Attic numerals

Last updated October 02, 2024

This article contains special characters. Without proper rendering support, you may see question marks, boxes, or other symbols.

Detail of stela showing tributes paid by allies of Athens in the League of Delos. The amounts are in Attic numerals, using the drachma sign "" instead of the generic unit sign "I". Some amounts are "" = 50, "EEE" = 300, "EEE" = 800, "DDD" = 33, "Kh" = 1000, and "KhD"? = 1562?. EPMA-IGI-3-259-272-Tribute-list-3-crop1-cbadj.png — Detail of stela showing tributes paid by allies of Athens in the League of Delos. The amounts are in Attic numerals, using the drachma sign "𐅂" instead of the generic unit sign "Ι". Some amounts are "𐅄" = 50, "ΗΗΗ" = 300, "𐅅ΗΗΗ" = 800, "ΔΔΔ𐅂𐅂𐅂" = 33, "Χ" = 1000, and "Χ𐅅𐅄Δ𐅂𐅂"? = 1562?.

The Attic numerals are a symbolic number notation used by the ancient Greeks. They were also known as Herodianic numerals because they were first described in a 2nd-century manuscript by Herodian; or as acrophonic numerals (from acrophony) because the basic symbols derive from the first letters of the (ancient) Greek words that the symbols represented.

The Attic numerals were a decimal (base 10) system, like the older Egyptian and the later Etruscan, Roman, and Hindu-Arabic systems. Namely, the number to be represented was broken down into simple multiples (1 to 9) of powers of ten — units, tens, hundred, thousands, etc.. Then these parts were written down in sequence, in order of decreasing value. As in the basic Roman system, each part was written down using a combination of two symbols, representing one and five times that power of ten.

Attic numerals were adopted possibly starting in the 7th century BCE and although presently called Attic, they or variations thereof were universally used by the Greeks. No other numeral system is known to have been used on Attic inscriptions before the Common Era.^[1]^[2] Their replacement by the classic Greek numerals started in other parts of the Greek World around the 3rd century BCE. They are believed to have served as model for the Etruscan number system, although the two were nearly contemporary and the symbols are not obviously related. ^{[ citation needed ]}

The system

Symbols

The Attic numerals used the following main symbols, with the given values:^[1]^[2]

Value	Symbol	Talents	Staters	Notes	Etruscan	Roman
1	Ι			Tally mark?	𐌠	I
5	Π	𐅈	𐅏	Old Greek: ΠΕΝΤΕ [pɛntɛ] Modern: πέντε	𐌡	V
10	Δ	𐅉	𐅐	Old Greek: ΔΕΚΑ [deka] Modern: δέκα	𐌢	X
50	𐅄	𐅊	𐅑	"Δ" in "Π": 10 × 5 = 50	𐌣	L
100	Η	𐅋	𐅒	Old Greek: ΗΕΚΑΤΟΝ [hɛkaton] Modern: εκατό	𐌟	C
500	𐅅	𐅌	𐅓	"Η" in "Π": 100 × 5 = 500	?	D
1000	Χ	𐅍	𐅔	Old Greek: ΧΙΛΙΟΙ [kʰilioi] Modern: χίλιοι	?	M
5000	𐅆	𐅎		"Χ" in "Π": 1000 × 5 = 5000	?	V
10000	Μ		𐅕	Old Greek: ΜΥΡΙΟΙ [myrioi] Modern: μύριοι	?	X
50000	𐅇		𐅖	"Μ" in "Π": 10000 × 5 = 50000	?	L

The symbols representing 50, 500, 5000, and 50000 were composites of an old form of the capital letter pi (with a short right leg) and a tiny version of the applicable power of ten. For example, 𐅆 was five times one thousand.

Special symbols

The fractions "one half" and "one quarter" were written "𐅁" and "𐅀", respectively.

The symbols were slightly modified when used to encode amounts in talents (with a small capital tau, "Τ") or in staters (with a small capital sigma, "Σ"). Specific numeral symbols were used to represent one drachma ("𐅂") and ten minas "𐅗".

