJUCHOM  fifth 
SHEH  six 
SHEHEM  sixth 


IL  ten 
ILEM  tenth 
We have almost the entire numerical system, produced by the mathematical solution of the ProtoBulgarian calendar terms, still present in the Pamirs and in the Hindu Kush. It was common in the mentioned area since oldest times  its signs were discovered in Khotan handwritings from the third, fourth century BC. The same system of counting is also found among peoples, emigrated from these areas a long time ago. It is partially preserved at present in the Eastern Caucasus, once affected by migration from the Pamirs. Some of the above cardinal numbers are used even as calendar terms.
Caucasian examples (Dagestani):
AL  one, ALHEN  first month
SHI  three
DIA  four
PHI, VID  five
EL  ten
In Caucasus and Dagestan, however, only the roots of these numbers were preserved, and they changed a lot: SHI instead of CHIT, DIA insted of TVIR, VID instead of VECH, etc. It shows they were taken from outside by the Caucasusian peoples, as individual words and not as a whole system.
Distant similarities are also found in the Georgian language, where ERT resembles our AL (one) and ERMETI corresponds to our ALEM (eleventh).
There are stronger parallels among some Celtic peoples, for example the Cymmrs, whose name reminds of the legendary eastern Cimmerians:
AL 
one, ALEN  first, initial
TU, DU  two
PIS  five, FIS  fifth.
In earlier times the word EL  ten, was also used. It led to the English ELEVEN  literally "ten and one".
The vestiges of the ProtoBulgarian cardinal numbers are most pronounced in the Pamirs and in the Hindu Kush. Indicative is that traces of this system were found exactly in those areas, that were once populated by peoples from the Pamirs.
The mathematical deciphering of the Nominalia is completely harmonious with the characteristics of the ProtoBulgarians derived from the other branches of science.
The ancient peoples of the East and the arithmetic of the ProtoBulgarians
The
question to be answered now, after the numerical system of the ProtoBulgarians
was nearly clarified, is:
was there another ancient people that counted in a similar way. Regarding the
names of the months, the Sumerian civilization has very interesting points of
contact with the ProtoBulgarian names. They refer, however, to individual
isolated words, while in the Pamir the whole system was discovered, with
specific endings EM and OM. But the problem is that there existed an older
people, who had whole system. The examples listed in the table below are to
clarify this difficult question.
Comparison of the names of the Months from the Nominalia and from the Pamirs
ProtoBulgarian example 
Pamirian and Dardic analogies 
Precursors 
ALEM (first) 
ALAM, OLAM (first)  Ishkash., Chuf. 
Accad. ALEN, 
TUTOM (second) 
DU, TU (two); DUTA, DUDON (both)  Prasun 
Sanskr. DUTAMA; Pers. DUTOM (second) 
CHITEM (third) 
CHI, CHIT (three); 
Old Pers. CHITIJA (third); 
TVIREM (fourth) 
ZFIR (four), ZFIREM (fourth) Munj. 
Sanskr. TURIA, Avest. TURIA (tuyria), TUIRAM (fourth); TEOIR (four)  Irish 
VECHEM (fifth) 
VJUCH, VISH (five)  Prasun; 
PENCHEM from PENDSHAMA  Sanskr. 
SHEHTEM (sixth) 
SHEHT (six), SHEHEM (sixth) 
SASTAMA (sixth)  Sanskr. 
ALTEM (last, twelfth) 
ALSAM  Vaynakh., ALD  Wakh. 
ALSAM (rest, end)  Vaynakh, 
ES (eight) (discovered in Murfatlar's inscriptions) 
AZ (Torv.), AS (Bashk.), ASH, ASTE (Prasun), HESHT (Tal.) 
ASHTAU  Sanskr.; ES (eth)  Celt., EIGHT  Engl. 
Old Sanskrit or Avestan, and in some to cases Sumerian and Accadian words are behind almost all ProtoBulgarian and Pamirian words. The Accadian ALEN, which was changed to ALAM in Sanskrit is, corresponds to our term ALEM. Our TUTOM corresponds to the Sanskrit DUTAMA and the reconstructed Persian DUTOM (which was formed in the same way as the Old Persian EVAKTOM (first) from EVAK (one)).