The symbol for 100

The use of "Η" (capital eta) for 100 reflects the early date of this numbering system. In the Greek language of the time, the word for a hundred would be pronounced [hɛkaton] (with a "rough aspirated" sound /h/) and written "ΗΕΚΑΤΟΝ", because "Η" represented the sound /h/ in the Attic alphabet. In later, "classical" Greek, with the adoption of the Ionic alphabet throughout the majority of Greece, the letter eta had come to represent the long e sound while the rough aspiration was no longer marked.^[3]^[4] It was not until Aristophanes of Byzantium introduced the various accent markings during the Hellenistic period that the spiritus asper began to represent /h/, resulting in the spelling ἑκατόν.^[5]

Simple multiples of powers of ten

Multiples 1 to 9 of each power of ten were written by combining the two corresponding "1" and "5" digits, namely:

Units	Ι	II	III	IIII	Π	ΠI	ΠII	ΠIII	ΠIIII
Units	1	2	3	4	5	6	7	8	9

Tens	Δ	ΔΔ	ΔΔΔ	ΔΔΔΔ	𐅄	𐅄Δ	𐅄ΔΔ	𐅄ΔΔΔ	𐅄ΔΔΔΔ
Tens	10	20	30	40	50	60	70	80	90

Hundreds	Η	ΗΗ	ΗΗΗ	ΗΗΗΗ	𐅅	𐅅Η	𐅅ΗΗ	𐅅ΗΗΗ	𐅅ΗΗΗΗ
Hundreds	100	200	300	400	500	600	700	800	900

Thousands	Χ	ΧΧ	ΧΧΧ	ΧΧΧΧ	𐅆	𐅆Χ	𐅆ΧΧ	𐅆ΧΧΧ	𐅆ΧΧΧΧ
Thousands	1000	2000	3000	4000	5000	6000	7000	8000	9000

Tens of thousands	Μ	ΜΜ	ΜΜΜ	ΜΜΜΜ	𐅇	𐅇Μ	𐅇ΜΜ	𐅇ΜΜΜ	𐅇ΜΜΜΜ
Tens of thousands	10000	20000	30000	40000	50000	60000	70000	80000	90000

Unlike the more familiar Roman numeral system, the Attic system used only the so-called "additive" notation. Thus, the numbers 4 and 9 were written ΙΙΙΙ and ΠΙΙΙΙ, not ΙΠ and ΙΔ.

General numbers

In general, the number to be represented was broken down into simple multiples (1 to 9) of powers of ten — units, tens, hundred, thousands, etc.. Then these parts would be written down in sequence, from largest to smallest value. For example:

49 = 40 + 9 = ΔΔΔΔ + ΠΙΙΙΙ = ΔΔΔΔΠΙΙΙΙ
2001 = 2000 + 1 = ΧΧ + I = ΧΧΙ
1982 = 1000 + 900 + 80 + 2 = Χ + 𐅅ΗΗΗΗ + 𐅄ΔΔΔ + ΙΙ = Χ𐅅ΗΗΗΗ𐅄ΔΔΔΙΙ
62708 = 60000 + 2000 + 700 + 8 = 𐅇Μ + ΧΧ + 𐅅ΗΗ + ΠΙΙΙ = 𐅇ΜΧΧ𐅅ΗΗΠΙΙΙ.

Unicode

Ancient Greek Numbers ^[1]^[2] Official Unicode Consortium code chart (PDF)
	0	1	2	3	4	5	6	7	8	9	A	B	C	D	E	F
U+1014x	𐅀	𐅁	𐅂	𐅃	𐅄	𐅅	𐅆	𐅇	𐅈	𐅉	𐅊	𐅋	𐅌	𐅍	𐅎	𐅏
U+1015x	𐅐	𐅑	𐅒	𐅓	𐅔	𐅕	𐅖	𐅗	𐅘	𐅙	𐅚	𐅛	𐅜	𐅝	𐅞	𐅟
U+1016x	𐅠	𐅡	𐅢	𐅣	𐅤	𐅥	𐅦	𐅧	𐅨	𐅩	𐅪	𐅫	𐅬	𐅭	𐅮	𐅯
U+1017x	𐅰	𐅱	𐅲	𐅳	𐅴	𐅵	𐅶	𐅷	𐅸	𐅹	𐅺	𐅻	𐅼	𐅽	𐅾	𐅿
U+1018x	𐆀	𐆁	𐆂	𐆃	𐆄	𐆅	𐆆	𐆇	𐆈	𐆉	𐆊	𐆋	𐆌	𐆍	𐆎
Notes 1. ^ As of Unicode version 16.0 2. ^ Grey area indicates non-assigned code point

Notes and references

1 2 Gow, James (1883). "The Greek numerical alphabet". The Journal of Philology. XXII. Cambridge: 278–9.
1 2 Smith, David Eugene (1958). "Reading and writing numbers: Greek numerals". History of Mathematics. Vol. 2. New York: Dover Publications. pp. 49–51. ISBN 9780486204307.
↑ Woodhead, Arthur Geoffrey (1981). The Study of Greek Inscriptions (Second ed.). Cambridge: Cambridge University Press. p. 18. ISBN 0-521-23188-4.
↑ Smyth, Herbert Weir; Messing, Gordon M. (2002) [1920]. "§14". Greek Grammar (Revised ed.). Cambridge, MA: Harvard University Press. p. 10. ISBN 0-674-36250-0.
↑ As found in Katharevousa, polytonic Greek in general and Modern Greek in particular before the 1982 official adoption of the monotonic system; however, neither the /h/ phoneme nor the spiritus asper, or "rough breathing mark", are present in monotonic Standard Modern Greek, resulting in the standard modern spelling εκατό.

Related Research Articles

Alpha is the first letter of the Greek alphabet. In the system of Greek numerals, it has a value of one. Alpha is derived from the Phoenician letter aleph , which is the West Semitic word for "ox". Letters that arose from alpha include the Latin letter A and the Cyrillic letter А.

Eta is the seventh letter of the Greek alphabet, representing the close front unrounded vowel,. Originally denoting the voiceless glottal fricative,, in most dialects of Ancient Greek, its sound value in the classical Attic dialect was a long open-mid front unrounded vowel,, which was raised to in Hellenistic Greek, a process known as iotacism or itacism.

<span class="mw-page-title-main">Roman numerals</span> Numbers in the Roman numeral system

Roman numerals are a numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers are written with combinations of letters from the Latin alphabet, each letter with a fixed integer value. Modern style uses only these seven:

Greek numerals, also known as Ionic, Ionian, Milesian, or Alexandrian numerals, is a system of writing numbers using the letters of the Greek alphabet. In modern Greece, they are still used for ordinal numbers and in contexts similar to those in which Roman numerals are still used in the Western world. For ordinary cardinal numbers, however, modern Greece uses Arabic numerals.

Omicron is the fifteenth letter of the Greek alphabet. This letter is derived from the Phoenician letter ayin: . In classical Greek, omicron represented the close-mid back rounded vowel IPA:[o] in contrast to omega which represented the open-mid back rounded vowel IPA:[ɔː] and the digraph ου which represented the long close-mid back rounded vowel IPA:[oː]. In modern Greek, both omicron and omega represent the mid back rounded vowel IPA:[o̞] or IPA:[ɔ̝]. Letters that arose from omicron include Roman O and Cyrillic O. The word literally means "little O" as opposed to "great O". In the system of Greek numerals, omicron has a value of 70.

In the polytonic orthography of Ancient Greek, the rough breathing character is a diacritical mark used to indicate the presence of an sound before a vowel, diphthong, or after rho. It remained in the polytonic orthography even after the Hellenistic period, when the sound disappeared from the Greek language. In the monotonic orthography of Modern Greek phonology, in use since 1982, it is not used at all.

The smooth breathing is a diacritical mark used in polytonic orthography. In Ancient Greek, it marks the absence of the voiceless glottal fricative from the beginning of a word.

The Cyrillic I is a letter used in almost all modern Cyrillic alphabets with the exception of Belarusian.

The Greek alphabet has been used to write the Greek language since the late 9th or early 8th century BC. It is derived from the earlier Phoenician alphabet, and was the earliest known alphabetic script to have distinct letters for vowels as well as consonants. In Archaic and early Classical times, the Greek alphabet existed in many local variants, but, by the end of the 4th century BC, the Euclidean alphabet, with 24 letters, ordered from alpha to omega, had become standard and it is this version that is still used for Greek writing today.

The system of ancient Egyptian numerals was used in Ancient Egypt from around 3000 BC until the early first millennium AD. It was a system of numeration based on multiples of ten, often rounded off to the higher power, written in hieroglyphs. The Egyptians had no concept of a positional notation such as the decimal system. The hieratic form of numerals stressed an exact finite series notation, ciphered one-to-one onto the Egyptian alphabet.

Romanization of Greek is the transliteration (letter-mapping) or transcription (sound-mapping) of text from the Greek alphabet into the Latin alphabet.

Ancient Greek phonology is the reconstructed phonology or pronunciation of Ancient Greek. This article mostly deals with the pronunciation of the standard Attic dialect of the fifth century BC, used by Plato and other Classical Greek writers, and touches on other dialects spoken at the same time or earlier. The pronunciation of Ancient Greek is not known from direct observation, but determined from other types of evidence. Some details regarding the pronunciation of Attic Greek and other Ancient Greek dialects are unknown, but it is generally agreed that Attic Greek had certain features not present in English or Modern Greek, such as a three-way distinction between voiced, voiceless, and aspirated stops ; a distinction between single and double consonants and short and long vowels in most positions in a word; and a word accent that involved pitch.