CHITEM (third) corresponds to the Old Persian form CHITIJA (hyia) and to the Avestan CHITIJEM (cityiem); TVIREM (fourth)  to the Sanskrit double word TURIATURIAMA abd to the Avestan TUIRIATUIRIEM (tuiriyem); VECHEM (fifth)  to the Avestan PENCHA and PENCHEMA, changed in Pamir to VISH and VISHEM; SHEHTEM (sixth)  to the Sanskrit SASTAMA and the Gaelic SEATHAMH; ES (eight)  to the Sanskrit number ASHTA, which was transformed in the Pamirs into AST and ESHT (HESHT).
All ProtoBulgarian cardinal numbers have analogies with Sanskrit and Avestan, i.e. with the peoples known today under the general term IndoIranians. The developments the ProtoBulgarian numbers underwent were identical to the developments undergone by the Pamirian and Dardic numbers, they were marked by modifications of the same type. Both the Pamirian peoples and the Protobulgarians had the endings OM and EM in place of the former endings AMA and EMA, and in both of them in the cardinal number four appeared an intermediate sound V or F: TUIREM became TVIREM or ZFIREM. In both the word DU (two) became TU, and in the word PENCH the P changed to V. The ProtoBulgarian and the Pamirian cardinal numbers not only possess a common source, but common modifications as well. It is a proof that these peoples had lived for a long time in close contact and had a long common development. The times, when the ProtoBulgarians and the ancestors of the Pamir peoples had a common life are far in the past, now we could compare the ProtoBulgarian cardinal numbers to that of the oldest settlers from the east  the Celts.
Among the Celts, who already in the fourth/fifth c. BC immigrated from the Pamir area, there were also a people named BOLGI, whose name in OldCeltic generally sounded as BOLGAR. There are many similarities between the ProtoBulgarian and the Celtic cardinal numbers  the word TU (two) from the British islands (once under a strong Celtic influence) corresponds to the former Sogdian and ProtoBulgarian word DO (two), which survived partly in Pamir. The Celtic language is the only one which have preserved the old word TEOIR (four), derived from the Avestan TUIRIA, i.e. from the prototype of the ProtoBulgarian TVIREM (fourth). The word PIMP (five) and FIFS (fifth) is similar to the Pamirian VISH and the ProtoBulgarian VECHEM (fifth); ES and EIGHT resemble the ProtoBulgarian form ES. If we add that in the Irish language the month of May, the third month of the spring, is called CHITEAM and the Old Irish form was CHEATAM, it becomes clear that the former Celts not only had a similar system as the peoples of Pamir, but that this system was also used for calendar purposes.
The list of the ProtoBulgarian numerals and their Old Celtic analogies:
ProtoBulgarian word 
Old Celtic analogies 
EL (1), ELEM (first) 
EL (one), from which  ELEVEN (11) 
TE (2), TUTOM (second) 
TU (two), from which the English TWO 
CHIT (3), CHITEM (third) 
CHITEAM (the 3rd month of the spring)  Irish 
TVIR (4), TVIREM (fourth) 
TEOIR (four)  Irish 
VECH (5), VECHEM (fifth) 
FIF, from which the English FIFTH 
SHEHT (6), SHEHTEM (sixth) 
SEAHT (seven)  Irish 
ES (8), ESTEK (80) 
ES (eight)  Cornish, ESDEK (eth, ethdek)  80 
ALT (11), ALTEM (eleventh) 
EALTA (multiplicity), ALT (added to the end, old) 
The similarities with the Celts, the earliest settlers from the east, show that this type of counting was very old. It existed in an accomplished form already in the first millennium BC, at the time, when the first groups of emigrants from the Pamirs made their way to Europe, taking with them this special system of counting.
As this system was so old it is to be assumed that also the calendar, where it appears  the ProtoBulgarian calendar, was quite old. It did not develop after their settlement in Europe, but much earlier. A proof to this are the KhotanoSaka handwritings from the IVV c. BC found at the northern edge of the Pamir mountains, with cardinal numbers of the same type as that in the ProtoBulgarian calendar, for example  PENCHEM (fifth) and PAMJEM with the specific ending "EM".