In a writing system, a letter is a grapheme that generally corresponds to a phoneme—the smallest functional unit of speech—though there is rarely total one-to-one correspondence between the two. An alphabet is a writing system that uses letters.

The orthography of the Greek language ultimately has its roots in the adoption of the Greek alphabet in the 9th century BC. Some time prior to that, one early form of Greek, Mycenaean, was written in Linear B, although there was a lapse of several centuries between the time Mycenaean stopped being written and the time when the Greek alphabet came into use.

A numeral is a character that denotes a number. The decimal number digits 0–9 are used widely in various writing systems throughout the world, however the graphemes representing the decimal digits differ widely. Therefore Unicode includes 22 different sets of graphemes for the decimal digits, and also various decimal points, thousands separators, negative signs, etc. Unicode also includes several non-decimal numerals such as Aegean numerals, Roman numerals, counting rod numerals, Mayan numerals, Cuneiform numerals and ancient Greek numerals. There is also a large number of typographical variations of the Western Arabic numerals provided for specialized mathematical use and for compatibility with earlier character sets, such as ² or ②, and composite characters such as ½.

Heta is a conventional name for the historical Greek alphabet letter Eta (Η) and several of its variants, when used in their original function of denoting the consonant.

Greek orthography has used a variety of diacritics starting in the Hellenistic period. The more complex polytonic orthography, which includes five diacritics, notates Ancient Greek phonology. The simpler monotonic orthography, introduced in 1982, corresponds to Modern Greek phonology, and requires only two diacritics.

Many local variants of the Greek alphabet were employed in ancient Greece during the archaic and early classical periods, until around 400 BC, when they were replaced by the classical 24-letter alphabet that is the standard today. All forms of the Greek alphabet were originally based on the shared inventory of the 22 symbols of the Phoenician alphabet, with the exception of the letter Samekh, whose Greek counterpart Xi (Ξ) was used only in a sub-group of Greek alphabets, and with the common addition of Upsilon (Υ) for the vowel. The local, so-called epichoric, alphabets differed in many ways: in the use of the consonant symbols Χ, Φ and Ψ; in the use of the innovative long vowel letters, in the absence or presence of Η in its original consonant function ; in the use or non-use of certain archaic letters ; and in many details of the individual shapes of each letter. The system now familiar as the standard 24-letter Greek alphabet was originally the regional variant of the Ionian cities in Anatolia. It was officially adopted in Athens in 403 BC and in most of the rest of the Greek world by the middle of the 4th century BC.

Psilosis is the sound change in which Greek lost the consonant sound during antiquity. The term comes from the Greek ψίλωσις psílōsis and is related to the name of the smooth breathing, the sign for the absence of initial in a word. Dialects that have lost are called psilotic.

An alphabetic numeral system is a type of numeral system. Developed in classical antiquity, it flourished during the early Middle Ages. In alphabetic numeral systems, numbers are written using the characters of an alphabet, syllabary, or another writing system. Unlike acrophonic numeral systems, where a numeral is represented by the first letter of the lexical name of the numeral, alphabetic numeral systems can arbitrarily assign letters to numerical values. Some systems, including the Arabic, Georgian and Hebrew systems, use an already established alphabetical order. Alphabetic numeral systems originated with Greek numerals around 600 BC and became largely extinct by the 16th century. After the development of positional numeral systems like Hindu–Arabic numerals, the use of alphabetic numeral systems dwindled to predominantly ordered lists, pagination, religious functions, and divinatory magic.

This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.

[Gow-1] 1 2 Gow, James (1883). "The Greek numerical alphabet". The Journal of Philology. XXII. Cambridge: 278–9.

[Smith-2] 1 2 Smith, David Eugene (1958). "Reading and writing numbers: Greek numerals". History of Mathematics. Vol. 2. New York: Dover Publications. pp. 49–51. ISBN 9780486204307.

[3] Woodhead, Arthur Geoffrey (1981). The Study of Greek Inscriptions (Second ed.). Cambridge: Cambridge University Press. p. 18. ISBN 0-521-23188-4.

[4] Smyth, Herbert Weir; Messing, Gordon M. (2002) [1920]. "§14". Greek Grammar (Revised ed.). Cambridge, MA: Harvard University Press. p. 10. ISBN 0-674-36250-0.

[5] As found in Katharevousa, polytonic Greek in general and Modern Greek in particular before the 1982 official adoption of the monotonic system; however, neither the /h/ phoneme nor the spiritus asper, or "rough breathing mark", are present in monotonic Standard Modern Greek, resulting in the standard modern spelling εκατό.

[1]

[2]

[3]

[4]

[5]